JP7832968B2 - Information processing device, information processing method, and program - Google Patents

Description

This disclosure relates to an information processing device, an information processing method, and a program.

In inventory management, it is conceivable that order quantities would be determined based on predicted demand for a product in order to reduce unnecessary inventory and stockouts. Furthermore, in recent years, various systems for predicting future demand have been proposed, as illustrated by the inventory management example above. For example, Patent Document 1 discloses an example of a system that calculates the order quantity for each product by predicting demand using a forecasting model that predicts demand on a daily basis.

International Publication No. 2018/042950

The system disclosed in Patent Document 1 assumes that the probability of the calculated demand forecast number follows a normal distribution when predicting demand. However, in reality, the probability of the predicted demand number often does not follow a normal distribution. Therefore, the demand forecast results obtained under the assumption of a normal distribution may not accurately reflect reality.

In view of the above-mentioned problems, this invention aims to enable more accurate forecasting of demand.

The information processing device according to the present invention comprises: a first estimation means for estimating a first distribution that indicates the likelihood of each quantity of demand that falls within a first range of demand that is estimated to be actually observed for a unit period targeted for demand forecasting, based on past demand performance; and a second estimation means for estimating a second distribution used for forecasting demand during a target period , by integrating probability density functions representing the first distribution estimated for each of a plurality of unit periods included in the target period for demand forecasting, and deriving a probability density function representing a second distribution that indicates the likelihood of each quantity of demand that falls within a second range of demand that is estimated to be actually observed for the target period .

According to this invention, it becomes possible to predict demand levels that more accurately reflect actual conditions.

This diagram shows an example of the system configuration of an information processing system. This diagram shows an example of the hardware configuration of an information processing device. This is a functional block diagram showing an example of the functional configuration of an information processing system. This is a flowchart illustrating an example of the processing performed by an information processing system. This is a flowchart illustrating an example of the processing steps in an information processing system. This figure shows an example of a method for constructing a trained model related to quantile estimation. This figure shows an example of a probability density function that represents the distribution of demand. This figure shows an example of a method for determining the parameters of a split normal distribution. This figure shows an example of the estimation results of the probability density function representing the distribution of demand. This figure shows an example of a method for estimating the probability density function that represents the distribution of demand. This figure shows an example of how to construct and apply an error prediction model. This figure shows an example of a method for estimating quantiles using error prediction results. This figure shows an example of the estimated probability density function of the demand forecast. This figure shows an example of a probability density function for the quantity demanded. This figure shows an example of the MA calculation results. This figure shows an example of a method for correcting the results of quantile prediction. This figure illustrates an example of a method for estimating the demand distribution over a given period. This figure shows an example of a method for estimating quantiles by applying multiple models. This figure shows an example of a method for estimating quantiles by applying multiple models.

Preferred embodiments of this disclosure will be described in detail below with reference to the attached drawings. In this specification and the drawings, components having substantially the same functional configuration are denoted by the same reference numerals, thus omitting redundant descriptions.

<System Configuration>
Referring to Figure 1, an example of the system configuration of the information processing system according to this embodiment will be described. The information processing system 1 according to this embodiment includes an information processing device 100 and one or more terminal devices 200. In the example shown in Figure 1, terminal devices 200a and 200b are provided as terminal devices 200. The information processing device 100 and the terminal devices 200 are connected via a network N1 so that various information and data can be sent and received from each other.

The type of network N1 connecting the devices constituting the information processing system 1 is not particularly limited. For example, network N1 may consist of a LAN (Local Area Network), the Internet, a dedicated line, or a WAN (Wide Area Network). Furthermore, network N1 may consist of a wired network or a wireless network. Network N1 may also include multiple networks, and some networks may be of a different type than the others. Moreover, the physical configuration of network N1 is not particularly limited; it is sufficient that communication between the devices is logically established. For example, communication between the devices may be relayed by other communication devices. In addition, the series of devices constituting the information processing system 1 do not necessarily have to be connected to a common network. That is, as long as it is possible to establish communication between devices that transmit and receive information and data, some devices and others may be directly connected to different networks.

The information processing device 100 estimates a probability density function representing the distribution of demand during a target period (hereinafter also referred to as the target period) based on past demand data managed as history, and predicts the demand during the target period based on this probability density function.
In this embodiment, the probability density function representing the distribution of demand corresponds to a distribution that shows the likelihood (e.g., likelihood, certainty, etc.) of each demand within the range of demand estimated to be actually observed.
Furthermore, the above-mentioned functions of the information processing device 100 and the processes for realizing those functions will be described in detail separately later.

The terminal device 200 serves as an input interface for receiving input related to the use of functions provided by the information processing device 100, and as an output interface for presenting various types of information to the user.

The configuration shown in Figure 1 is merely an example, and the system configuration of the information processing system 1 is not necessarily limited as long as it is possible to realize the functions of each component of the information processing system 1, which will be described separately. As a specific example, the information processing system 1 may be implemented as a so-called standalone environment in which the information processing device 100 and the terminal device 200 are configured as an integrated unit. Furthermore, as another example, the component corresponding to the information processing device 100 may be realized through the cooperation of multiple devices, or as a so-called network service.

<Hardware Configuration>
Referring to Figure 2, an example of the hardware configuration of an information processing device 900 applicable as an information processing device 100 or terminal device 200 in the information processing system 1 according to this embodiment will be described. As shown in Figure 2, the information processing device 900 according to this embodiment includes a CPU (Central Processing Unit) 910, a ROM (Read Only Memory) 920, and a RAM (Random Access Memory) 930. The information processing device 900 also includes an auxiliary storage device 940 and a network I/F 970. The information processing device 900 may also include at least one of an output device 950 and an input device 960. The CPU 910, ROM 920, RAM 930, auxiliary storage device 940, output device 950, input device 960, and network I/F 970 are interconnected via a bus 980.

The CPU 910 is a central processing unit that controls various operations of the information processing device 900. For example, the CPU 910 may control the operation of the entire information processing device 900. The ROM 920 stores control programs and boot programs that can be executed by the CPU 910. The RAM 930 is the main memory of the CPU 910 and is used as a work area or temporary storage area for deploying various programs.

The auxiliary storage device 940 stores various data and programs. The auxiliary storage device 940 is implemented using a storage device capable of temporarily or continuously storing various data, such as a non-volatile memory like an HDD (Hard Disk Drive) or an SSD (Solid State Drive).

The output device 950 is a device that outputs various types of information and is used to present various types of information to the user. For example, the output device 950 may be implemented by a display device such as a display. In this case, the output device 950 presents information to the user by displaying various types of display information. As another example, the output device 950 may be implemented by an acoustic output device that outputs sounds such as voice or electronic sounds. In this case, the output device 950 presents information to the user by outputting sounds such as voice or telegraph signals. Furthermore, the device to which the output device 950 is applied may be appropriately changed depending on the medium used to present information to the user.

The input device 960 is used to receive various instructions from the user. In this embodiment, the input device 960 includes input devices such as a mouse, keyboard, and touch panel. Alternatively, the input device 960 may include a sound collection device such as a microphone to collect the user's voice. In this case, various analysis processes, such as acoustic analysis and natural language processing, are applied to the collected voice so that the content of the voice is recognized as an instruction from the user. Furthermore, the device applied as the input device 960 may be appropriately changed depending on the method of recognizing the user's instructions. Multiple types of devices may also be applied as the input device 960.

The Network I/F 970 is used for communication with external devices via a network. The device used as the Network I/F 970 may be changed as appropriate depending on the type of communication path and the applicable communication method.

The CPU 910 loads the program stored in the ROM 220 or auxiliary storage device 940 into the RAM 930 and executes this program. This enables the functional configuration of the information processing device 100 shown in Figure 3, and the processing of the information processing device 100 described later with reference to Figures 4 and 5.

<Functional Configuration>
Referring to Figure 3, an example of the functional configuration of the information processing system according to this embodiment will be described, with particular attention paid to the configuration of the information processing device 100. As shown in Figure 3, the information processing device 100 includes a demand distribution estimation unit 110, an integrated processing unit 120, and a demand forecasting unit 130. In the example shown in Figure 3, a storage unit 190 is provided as a storage area for managing past demand data.

The memory unit 190 schematically represents a memory area for storing various types of data. As mentioned above, in the example shown in Figure 3, the memory unit 190 stores historical data of past demand, which is managed as history, etc. The memory unit 190 may be implemented, for example, by an auxiliary storage device 940, or by an external device that manages various types of data, such as a database server.

The demand distribution estimation unit 110 estimates a probability density function representing the distribution of demand for each unit period targeted for demand forecasting (for example, a period that serves as a management unit for past demand data, such as daily periods), based on past demand data. In this embodiment, for convenience, the above unit period is set to a day. That is, the demand distribution estimation unit 110 estimates a probability density function representing the distribution of demand for each day targeted for demand forecasting.

As a specific example, the demand distribution estimation unit 110 estimates the demand for the day to be forecasted as a quantile of the demand distribution, based on past demand data, for the base demand, the demand if it exceeds the base, and the demand if it falls below the base.
Hereafter, the quantile of the forecast result for the baseline demand will be referred to as the first quantile, the quantile of the forecast result for demand when it is above the baseline will be referred to as the second quantile, and the quantile of the forecast result for demand when it is below the baseline will be referred to as the third quantile. In this embodiment, for convenience, the first quantile will be referred to as the 50th percentile, the second quantile as the 95th percentile, and the third quantile as the 5th percentile. In this disclosure, the 50th percentile corresponds to the quantile of demand that includes 50% of the sample data from past demand data under similar conditions to the day for which the demand forecast is being made, counting from the sample data with the smallest demand. Similarly, the 95th percentile corresponds to the quantile of demand that includes 95% of the sample data, and the 5th percentile corresponds to the quantile of demand that includes 5% of the sample data.
Furthermore, the demand distribution estimation unit 110 may estimate a probability density function representing the distribution of demand on the day for which demand is to be forecasted, based on the estimation results of the three quantiles mentioned above. In this case, the demand distribution estimation unit 110 may estimate the probability density function representing the distribution of demand as a split normal distribution that shows both the case where demand is above the 50th percentile and the case where demand is below the 50th percentile. In this case, the demand distribution estimation unit 110 should estimate a probability density function that takes into account the extent of the upward and downward fluctuations in demand, based on the estimation results of the 50th percentile, the 95th percentile, and the 5th percentile.
Further details regarding the above-mentioned examples will be provided separately later. The range of demand estimated to be actually observed for a given period, as shown as the domain of the probability density function representing the distribution of demand for each unit period, corresponds to an example of the "first range." The probability density function representing the distribution of demand for each unit period corresponds to an example of the "first distribution," indicating the likelihood of each demand within the first range. The demand distribution estimation unit 110 corresponds to an example of the "first estimation unit."

The integrated processing unit 120 estimates a probability density function representing the distribution of demand during a given period by integrating the probability density functions representing the distribution of demand estimated for each of the multiple unit periods included in the target period for demand forecasting.
As a specific example, the integrated processing unit 120 may receive a specified period for demand forecasting from the user and estimate a probability density function representing the distribution of demand during that period.
Furthermore, the integrated processing unit 120 may estimate a probability density function representing the distribution of demand during the target period by performing a convolution operation on the probability density function representing the daily distribution of demand estimated by the demand distribution estimation unit 110 for each day included in the target period of demand forecasting.
Furthermore, the range of demand quantities that are estimated to be actually observed during the target period, as shown as the domain of the probability density function representing the distribution of demand quantities during the target period, corresponds to an example of the "second range." Also, the probability density function representing the distribution of demand quantities during the target period corresponds to an example of the "second distribution," which indicates the likelihood of each demand quantity included in the second range. In addition, the integrated processing unit 120 corresponds to an example of the "second estimation unit."

The demand forecasting unit 130 forecasts the amount of demand for a given period based on the estimation result of a probability density function that represents the distribution of demand during that period.
As a specific example, the demand forecasting unit 130 may receive a specification from the user of an acceptable error for the forecast result of the demand for the target period, and then perform a forecast of the demand for that period. In this case, the demand forecasting unit 130 may decide, based on the acceptable error, which percentage point of the probability density function representing the distribution of demand for the target period to focus on. By estimating the probability density function representing the distribution of demand, it becomes possible to derive a result indicating the probability that the demand will fall within a certain range during the target period of demand forecasting. Therefore, the point of focus (percentage point) determined in this manner can be said to be the target demand that can be requested during the target period without exceeding the acceptable error. By applying such a mechanism to inventory management of goods, for example, by setting the acceptable stockout rate as the above error, it becomes possible to determine a target inventory amount that takes into account preventing stockouts during the inventory management target period.

It should be noted that the above configuration is merely an example, and the functional configuration of the information processing system according to this embodiment is not necessarily limited to the example shown in Figure 3. For example, the functional configuration of the information processing device 100 described with reference to Figure 3 may be realized by the cooperation of multiple devices. As a specific example, the functions of some of the components of the information processing device 100 may be realized by other devices. As another example, the processing load of at least some of the components of the information processing device 100 may be distributed among multiple devices. Furthermore, the functions of at least some of the components of the information processing device 100 may be realized as a so-called network service, such as a cloud service.
The above explanation, with reference to Figure 3, describes an example of the functional configuration of the information processing system according to this embodiment, with particular attention to the configuration of the information processing device 100.

<Processing>
Referring to Figures 4 and 5, an example of the processing of the information processing system according to this embodiment will be described, with particular attention to the processing of the information processing device 100.

First, refer to Figure 4. In S110, the demand distribution estimation unit 110 estimates a probability density function representing the distribution of demand for each unit period targeted for demand forecasting, based on past demand data. As mentioned earlier, in this embodiment, the unit period is defined as days. Furthermore, to make the features of this embodiment easier to understand, the following explanations will focus on the case where, in product inventory management, the target inventory quantity to be secured for a future period is determined by forecasting the demand for that product.

Now, with reference to Figure 5, the process of S110 shown in Figure 4 will be explained in more detail.
In S111, the demand distribution estimation unit 110 estimates, based on past demand data, the first quantile of the forecast result for the base demand for the day to be forecasted, the second quantile of the forecast result for the case where the demand exceeds the base, and the third quantile of the forecast result for the case where the demand falls below the base. In this case, the demand distribution estimation unit 110 may use a trained model constructed based on so-called machine learning to estimate the first, second, and third quantiles. As mentioned above, in this embodiment, for convenience, the first quantile is set to the 50th percentile, the second quantile to the 95th percentile, and the third quantile to the 5th percentile.

Here, referring to Figure 6, we will explain an example of how to construct a trained model built based on machine learning when estimating the quantiles of the demand forecast results using such a trained model.
In the example shown in Figure 6, pre-trained models are constructed individually for the first quantile (50th percentile), the second quantile (95th percentile), and the third quantile (5th percentile). That is, pre-trained models M101, M102, and M103 are pre-trained models constructed to estimate the first quantile, the second quantile, and the third quantile, respectively. Specifically, pre-trained models M101, M102, and M103 are pre-trained models that take characteristic variables for identifying the target of demand forecasting as input and output the quantiles of the demand distribution. Hereafter, when pre-trained models M101, M102, and M103 are not specifically distinguished, they will also be referred to as pre-trained model M100 for convenience. Furthermore, the trained model M100, that is, the trained models M101, M102, and M103, each correspond to an example of the "first trained model".

The trained model M100 is constructed based on supervised learning, using training data generated from historical demand data as input.
The above training data is generated by associating the "past sales quantities of products (i.e., actual demand)" shown by actual data corresponding to the conditions for identifying the target of demand forecasting with the correct labels. Examples of conditions for identifying the target of demand forecasting include "date,""productinformation,""store information (information of stores that secure inventory),""presence or absence of events (presence or absence of events on the target day and the type of event)," and "weather information." For example, suppose there is data for "product sales quantities" corresponding to the conditions "date = August 1st,""product information = beer,""store information = store A," and "weather information = sunny." From this data, training data is generated by associating the above "product sales quantities" with the features (e.g., feature vectors in the feature space) represented by "date = August 1st,""product information = beer,""store information = store A," and "weather information = sunny" with the correct labels.
Through supervised learning based on the training data exemplified above, a trained model is constructed that takes the characteristic features of the conditions for identifying the target of demand forecasting as input and outputs the demand forecast result.

Furthermore, in this embodiment, a pre-trained model M100 is constructed by applying a so-called regression model to quantile regression, thereby training the model to minimize the pinball loss (quantile loss) corresponding to the target quantile. The pinball loss is expressed by the following equation (Equation 1).

As a specific example, the trained model M101 corresponding to the first quantile (50th percentile) is constructed by setting τ = 0.5 and training the model to minimize the loss L. Similarly, when constructing the trained model M102 corresponding to the second quantile (95th percentile), the pinball loss L (τ = 0.95) is used. Furthermore, when constructing the trained model M103 corresponding to the third quantile (5th percentile), the pinball loss L (τ = 0.05) is used.
Examples of commonly known regression models include LightGBM, MLP, and XGBost.

By utilizing the trained models M101, M102, and M103 constructed as described above, it becomes possible to obtain estimation results for the first, second, and third quantiles by inputting the characteristic features of the conditions for identifying the target of demand forecasting.

Now, let's refer to Figure 5 again. In S112, the demand distribution estimation unit 110 estimates a probability density function representing the distribution of demand on a given day, based on the estimation results of the first, second, and third quantiles for that day, which is the target of the demand forecast in S111. In this process, the demand distribution estimation unit 110 may estimate a so-called split normal distribution as the probability density function representing the distribution of demand on the target day, using the first quantile as a reference point, with parameters set to represent different distribution spreads for cases where demand is above the reference point and cases where demand is below the reference point.

Here, referring to Figure 7, we will explain an example of a probability density function that represents the distribution of demand on a given day for which demand forecasting is performed, and an example of the estimation method when a split normal distribution is estimated. Figure 7 shows an example of a probability density function with demand on the horizontal axis and the probability density of the demand forecast result on the vertical axis.
The split-normal distribution is a probability distribution that assumes different distribution spreads above and below the mode μ. The probability density function of the split-normal distribution is expressed by the condition shown below as (Equation 2).

Furthermore, in Figure 7, the probability density function G121 corresponds to the distribution of demand that would be expected if the demand were to exceed the first quantile (50th percentile). Specifically, the probability density function G121 corresponds to the probability density function expressed as a normal distribution with a standard deviation of _σ² .
Furthermore, the probability density function G122 corresponds to the distribution of demand that would be expected if the demand were to fall below the first quantile (50th percentile). Specifically, the probability density function G122 corresponds to the probability density function expressed as a normal distribution with a standard deviation of σ _1. In addition, the probability density function G110 represents the distribution of demand expressed by a probability density function that is a split normal distribution with a parameter σ ₂ indicating the spread of the distribution above the first quantile (50th percentile) and a parameter σ ₁ indicating the spread of the distribution below the first quantile (50th percentile).

Here, referring to Figure 8, we will explain an example of a method for determining the parameters μ, _σ1 , and _σ2 of the split normal distribution shown as (Equation 2) based on the estimated results of the first, second, and third quantiles. Figure 8 shows an example of a probability density function with the quantity demanded on the horizontal axis and the probability density of the quantity demanded on the vertical axis. In the example shown in Figure 8, quantile _q1-α represents the quantile of pinball loss L(τ=1-α) (0 < α < 0.5), and corresponds to an example of a quantile (second quantile) of the predicted quantity demand when it deviates above the standard. Similarly, quantile _qα represents the quantile of pinball loss L(τ=α), and corresponds to an example of a quantile (third quantile) of the predicted quantity demand when it deviates below the standard. Area _A1 represents the probability that the quantity demanded is less than or equal to quantile _qα . Furthermore, area _A2 indicates the probability that the demand quantity is below the quantile _q1-α .
The demand distribution estimation unit 110 uses the quantile q _0.5 as a parameter μ, and estimates the parameters _σ1 and _σ2 , which indicate the spread of the distribution, as the values that minimize the loss function shown below as (Equation 3).

In other words, when the first quantile is q _0.5 , the second quantile is q _0.95 , and the third quantile is q _0.05 , the demand distribution estimation unit 110 estimates the parameters _σ1 and _σ2 , which indicate the spread of the distribution, by minimizing the loss function shown in (Equation 2) such that _A1 = 0.05 and _A2 = 0.95.
As described above, the demand distribution estimation unit 110 estimates a probability density function representing the distribution of demand for each day that is the target of the demand forecast.
The above shows an example of how the second and third quantiles are derived to have a symmetrical relationship with respect to the first quantile (quantile q _0.5 ), as shown by quantile q _α and quantile q _{1-α. However} , this is merely an example, and symmetry is not necessarily required. In other words, as long as a second quantile representing the forecast result of demand when it exceeds the baseline and a third quantile representing the forecast result of demand when it falls below the baseline are derived with respect to quantile q 0.5, the method for setting the second and third quantiles is not particularly limited.

Now, let's refer to Figure 4 again.
In S120, the integrated processing unit 120 estimates a probability density function that indicates the likelihood of each demand amount falling within the range of demand amounts that are estimated to actually be observed during the period, based on the probability distribution of the forecast results of the demand amounts estimated for each day included in the period subject to demand forecasting.

For example, Figure 9 shows an example of the estimated result of a probability density function representing the distribution of daily demand within a period that may be subject to demand forecasting. In the graph shown at the bottom of Figure 9, the horizontal axis is date and the vertical axis is demand. The vertical axis of the graph shown at the bottom of Figure 9 corresponds to the horizontal axis in the probability density function exemplified in Figure 7. Also, the depth direction of the graph shown at the bottom of Figure 9 (i.e., the direction perpendicular to the drawing) corresponds to the direction of the vertical axis in the probability density function exemplified in Figure 7.
As illustrated in Figure 9, the integrated processing unit 120, having obtained estimation results for probability density functions representing the daily distribution of demand, receives a specified period for which demand should be forecasted and extracts estimation results for probability density functions representing the daily distribution of demand within that period. Then, the integrated processing unit 120 integrates the extracted daily estimation results for probability density functions representing the distribution of demand to estimate a probability density function representing the distribution of demand for the specified period.
For example, the integrated processing unit 120 may estimate a probability density function representing the distribution of demand during a specified period by performing a convolution operation on the estimation results of the probability density function representing the distribution of demand on each day included in that period.

Here, referring to Figure 10, we will explain an example of a method for estimating the probability density function that represents the distribution of demand over the period for which demand is to be predicted, focusing on the case where convolution is used.
First, the integrated processing unit 120 identifies the range of demand that is estimated to be actually observed during the period for which demand is to be predicted. The lower limit of this range of demand is identified as the demand when the predicted daily demand for each day included in the period is the minimum value. The upper limit of this range of demand is identified as the demand when the predicted daily demand for each day included in the period is the maximum value.
Furthermore, as shown in Figure 10, the integrated processing unit 120 performs convolution on the probability density functions of the daily demand quantities included in the above period to estimate the probability density function that indicates the likelihood of each demand quantity included in the above range of demand quantities.

The convolution of the probability density function is calculated, for example, based on the formula shown below as (Equation 4). In (Equation 4) below, f(x) represents the probability density function representing the distribution of demand x in period t1. g(z-x) represents the probability density function representing the distribution of demand z-x in period t2. h(z) represents the probability density function representing the distribution of demand z in period t1 + t2.

As described above, the integrated processing unit 120 estimates a probability density function that indicates the likelihood of each demand quantity falling within the range of demand quantities that are actually expected to be observed during the period, based on the probability distribution of the forecast results of the demand quantities estimated for each day within the period covered by the demand quantity forecast.

Now, let's refer to Figure 4 again. In S130, the demand forecasting unit 130 forecasts the demand for the target period based on the estimation result of the probability density function representing the distribution of demand during that period. As a specific example, the demand forecasting unit 130 receives a specification from the user regarding the target period for inventory management and the acceptable stockout rate, and determines, based on the stockout rate, which percentage point to focus on in the estimation result of the probability density function representing the distribution of demand during that period. Then, based on the determination of the point of focus (percentage point), the demand forecasting unit 130 forecasts the demand, taking into account upward and downward deviations.

As described above, obtaining demand forecast results makes it possible to determine, for example, a target inventory level that takes into account preventing stockouts during the inventory management period (i.e., the demand forecast period).

Furthermore, the demand forecasting mechanism described above can be linked to the ordering system for the products subject to inventory management. In this case, for example, the order quantity for the product may be determined by the difference between the estimated future inventory quantity of the product and the target inventory quantity for that product based on the demand forecast results described above. The estimated inventory quantity above represents the inventory quantity for each product one lead time from the present. The method for determining this estimated inventory quantity may be modified as appropriate depending on the use case. As a specific example, an existing algorithm may be used to determine the estimated inventory quantity. As another example, if the product in question is a new product, the estimated inventory quantity may be set to zero. As yet another example, similar to the demand forecasting, the estimated inventory quantity may be determined by calculating the total demand distribution for the lead time using convolution and then taking the difference from the current inventory quantity.

<Different example>
A modified example of the information processing system according to this embodiment is described below.

(Variation 1)
First, as Modification 1, another example of a method for estimating the quantiles of the demand forecast results will be described with reference to Figures 11 and 12. In the embodiment described above, the first quantile corresponding to the forecast result of the baseline demand, the second quantile corresponding to the forecast result of the demand when it is above the baseline, and the third quantile corresponding to the forecast result of the demand when it is below the baseline were estimated by quantile regression. In contrast, in this modification, as an example of a method for estimating the first, second, and third quantiles without using quantile regression, an example of a method for estimating these quantiles by estimating the errors that may occur in the demand forecast results will be described.

In this modified version, the estimation of quantiles in the demand forecast results utilizes two models: a demand forecast model M210, which is a pre-trained model for forecasting demand, and an error forecast model M220 (uncertainty model) that predicts the errors that occur in the demand forecast results from the demand forecast model M210. The demand forecast model M210, like the pre-trained model M100 mentioned earlier, is a pre-trained model that takes characteristic quantities of conditions for identifying the target of demand forecasting as input and outputs a demand forecast result. In this modified version, the error forecast model M220 is used to predict the errors that occur in the demand forecast results from the demand forecast model M210, and the estimation of each quantile is performed using these error prediction results.

Now, with reference to Figure 11, we will explain the error prediction model M220 in more detail.
First, let's explain Figure 11(A). Figure 11(A) shows an example of how to construct the error prediction model M220 based on machine learning (i.e., how to train the model). The error prediction model M220 is constructed based on supervised learning. The training data used in this process is generated by associating the error between the predicted demand and the actual demand as a correct label for the features of the conditions that serve as input to the demand prediction model M210 (conditions for identifying the target of demand prediction) and the demand prediction results from the demand prediction model M210. For example, in the case of inventory management of goods, the conditions that serve as input to the demand prediction model M210 include "date,""productinformation,""store information (information of the store that secures the inventory),""presence or absence of an event," and "weather information." In this way, the error prediction model M220 learns how much error occurs in the prediction results when certain conditions are input and the demand prediction model M210 outputs certain prediction results.

Next, Figure 11(B) will be explained. Figure 11(B) shows an example of a method for estimating the error that occurs in the demand forecast result by the demand forecast model M210 using the error prediction model M220. As shown in Figure 11(B), by inputting feature quantities of conditions for identifying the target of demand forecasting to the demand forecast model M210, the demand forecast model M210 outputs a demand forecast result when those conditions are met. The error prediction model M220 is input the above conditions input to the demand forecast model M210 and the feature quantities of the demand forecast result output from the demand forecast model M210 with those conditions as input. As a result, the error prediction model M220 outputs a prediction result of the error that occurs in the demand forecast result output from the demand forecast model M210 with the above conditions as input.
Specifically, if the target demand quantity to be predicted (in other words, the actual demand quantity) is y, and the predicted value of that demand quantity is y', the error prediction model M220 will predict the error z shown below as (Equation 5). In the following explanation, the prediction result of the error z by the error prediction model M220 will also be referred to as the predicted error value z'.

Next, referring to Figure 12, an example of a method for estimating the quantiles of the demand forecast result using the error forecast result from the error forecasting model M220 will be explained. In this modified example, the error forecast result (error forecast value z') from the error forecasting model M220 is considered as the average value of the error z, and the error forecast value z' is corrected (multiplied by a coefficient) so that it can be treated as a quantile. In this case, the proportion of sample data of actual demand (past demand) included in the corrected error forecast result is used as the criterion for determining the coefficient to be applied.
For example, Figure 12 schematically shows a plot of a series of sample data included in historical demand data in the feature space. Furthermore, region R1 schematically shows the region in the feature space corresponding to the interval defined as [-∞, y'+z'] based on the demand forecast result y' derived by the demand forecast model M210 and the error forecast value z' derived by the error forecast model M220.
Furthermore, region R2 schematically represents the region in the feature space corresponding to a given interval, when the interval is defined as [-∞, y'+εz'] by multiplying the error prediction value z' derived by the error prediction model M220 by a correction coefficient ε. By adjusting the correction coefficient ε, it is possible to adjust the size of region R2 to be wider than or narrower than region R1.
Under the above premises, if p' is the proportion of sample data included in region R2 from the plotted series of data, and p is the cumulative probability at the desired quantile, then it is possible to derive the quantile _qp by adjusting the correction coefficient ε so that p' = p. Specifically, the first quantile (50th percentile), the second quantile (95th percentile), and the third quantile (5th percentile) can be derived by adjusting the correction coefficient ε so that p' = p depending on the target quantile.
The demand forecasting model M210 is an example of a "second pre-trained model" that takes the features of the target of demand forecasting as input and outputs a forecast result for the demand. The error forecasting model M220 is an example of a "third pre-trained model" that takes the above features input to the second pre-trained model and the forecast result for the demand output from the second pre-trained model as input and predicts the error that occurs in the forecast result for the demand.

The above describes another example of a method for estimating the quantiles of the demand distribution, as a modified example (Modification 1), with reference to Figures 11 and 12.

(Variation 2)
Next, as a second modification, with reference to Figure 13, we will describe an example of a probability density function that represents the distribution of demand in a given unit period (for example, daily) that is estimated for each unit period targeted for demand forecasting. In the embodiment described above, the probability density function representing the distribution of demand for each unit period was estimated using a split normal distribution with parameters σ that show different distribution spreads for cases above and below the standard. On the other hand, the form of the probability density function representing the distribution of demand for each unit period is not necessarily limited to a split normal distribution, as long as the parameters that show different distribution spreads for cases above and below the standard are set for the distribution.

For example, Figure 13 shows an example of the estimation result of the probability density function representing the distribution of demand for each unit period. In the example shown in Figure 13, the probability density function representing the distribution of demand for each unit period is calculated by first determining a normal distribution with a parameter σ indicating the spread of the distribution, set separately for cases where the distribution deviates above the mean or median, and for cases where it deviates below the mean. These normal distributions are then combined. The probability density function of the distribution exemplified in Figure 13 is expressed by the conditional equation shown below as (Equation 6).

As illustrated above, the probability density function representing the distribution of demand for each unit period targeted by demand forecasting is not particularly limited in its form, as long as it is a distribution with parameters that show different distribution spreads for cases where the demand is above the baseline and cases where it is below the baseline.

In the above, as a modification example (2), we have explained an example of a probability density function that represents the distribution of demand during a given unit period (for example, daily), which is estimated for each unit period targeted by demand forecasting, with reference to Figure 13.

(Variation 3)
As a third modification, an example of using multiple models for quantile estimation will be described. In the embodiment described above, an example was described in which a single trained model is applied to the estimation of the first, second, and third quantiles. On the other hand, by using multiple trained models to estimate the first, second, and third quantiles and integrating (for example, averaging) the estimation results of each trained model, it may be possible to estimate each quantile in a more favorable manner.

For the multiple pre-trained models used to estimate each quantile, models with different characteristics may be applied.
As a concrete example, different training and evaluation data may be applied to each of the multiple pre-trained models during their construction (training). One example of a method for constructing such pre-trained models is K-fold cross-validation. As a concrete example, if five pre-trained models are to be applied to the estimation of each quantile, the five pre-trained models can be constructed using K-fold cross-validation with K=5.
As another example, multiple pre-trained models with different algorithms may be applied. In this case, for example, "LightGBM for the first model, RandomForest for the second model, ..." several algorithms may be applied individually to construct the pre-trained models, thereby creating multiple pre-trained models with different characteristics from each other.
Another example is that the random number seed may be changed when constructing each of the multiple pre-trained models. For instance, in algorithms such as LightGBM, the characteristics of the constructed pre-trained model tend to be influenced by the random numbers applied during training. Considering this property, by not fixing the random numbers when constructing each of the multiple pre-trained models, it is possible to construct multiple pre-trained models with different characteristics from one another.

As described above, the target quantile may be determined by having each of the multiple trained models estimate the target quantile, and then integrating (for example, averaging) the estimation results of each of the multiple trained models.
As described above, by having multiple trained models estimate quantiles and integrating the estimation results of each trained model, it may be possible to estimate each quantile in a more favorable manner.

The above describes an example of variation 3, where multiple models are used to estimate quantiles.

(Variation 4)
As a fourth modification, we will describe an example of how to adjust τ during training of a regression model (a trained model for estimating each quantile). In the embodiment described above, we explained an example where fixed values (0.05, 0.50, and 0.95) were applied as the three values of τ when estimating the first, second, and third quantiles. On the other hand, when considering actual operation, it may be desirable to adjust the value of τ while confirming the validity of the output of the regression model. In light of this situation, this modification will describe an example of a method for adjusting the value of τ while confirming the validity of the output of the regression model.

Methods for verifying the validity of regression model outputs include, for example, using PICP (Prediction Interval Coverage Probability) or MA (Miscaliburation Area). The methods using PICP and MA are explained separately below.

First, we will explain one example of how to verify the validity of a regression model's output using PICP. PICP, also known as the prediction interval coverage probability, is an indicator that expresses what percentage of historical data actually falls within a given range of the demand distribution. When using PICP, the smaller the discrepancy between the range of focus and the proportion of data included, the more valid the demand distribution output can be considered to be. PICP is expressed by the following relational equation (Equation 7).

For example, if we focus on the range of "5% to 95%" as the target range, this range accounts for 90% of the whole, so it is desirable that the PICP also be closer to 90%. In this case, when calculating the PICP, the lower limit _yLi in (Equation 6) above will be the value predicted as the 5th percentile, and the upper limit _yUi will be the value predicted as the 95th percentile.

Here, we focus on the case where τ = [0.05, 0.50, 0.95], that is, when training the 5th percentile prediction model, the 50th percentile prediction model, and the 95th percentile prediction model. In this case, it is desirable that 90% of the actual results (0.95 - 0.05 = 0.90) fall within the range indicated by "prediction result of the 5th percentile prediction model ≤ y ≤ prediction result of the 95th percentile prediction model". As an indicator of this idea, it is possible to apply PICP, which is an indicator that shows the proportion of actual results that fall within the range indicated by "prediction result of the 5th percentile prediction model ≤ y ≤ prediction result of the 95th percentile prediction model".
In this case, when training the regression model, you can calculate the difference between the target ratio (0.90 in the example above) and PICP, and adjust the value of τ so that this difference becomes smaller.

Next, we will explain an example of how to verify the validity of the regression model's output using MA. The previously mentioned PICP focused on the discrepancy between the expected range ("prediction result of the lower-bound prediction model ≤ y ≤ prediction result of the upper-bound prediction model") and the actual results. In contrast, MA uses a split normal distribution obtained in subsequent steps, varying the range multiple times, calculating each PICP, and accumulating the discrepancies to achieve a comprehensive evaluation of validity.

MA is determined by the procedure described below.
First, the range is gradually expanded upwards and downwards from the 50th percentile, and the PICP for each range is calculated. Then, the actual data is plotted with the magnitude of the proportion represented by the range on the horizontal axis and the PICP on the vertical axis. In the case of ideal behavior, the line connecting the plotted samples will be a straight line. The area value of the region defined by this straight line representing ideal behavior and the line connecting the series of actual data plotted samples (for example, a curve) is applied as an evaluation index called MA. The closer this evaluation index is to 0, the better (indicating that it is closer to ideal behavior).

Here, we will explain the method for calculating MA in more detail. In order to calculate MA, we will calculate PICP for multiple assumed ranges, so instead of the quantiles used to calculate PICP, the probability distribution itself estimated based on the quantiles is used.
Here, referring to Figure 14, we will explain an example of a method for calculating MA, focusing particularly on the part where PICP is calculated for a single assumed range. Figure 14 shows an example of a probability density function with the horizontal axis representing the quantity demanded and the vertical axis representing the probability density of the quantity demanded. Furthermore, the example shown in Figure 14 shows an example of a method for calculating PICP when a 30% range is assumed.
When considering a 30% range, the 35th and 65th percentiles are determined by moving 15% above and below the 50th percentile. The probability density function of the split normal distribution allows us to determine the probability corresponding to a value from the 50th percentile to the 50th percentile when the value is moved from the 50th percentile. Therefore, by moving the value in both the positive and negative directions from the 50th percentile so that the probability is 15%, the 35th and 65th percentiles can be determined. By calculating the proportion of actual results that fall between the 35th and 65th percentiles determined in this way, it is possible to determine the "PICC when considering a 30% range". For example, if the PICC in this case is 0.18, the point (0.3, 0.18) will be plotted as part of the curve when calculating the MA.

For example, Figure 15 shows an example of the MA calculation result. As illustrated in Figure 15, a straight line corresponding to the ideal behavior and a curve formed based on the plotting of the series of PICP calculation results are obtained. In MA, the area of the region formed by this straight line representing the ideal behavior and the curve obtained by plotting the PICP calculation results is used as the evaluation index. Specifically, the closer this area (evaluation index) is to 0, the better the evaluation result. In other words, the value of τ should be adjusted so that the area of the above region approaches 0.

The above describes an example of how to adjust τ during training of a regression model (a trained model for estimating each quantile) as Modification 4.

(Variation 5)
As a fifth modification, we will describe an example of correcting the relative magnitudes of the quantile prediction results. In the embodiment described above, we explained an example in which the quantile prediction results for each of the first to third quantiles naturally satisfy the relationships "third quantile < first quantile" and "first quantile < second quantile" through learning. On the other hand, there are cases in which the relative magnitudes of the quantile prediction results between quantiles are reversed from the example described above, such as "5% quantile > 50% quantile" or "50% quantile > 95% quantile". Therefore, in this modification, we will describe an example of a method for correcting the quantile prediction results when a reversal occurs in the relative magnitudes of quantiles as described above.

One correction method is to simply swap the quantiles that have been reversed in their relative order.
Another correction method involves analyzing the relationships between combinations of quantiles where no reversal has occurred, and then estimating new candidate quantiles based on the relationships between the quantiles corresponding to these combinations (for example, the 5th percentile is X times the 50th percentile).

Here, we will explain the second correction method in more detail with a specific example. For example, Figure 16 shows an example of a method for correcting the quantile prediction results when a reversal of the relative magnitudes of the quantiles occurs. In the example shown in Figure 16, the relationship analysis and correction of the quantile prediction results are performed for the 50th percentile (first quantile), the 95th percentile (second quantile), and the 5th percentile (third quantile).

Figure 16(a) shows an example of a sample from the quantile prediction results in which no reversal of magnitude relationship occurred. Specifically, the quantile prediction results for the 50th percentile, 5th percentile, and 95th percentile in each sample exemplified in Figure 16(a) satisfy the conditions "5th percentile < 50th percentile" and "50th percentile < 95th percentile".
Next, we analyze the relationships between quantiles for each sample in which the reversal of magnitude relationship exemplified in Figure 16(a) has not occurred. For example, in the example shown in Figure 16(b), for each sample, we calculate the ratio of the prediction results between quantiles as "5% quantile prediction result ÷ 50% quantile prediction result" and "95% quantile prediction result ÷ 50% quantile prediction result".
Then, the average value of the ratio of the predicted results between quantiles for each sample, as illustrated in Figure 16(b), is calculated. Figure 16(c) shows an example of the calculation results of the average values of "5% quantile prediction result ÷ 50% quantile prediction result" and "95% quantile prediction result ÷ 50% quantile prediction result" calculated for each sample in Figure 16(b). Note that in Figure 16(c), an example is shown where a common ratio is calculated for all products for the sake of simplicity, but this is just one example, and for example, the ratio may be calculated individually for each product category.

Next, we will explain an example of a process for correcting quantile prediction results when a reversal occurs in the relative magnitudes of the quantile prediction results. For example, Figure 16(d) shows an example of a sample where a reversal occurs in the quantile prediction results. Here, we will explain an example of correcting the quantile prediction results where a reversal occurs, using each sample exemplified in Figure 16(d), based on the ratio of the prediction results between quantiles obtained in the example shown in Figure 16(c).

As a specific example, the sample for the product name "CCCCCC" shows a reversal in the relationship between the 5% quantile prediction result and the 50% quantile prediction result, where "5% quantile > 50% quantile". Therefore, in this case, it is advisable to correct the 5% quantile prediction result based on the average value of "5% quantile prediction result ÷ 50% quantile prediction result" calculated in the example shown in Figure 16(c). For example, in the example shown in Figure 16(c), the 5% quantile prediction result is corrected by multiplying it by the average value of "5% quantile prediction result ÷ 50% quantile prediction result". This corrects the relationship between the 5% quantile prediction result and the 50% quantile prediction result to "5% quantile < 50% quantile". Note that in this sample, there is no reversal in the relationship between the 95% quantile prediction result and the 50% quantile prediction result; in this case, the value is applied as is without correction.

As another example, the sample for the product name "DDDDDD" shows that "50th percentile > 95th percentile," indicating a reversal in the relative magnitudes of the 5th percentile prediction and the 50th percentile prediction. Therefore, in this case, it is advisable to correct the 95th percentile prediction based on the average value of "95th percentile prediction result ÷ 50th percentile prediction result" calculated in the example shown in Figure 16(c). For example, in the example shown in Figure 16(c), the 95th percentile prediction result is corrected by multiplying it by the average value of "95th percentile prediction result ÷ 50th percentile prediction result." This corrects the relative magnitudes of the 95th percentile prediction and the 50th percentile prediction result to "50th percentile < 95th percentile." In this particular sample, there is no reversal of the relative magnitudes between the 5th percentile prediction and the 50th percentile prediction. Therefore, in this case, the values are applied as they are, without any correction.

The above describes an example of modification 5, which involves correcting the relative magnitudes of the quantile prediction results.

(Variation 6)
As a sixth modification, we will describe an example of estimating multiple quantiles (for example, the first to third quantiles) using a single model (a common model). In the embodiment described above, we described an example in which a pre-trained model, individually constructed for each quantile, is used when estimating the first to third quantiles. In contrast, this modification describes an example in which multiple quantiles (for example, the first to third quantiles) are estimated using a single model.

As a concrete example, when estimating multiple quantiles using a neural network model, the model should be constructed to estimate those multiple quantiles. Another example is when estimating multiple quantiles using a tree-based model; in this case, information indicating "which quantiles to estimate" should be added as column information during prediction.

The above describes an example of variation 6, where multiple quantiles are estimated using a single model.

(Variation 7)
As a seventh variation, we will describe an example of a case where, when estimating multiple quantiles (for example, the first to the third quantiles) using a single model, constraints are imposed during the training of the model so that the relative magnitudes of the quantile prediction results for each of the multiple quantiles are maintained. In the embodiments described above, we explained an example in which the quantile prediction results for each of the first to the third quantiles naturally satisfy the relationships "third quantile < first quantile" and "first quantile < second quantile" through training. On the other hand, as explained in the fifth variation, there are cases in which the relative magnitudes of the quantile prediction results between quantiles are reversed, and the example shown in the fifth variation describes an example in which this reversal of the relative magnitudes is resolved by correcting the quantile prediction results afterward.

In contrast, as explained in Modification Example 6, when multiple quantiles are estimated using a single model, it is possible to impose constraints during the model's training to maintain the relative magnitudes of the quantile prediction results among the multiple quantiles. Specifically, by imposing a monotonically increasing constraint on the column containing information indicating "which quantiles to estimate" during the training of the single model, it becomes possible to prevent a reversal of the relative magnitudes of the quantile prediction results among the multiple estimated quantiles.

The above describes an example of Modification 7, where, when estimating multiple quantiles using a single model, constraints are imposed during the model's training to ensure that the relative magnitudes of the quantile prediction results for each of the multiple quantiles are maintained.

(Variation 8)
As variation 8, an example of a method for estimating the demand distribution for a target period by summing the mean and variance of the demand distribution for each unit period (for example, each day) will be described. In the embodiment described above, the integrated processing unit 120 estimated the demand distribution for the target period by performing a convolution operation on the estimated daily demand distribution. In contrast, this variation describes an example of estimating the demand distribution for the target period by applying a simple sum of the mean and variance instead of a convolution operation.

Specifically, the probability density function representing the distribution of demand during the target period may be estimated by summing the "mode μ," the "parameter _σ1 representing the downward spread," and the "parameter _σ2 representing the upward spread" of the daily probability density function for each day.

For example, Figure 17 shows an example of a method for estimating the demand distribution over a target period. It illustrates a method of estimating the demand distribution over a target period by summing the mean and variance of the daily demand distribution. For simplicity, Figure 17 explains an example where the demand distribution over three days is estimated based on the demand distribution over those three days.

In the example shown in Figure 17, the mode μ, the parameter σ1 representing the downward spread, and the parameter _σ2 representing the upward spread of the daily probability density function are shown for each of the three days: day 1, day 2, and day 3. Furthermore, the estimated results for days 1 through 3 are shown, which are the sum of the mode μ, the parameter _σ1 representing the downward spread, and the parameter _σ2 representing the upward spread of the daily probability density function for each of the three days, taking into account the additivity of the normal distribution. By applying the mode and the parameters representing the spread of the distribution obtained as the estimated results for days 1 through 3 to the relationship shown below as (Equation ₈ ), it is possible to estimate the demand distribution for the three-day period from day 1 to day 3.

The above describes an example of a modification (Modification 8) for estimating the demand distribution over a given period by summing the mode and spread of the demand distribution for each unit period (e.g., daily).

(Variation 9)
As a variation 9, we will describe an example of a mechanism that allows for the estimation of more suitable quantiles by considering the variability of the estimation results from multiple models, as an example of applying multiple models to the estimation of each quantile.

Figure 18 shows an example of applying multiple models to the estimation of each of several quantiles. In the example shown in Figure 18, five models are applied to the estimation of the q _0.5 quantile, the q _α quantile, and the q _1-α quantile.
Specifically, for the q _0.5 quantile, the average of the estimated results of the quantile q _0.5 from each of the five models is applied. In contrast, for the q _α quantile, the average value of the q _α quantile from each of the five models is added to the average value of the q α quantile from each of the five models, multiplied by the α quantile z _α of the standard normal distribution and the standard deviation of the q _α quantile obtained from each of the five models. Similarly, for the q _1-α quantile, the average value of the q _1-α quantile from each of the five models is added to the value of the 1-α quantile z _1-α of the standard normal distribution and the standard deviation of the q _1-α quantile obtained from each of the five models.

Here, referring to Figure 19, we will explain with specific examples the estimation methods for the q _0.5 quantile, q _α quantile, and q _1-α quantile, as illustrated in Figure 18, focusing on the estimation of the q _0.5 quantile, q _0.05 quantile, and q _0.95 quantile. In the example shown in Figure 19, examples of estimation results for the q _0.5 quantile, q _0.05 quantile, and q _0.95 quantile are shown for each of Models 1 to 5.

For example, in the example shown in Figure 19, the q _0.5 quantile is calculated as the average of the estimated results for each model quantile, so the calculation formula is as follows.

Furthermore, in the example shown in Figure 19, the q _0.05 quantile is calculated by adding the value obtained by multiplying the q _0.05 quantile z _0.05 of the standard normal distribution by the standard deviation to the mean value of the estimated results of each model quantile, so the calculation formula is as follows.

Furthermore, the q _0.95 quantile in the example shown in Figure 19 is calculated by adding the value obtained by multiplying the q _0.95 quantile z _0.95 of the standard normal distribution by the standard deviation to the mean of the estimated results of each model quantile, so the calculation formula is as follows.

In summary, as variation 9, we have described an example of a mechanism that allows for the estimation of more suitable quantiles by considering the variability of the estimation results from multiple models, as an example of applying multiple models to the estimation of each quantile.

<Conclusion>
As described above, the information processing device according to this embodiment estimates a first distribution that shows the likelihood of each demand quantity within a first range of demand quantities that are estimated to be actually observed for a given unit period, based on past demand data. Furthermore, the information processing device estimates a second distribution that shows the likelihood of each demand quantity within a second range of demand quantities that are estimated to be actually observed for a given unit period, based on the first distribution estimated for each of the multiple unit periods included in the target period for demand forecasting. Then, in this embodiment, a forecast of demand quantities for the target period is made based on the estimation results of the second distribution.

With the above configuration, it becomes possible to make more accurate demand forecasts, even in situations where the trends differ depending on whether the demand exceeds or falls below the baseline, depending on the conditions of the demand forecast target. Furthermore, even in situations where the period for which demand is forecasted is appropriately switched, the probability density of demand corresponding to that period can be estimated by convolving the probability density function representing the distribution of demand estimated for each unit period included in that period. In other words, in this embodiment, the processing load related to forecasting demand for each period can be reduced compared to constructing a demand forecasting model for each period targeted for forecasting.

It should be noted that the embodiments described above are merely examples and do not necessarily limit the configuration or processing of the present invention. Various modifications and changes may be made without departing from the technical concept of the present invention.
Furthermore, the present invention includes a program that realizes the functions of the embodiments described above, and a recording medium that can be read by a computer storing the program.
Furthermore, various modifications can be made as long as they do not deviate from the basic technical concept of the information processing device according to the above embodiment. For example, in the above embodiment, an example was described in which a first quantile, a second quantile, and a third quantile are used to estimate a probability density function representing the distribution of demand for each unit period. On the other hand, if it is possible to estimate a probability density function representing the distribution of demand with parameters that show different distribution spreads when the demand is above the standard and when it is below the standard, the method is not necessarily limited to the method using the above quantiles. Also, in the above embodiment, an example was described in which a convolution process is used to integrate the probability density functions representing the distribution of demand estimated for each of the multiple unit periods included in the target period of demand forecasting. On the other hand, if it is possible to derive a probability density function representing the distribution of demand in the target period by integrating the probability density functions representing the distribution of demand estimated for each of the multiple unit periods included in the target period of demand forecasting, the method is not necessarily limited to the method using convolution.
Furthermore, the application of this embodiment is not limited to inventory management of the products exemplified above. In other words, the information processing device according to this embodiment can be applied in any situation where demand is predicted based on past performance.

Furthermore, the following configurations also fall within the technical scope of this disclosure.
(1) An information processing device comprising: a first estimation means for estimating a first distribution indicating the likelihood of each demand quantity that falls within a first range of demand quantities that are estimated to be actually observed for a unit period subject to demand forecasting, based on past demand performance; and a second estimation means for estimating a second distribution indicating the likelihood of each demand quantity that falls within a second range of demand quantities that are estimated to be actually observed for a target period, based on the first distribution estimated for each of a plurality of unit periods included in the target period for demand forecasting, wherein a forecast of demand quantities for the target period is performed based on the second distribution.
(2) The information processing device according to (1), wherein the first estimation means estimates, based on the actual past demand, a first quantile corresponding to the forecast result of a standard demand for a unit period subject to the demand forecast, a second quantile corresponding to the forecast result of the demand assumed to occur when the demand exceeds the standard, and a third quantile corresponding to the forecast result of the demand assumed to occur when the demand falls below the standard, and estimates, based on the estimation results of the first quantile, the second quantile, and the third quantile, a first range and a first distribution indicating the likelihood of each demand included in the first range.
(3) The information processing apparatus according to (2), wherein the first estimation means estimates, based on the first quantile, the second quantile, and the third quantile, a first probability density function that shows the likelihood of each demand quantity when the predicted demand quantity is greater than the first quantile, and a second probability density function that shows the likelihood of each demand quantity when the predicted demand quantity is less than the first quantile, and estimates the first distribution based on the first probability density function and the second probability density function.
(4) The information processing apparatus according to (2) or (3), wherein the first distribution is a split normal distribution in which the parameter representing the spread of the distribution differs depending on whether the predicted demand is greater or less than the first quantile.
(5) The information processing device according to any one of (2) to (4), wherein the first estimation means has a first trained model that takes as input feature quantities of the target of demand forecasting as input, and outputs a forecast result of the demand quantity, which is constructed such that the corresponding pinball loss is smaller for each of the first quantile, the second quantile, and the third quantile, based on the actual past demand quantity, and the first trained means obtains the forecast results of the first quantile, the second quantile, and the third quantile as output of the first trained model by inputting feature quantities of the target of demand forecasting as input.
(6) The information processing device according to (5), wherein the first estimation means applies a plurality of trained models as the first trained model to be applied to the estimation of each quantile indicated as the first quantile, the second quantile, and the third quantile, and estimates the quantile by integrating the estimation results of the quantiles from each of the plurality of trained models.
(7) The information processing apparatus according to (6), wherein the first estimation means resolves the reversal of the magnitude relationship when the magnitude relationship of the estimation results of a plurality of quantiles is reversed by correcting the estimation result of one of the plurality of quantiles.
(8) The information processing apparatus according to (6) or (7), wherein the first estimation means integrates the quantile estimation results from each of the plurality of trained models based on the mean and variance of the quantile estimation results from each of the plurality of trained models.
(9) The information processing apparatus according to (5), wherein the first estimation means applies a common trained model as the first trained model applied to the estimation of each quantile indicated as the first quantile, the second quantile, and the third quantile.
(10) The information processing device according to (9), wherein the common trained model is constructed such that the relationship between the magnitudes of multiple quantiles to be estimated is preserved by imposing a monotonically increasing constraint during training.
(11) The information processing apparatus according to any one of (2) to (10), wherein the first estimation means determines the first quantile, the second quantile, and the third quantile to be applied to the estimation of the first distribution by confirming the validity of the estimation results of the first quantile, the second quantile, and the third quantile.
(12) The information processing apparatus according to any one of (2) to (4), wherein the first estimation means includes a second trained model that takes a feature quantity of the quantity to be predicted as input and outputs a prediction result of the quantity to be predicted, and a third trained model that takes the feature quantity and the prediction result of the quantity to be predicted output from the second trained model as input and predicts an error occurring in the prediction result of the quantity to be predicted, and estimates the first quantile, the second quantile, and the third quantile by determining the correction coefficient such that a number of sample data corresponding to the target quantile from the sample data of past demand performance corresponding to the input feature quantity falls within a range of quantity to be predicted, which is defined with the sum of the prediction result of the quantity to be predicted output from the second trained model and the value obtained by multiplying the error output from the third trained model by a correction coefficient, as the upper limit.
(13) The information processing apparatus according to any one of (1) to (12), wherein the second estimation means estimates the second distribution corresponding to the target period by convolution of the first distribution estimated for each of the multiple unit periods included in the target period.
(14) The information processing apparatus according to any one of (1) to (12), wherein the second estimation means estimates the second distribution corresponding to the target period based on the mode of the first distribution estimated for each of a plurality of unit periods included in the target period and parameters representing the spread of the distribution.
(15) An information processing apparatus according to any one of (1) to (14), comprising a prediction means for predicting the amount of demand during the target period based on the second distribution and the error in the prediction result of the allowable amount of demand.
(16) An information processing method performed by an information processing device, comprising: a first estimation step of estimating a first distribution indicating the likelihood of each quantity of demand that falls within a first range of quantities of demand that are estimated to be actually observed for a unit period subject to demand forecasting, based on past demand performance; and a second estimation step of estimating a second distribution indicating the likelihood of each quantity of demand that falls within a second range of quantities of demand that are estimated to be actually observed for a target period, based on the first distribution estimated for each of a plurality of unit periods included in the target period for demand forecasting, wherein a forecast of demand for the target period is performed based on the second distribution.
(17) A program that causes a computer to perform a first estimation step of estimating a first distribution showing the likelihood of each quantity of demand that falls within a first range of demand that is estimated to be actually observed for a unit period subject to demand forecasting, based on past demand performance; and a second estimation step of estimating a second distribution showing the likelihood of each quantity of demand that falls within a second range of demand that is estimated to be actually observed for a target period, based on the first distribution estimated for each of a plurality of unit periods included in the target period for demand forecasting, and then forecasts the quantity of demand for the target period based on the second distribution.

1 Information Processing System 100 Information Processing Device 110 Demand Distribution Estimation Unit 120 Integrated Processing Unit 130 Demand Forecasting Unit 190 Storage Unit 200 Terminal Device

Claims (17)

A first estimation means that estimates a first distribution showing the likelihood of each demand quantity within a first range of demand quantities that are estimated to be actually observed for a unit period targeted for demand quantity forecasting, based on past demand quantity performance,
A second estimation means for estimating the second distribution used to forecast demand during the target period , by integrating the probability density functions representing the first distribution estimated for each of the multiple unit periods included in the target period for demand forecasting , and deriving a second probability density function representing the probability of each demand within a second range of demand estimated to be actually observed during the target period .
An information processing device equipped with the following features. The first estimation means is,
Based on the aforementioned past demand data, a first quantile corresponding to the forecast result of the base demand for the unit period covered by the demand forecast is estimated, a second quantile corresponding to the forecast result of the demand expected when the demand exceeds the base, and a third quantile corresponding to the forecast result of the demand expected when the demand falls below the base.
Based on the estimation results of the first quantile, the second quantile, and the third quantile, the first range and the first distribution showing the likelihood of each demand quantity included in the first range are estimated.
The information processing apparatus according to claim 1. The first estimation means is,
Based on the first quantile, the second quantile, and the third quantile,
A first probability density function that indicates the likelihood of a given demand quantity when the predicted demand quantity is higher relative to the first quantile,
A second probability density function that shows the likelihood of each demand quantity when the predicted demand quantity is less than the first quantile,
We estimate,
The first distribution is estimated based on the first probability density function and the second probability density function.
The information processing apparatus according to claim 2. The information processing apparatus according to claim 2, wherein the first distribution is a split normal distribution in which the parameters representing the spread of the distribution differ depending on whether the predicted demand is greater or less than the first quantile. The first estimation means is,
Based on the aforementioned past demand data, the system has a first trained model that takes the features of the demand to be predicted as input and outputs a demand prediction result, constructed such that the corresponding pinball loss is smaller for each of the first, second, and third quantiles.
By inputting the feature quantities of the target of demand forecasting into the first trained model constructed for each of the first, second, and third quantiles, the estimation results for the first, second, and third quantiles are obtained as the output of the first trained model.
The information processing apparatus according to claim 2. The information processing device according to claim 5, wherein the first estimation means applies a plurality of trained models as the first trained model applied to the estimation of each quantile indicated as the first quantile, the second quantile, and the third quantile, and estimates the quantile by integrating the estimation results of each of the plurality of trained models. The information processing apparatus according to claim 6, wherein the first estimation means resolves the reversal of the magnitude relationship between the estimation results of multiple quantiles by correcting the estimation result of one of the multiple quantiles if the magnitude relationship is reversed. The information processing apparatus according to claim 6, wherein the first estimation means integrates the quantile estimation results from each of the multiple trained models based on the mean and variance of the quantile estimation results from each of the multiple trained models. The information processing apparatus according to claim 5, wherein the first estimation means applies a common trained model as the first trained model applied to the estimation of each quantile indicated as the first quantile, the second quantile, and the third quantile. The information processing device according to claim 9, wherein the common pre-trained model is constructed such that the relative magnitudes of multiple quantiles to be estimated are preserved by imposing a monotonically increasing constraint during training. The information processing apparatus according to claim 2, wherein the first estimation means determines the first, second, and third quantiles to be applied to the estimation of the first distribution by verifying the validity of the estimation results of the first, second, and third quantiles. The first estimation means is,
A second pre-trained model takes the features of the quantity to be predicted as input and outputs the predicted quantity of demand,
A third trained model takes the aforementioned features and the forecast result of the demand quantity output from the second trained model as input and predicts the error occurring in the forecast result of the said demand quantity.
It has,
The first, second, and third quantiles are estimated by determining the correction coefficient such that, among the sample data of past demand data corresponding to the input features, the number of sample data corresponding to the target quantile falls within a range of demand defined by the sum of the demand prediction result output from the second trained model and the value obtained by multiplying the error output from the third trained model by a correction coefficient.
The information processing apparatus according to claim 2. The information processing apparatus according to claim 1, wherein the second estimation means estimates the second distribution corresponding to the target period by convolution of the first distribution estimated for each of the multiple unit periods included in the target period. The information processing apparatus according to claim 1, wherein the second estimation means estimates the second distribution corresponding to the target period based on the mode of the first distribution estimated for each of the multiple unit periods included in the target period and parameters representing the spread of the distribution. The information processing apparatus according to claim 1, comprising a prediction means for predicting the amount of demand during the target period based on the second distribution and the error in the prediction result of the allowable amount of demand. An information processing method performed by an information processing device,
A first estimation step involves estimating a first distribution that shows the likelihood of each demand quantity falling within a first range of demand quantities that are estimated to be actually observed for a given unit period, based on past demand performance;
A second estimation step involves integrating the probability density functions representing the first distribution estimated for each of several unit periods included in the target period for demand forecasting, to derive a probability density function representing a second distribution that shows the likelihood of each demand within a second range of demand estimated to be actually observed during the target period, thereby estimating the second distribution used for forecasting demand during the target period ;
Information processing methods , including those mentioned above . On the computer,
A first estimation step involves estimating a first distribution that shows the likelihood of each demand quantity falling within a first range of demand quantities that are estimated to be actually observed for a given unit period, based on past demand performance;
A second estimation step involves integrating the probability density functions representing the first distribution estimated for each of several unit periods included in the target period for demand forecasting, to derive a probability density function representing a second distribution that shows the likelihood of each demand within a second range of demand estimated to be actually observed during the target period, thereby estimating the second distribution used for forecasting demand during the target period ;
A program that executes something.