JP6940184B2 - Skill estimation device, learning support device, skill estimation method and program - Google Patents

Description

The present invention relates to a skill estimation device, a learning support device, a skill estimation method and a program.

One of the learning support systems is a system that presents problems to learners. When presenting a question, if the learner's ability can be grasped, a more appropriate question can be presented. Therefore, a technique for grasping the learner's ability has been proposed.
For example, in the technique described in Non-Patent Document 1, the importance of the ability (Concept) in solving a problem and the ability possessed by the learner are shown by a real number matrix. In this technique, the learner minimizes the difference between the estimated value calculated by the ability required to solve the problem and the ability of the learner and the actual value of the answer result by the answerer. Estimate the ability of the learner.

Shaghayegh Sahebi, 2 outsiders, "Tensor Factorization for Student Modeling and Performance Prediction in Unstructured Domain", Proceedings of the 9th International Conference on Educational Data Mining, 2016, p. 502-506

It is considered that the technique described in Non-Patent Document 1 cannot easily interpret the estimation result even if a person sees it. In particular, with the technique described in Non-Patent Document 1, it is difficult for humans to interpret the content of the skill based on the estimation result.

An example of an object of the present invention is to provide a skill estimation device, a learning support device, a skill estimation method, and a program capable of solving the above-mentioned problems.

The skill estimation device according to the first aspect of the present invention includes a correct / incorrect data acquisition unit that acquires correct / incorrect data indicating the correct / incorrect answer of a problem solved by a learner as binary data, and a skill required for solving the problem. , And, using a model in which the skill held by the learner is represented by a binary probability variable indicating the presence or absence of the skill for each skill, a solution that maximizes the posterior probability based on the correct / incorrect data is searched for. It is equipped with a skill estimation unit that estimates the skills required to solve the problem and the skills held by the learner.

The learning support device according to the second aspect of the present invention includes a correct / incorrect data acquisition unit that acquires correct / incorrect data indicating the correct / incorrect answer of a problem solved by a learner as binary data, and a skill required for solving the problem. , And, using a model in which the skill held by the learner is represented by a binary probability variable indicating the presence or absence of the skill for each skill, a solution that maximizes the posterior probability based on the correct / incorrect data is searched for. The problem of selecting the problem to be presented to the learner based on the skills required to solve the problem and the skill estimation unit that estimates the skills held by the learner, and the estimation result of the skill estimation unit. It includes a selection unit.

According to the third aspect of the present invention, in the skill estimation method, the device acquires correct / incorrect data indicating the correctness of the answer in which the learner has solved the problem as binary data, and the device causes the problem. Maximize the posterior probability based on the correct / incorrect data by using a model that expresses the skills required to solve and the skills held by the learner with binary probability variables indicating the presence or absence of the skills for each skill. This includes performing a solution search to estimate the skills required to solve the problem and the skills possessed by the learner.

In the program according to the fourth aspect of the present invention, the computer acquires correct / incorrect data indicating the correctness of the answer in which the learner has solved the problem as binary data, the skill required to solve the problem, and the skill required to solve the problem. By searching for a solution that maximizes the posterior probability based on the correct / incorrect data, using a model in which the skill held by the learner is represented by a binary probability variable indicating the presence or absence of the skill for each skill. Estimate the skills required to solve the problem and the skills possessed by the learner, and let them perform.

According to the present invention, the content of the skill can be relatively easily interpreted by a human being based on the estimation result.

It is a schematic block diagram which shows the functional structure of the learning support system which concerns on embodiment of this invention. It is a schematic block diagram which shows the functional structure of the learning support apparatus which concerns on embodiment. It is a schematic block diagram which shows the functional structure of the terminal apparatus which concerns on embodiment. It is explanatory drawing which shows the outline of the estimation performed by the skill estimation part which concerns on embodiment. It is a figure which shows the model used for the skill estimation by the skill estimation part which concerns on embodiment as a graphical model. It is a figure which shows the value of a logistic function. It is a flowchart which shows the procedure of the process performed by the skill estimation part which concerns on embodiment. It is a figure which shows the example of the structure of the skill estimation apparatus which concerns on another embodiment of this invention. It is a figure which shows the example of the structure of the learning support apparatus which concerns on another embodiment of this invention.

Hereinafter, embodiments of the present invention will be described, but the following embodiments do not limit the inventions claimed. Also, not all combinations of features described in the embodiments are essential to the means of solving the invention.
FIG. 1 is a schematic block diagram showing a functional configuration of a learning support system according to an embodiment of the present invention. As shown in FIG. 1, the learning support system 1 includes a learning support device 100 and a terminal device 200. The learning support device 100 and the terminal device 200 communicate with each other via the communication network 900.

The learning support system 1 provides a user who is a learner with a problem according to the skill possessed by the user. Skills here are abilities required to solve problems and are not limited to specific types of abilities. For example, a skill may include knowledge or know-how.
The skill held by the user is also referred to as the user's skill.

The learning support device 100 estimates the skill of the user and provides a problem according to the estimated skill. The learning support device 100 is configured by using a computer such as a workstation. The learning support device 100 corresponds to an example of a skill estimation device and an example of a problem providing device.
FIG. 2 is a schematic block diagram showing a functional configuration of the learning support device 100. As shown in FIG. 2, the learning support device 100 includes a server-side communication unit 110, a server-side storage unit 180, and a server-side control unit 190. The server-side control unit 190 includes a skill estimation unit 191, a question selection unit 192, and an answer processing unit 193.

The server-side communication unit 110 communicates with other devices. In particular, the server-side communication unit 110 communicates with the terminal device 200 to transmit a problem, receives an answer (user's answer to the problem) that the user has solved the problem, and transmits a commentary on the answer.
The server-side storage unit 180 stores various information such as problems and answers and a model for skill estimation. The server-side storage unit 180 is configured by using the storage device included in the learning support device 100.
The server-side control unit 190 controls each unit of the learning support device 100 to perform various processes. The server-side control unit 190 is configured by a CPU (Central Processing Unit) included in the learning support device 100 reading a program from the server-side storage unit 180 and executing the program.

The skill estimation unit 191 estimates the skills held by the user and the skills required to solve each problem based on the correctness of the user's answer to the problem.
The problem selection unit 192 selects a problem to be provided to the user based on the skill estimated by the skill estimation unit 191.

The answer processing unit 193 processes the user's answer to the question. Specifically, the answer processing unit 193 determines whether the answer is correct or incorrect. Then, the answer processing unit 193 outputs the correct / incorrect data in which the binary data indicating the determination result (data indicating that the answer is correct or incorrect) is associated with the question number, the user number, and the date and time information on the server side. It is stored in the storage unit 180. The answer processing unit 193 corresponds to an example of a correct / incorrect data acquisition unit.
Further, the answer processing unit 193 selects a commentary according to the correctness of the answer from the commentary stored in the server-side storage unit 180, and transmits the answer to the terminal device 200 that has transmitted the answer via the server-side communication unit 110. do.

The terminal device 200 functions as a terminal device of the learning support system 1. In particular, the terminal device 200 receives a user operation of displaying a question transmitted from the learning support device 100 and inputting an answer. The terminal device 200 transmits the obtained answer to the learning support device 100, receives a commentary from the learning support device 100, and displays the received commentary. Further, when the terminal device 200 receives the next question from the learning support device 100, the terminal device 200 repeats the display of the question, the acquisition and transmission of the answer, and the reception and display of the commentary.

The terminal device 200 is configured by using a computer such as a personal computer (PC), a tablet terminal device, or a smartphone (Smartphone).
The number of terminals included in the learning support system 1 may be a plurality, and the larger the number, the better. Since it is expected that the accuracy of skill estimation by the learning support device 100 increases as the number of users increases, it is preferable that the number of terminal devices 200 increases.

FIG. 3 is a schematic block diagram showing a functional configuration of the terminal device 200. As shown in FIG. 3, the terminal device 200 includes a terminal-side communication unit 210, a display unit 220, an operation input unit 230, a terminal-side storage unit 280, and a terminal-side control unit 290.
The terminal-side communication unit 210 communicates with another device. In particular, the terminal-side communication unit 210 receives the question and the explanation by communicating with the learning support device 100, and also transmits the answer.
The display unit 220 has a display screen such as a liquid crystal panel or an LED (Light Emitting Diode) panel, and displays various images. In particular, the display unit 220 displays the problems and explanations transmitted by the learning support device 100.

The operation input unit 230 includes an input device such as a keyboard and a mouse, and receives user operations. In particular, the operation input unit 230 receives an answer input operation by the learner while the display unit 220 is displaying the question.
The terminal side storage unit 280 stores various information. For example, the terminal-side storage unit 280 stores an application program for operating as a terminal device of the learning support system 1. In addition, the terminal-side storage unit 280 temporarily stores problems and explanations transmitted by the learning support device 100. The terminal-side storage unit 280 is configured by using the storage device included in the terminal device 200.

The terminal-side control unit 290 controls each unit of the terminal device 200 to execute various processes. For example, the terminal-side control unit 290 controls the terminal-side communication unit 210 to cause the terminal-side communication unit 210 to communicate with the server-side communication unit 110 of the learning support device 100. Further, the terminal side control unit 290 controls the display unit 220 to display the problem and the explanation on the display unit 220. Further, the terminal-side control unit 290 converts the user operation received by the operation input unit 230 into data such as an answer.
The communication network 900 mediates communication between the learning support device 100 and the terminal device 200. The communication network 900 is not limited to a specific communication network. For example, the communication network 900 may be, but is not limited to, the Internet.

Next, the skill estimation performed by the skill estimation unit 191 will be described.
The following environment is assumed as the environment in which the skill estimation unit 191 estimates the skill.
A total of M problems are prepared, and N users solve the problems. Each problem requires one or more of the K skills to solve the problem. As mentioned above, the skill here is the ability to solve a problem and is not limited to a specific type. Skills may include the knowledge needed to solve a problem, or they may include abstract abilities that are not embodied. Further, the user referred to here is a person who solves the problem provided by the learning support device 100.

The server-side storage unit 180 records the order in which the users solve the problems and the answers for each user. Based on this information, the skill estimation unit 191 estimates the skills required to solve each problem and the skills held by each user (acquired skills).
The skill estimation unit 191 does not analyze the contents of each skill, but estimates the correspondence between the skill required to solve the problem and the skill held by the user. When one problem and one user are selected, the problem selection unit 192 then informs the user which of the skills required to solve the problem is possessed by the user. It can be used as a clue to select the problem to be presented (the problem to be solved by the user next).

FIG. 4 is an explanatory diagram showing an outline of estimation performed by the skill estimation unit 191. In FIG. 4, the skills R required to solve the problem, the skills Z _{1 to} Z _N held by each of the plurality of users, and the results (correct / incorrect) X _{1 to} X _{N of each user solving the problem are shown.} Is shown in the form of a binary matrix or vector.

In FIG. 4, the ^{superscript "T" in RT} (problem skill matrix) indicates the transpose of the matrix or vector. ^{Each column of RT} is associated with the problem. ^{Each line of RT} is associated with a skill. ^{The value "1" of the element of RT} indicates that the skill is required, and "0" indicates that the skill is not required.
Each column of Z _{1 to} Z _N (learner skill matrix) is associated with the timing at which the user solves the problem. Each line of Z _{1 to} Z _N is associated with a skill.
Each of X _{1 to} X _N (correct / wrong vector) is a row vector, and each column is associated with the user's timing for the problem.

Of these, the result of each user solving the problem is observable. On the other hand, it is not possible to directly observe the skills possessed by each user. Moreover, since the skill estimation unit 191 does not analyze the contents of each skill, the skill required to solve the problem cannot be directly observed.
Therefore, the skill estimation unit 191 estimates the skill required to solve the problem and the skill held by each user from the result of solving the problem by each user. The learning support device 100 estimates which skill is required to solve the problem and which skill each user holds, but does not analyze what kind of content each skill has.

FIG. 5 shows a graphical model used by the skill estimation unit 191 for skill estimation. In FIG. 5, circles indicate random variables. Arrows indicate data dependencies. When determining the value of the variable at the tip of the arrow, use the value of the variable before the arrow.
In FIG. 5, the user skills Zu, k ^(t) and correct / incorrect X _u ^(t) for one user u are shown. The model also includes per-user user skills and correctness for other users.
On the other hand, v, μ _{1 to μ k} , and w _{1 to w k} are common to each user.
Problem skill R is prepared in common for each user. The problem number of the problem solved by the user u in step t is indicated by _mu ^(t). Using the issue number _m ^{u (t),} shows the problem skill problems user u solved in step t with _{R mu (t).}

Use the variables or constants described below to describe the model for skill estimation.
M: Total number of problems.
Each question is identified by assigning question numbers 1 to M to the questions. The problem number is indicated by m. m is an integer of 1 ≦ m ≦ M. The problem with problem number m is referred to as problem m.

N: Total number of users In addition, each user is identified by assigning a user number of 1 to N to the user. The user number is indicated by u. u is an integer of 1 ≦ u ≦ N. The user with the user number u is referred to as the user u.
K: Total number of skills In addition, each skill is identified by assigning a skill number of 1 to K to the skill. The skill number is indicated by k. k is an integer of 1 ≦ k ≦ K. The skill with skill number k is referred to as skill k.

m _u ^(t): user u Note variable indicating the problem number of the problems solved in step _t, ^{m u (t)} is an integer of ^{_{1 ≦ m u (t) ≦}} M. The step here is the timing when the user solves the problem. It is assumed that each user solves one problem in one step. Step t is the timing at which the user solves the t-th problem. The problem solved by the user u in step t is the problem solved by the user u in the t-th position. The timing at which the user solves the problem may be arbitrary. In particular, it is not necessary for multiple users to solve the problem at the same time. Further, since the problem selection unit 192 provides the problem according to the skill of the user, the order of solving the problem is usually different for each user.

X _u ^(t) : Random variable indicating the correctness of the answer that the user u solved the problem in step t. X _u ^(t) takes any value of 0 or 1. “X _u ^(t) = 0” indicates that the answer was incorrect. “X _u ^(t) = 1” indicates that the answer was correct.
A row vector (horizontal vector) having X _u ^{(1) to} X _u ^(t) as an element is expressed _{as X u.}
In the following, it will be referred to as correct / incorrect X _u ^(t) and correct / incorrect X _u .

Z _{u, k} ^(t) : Random variable indicating whether or not the user u holds the skill k in step t. Z _{u, k} ^(t) takes any value of 0 or 1. "Z _{u, k} ^(t) = 0" indicates that the skill is not retained. “Z _{u, k} ^(t) = 1” indicates that the skill is retained.
A column vector (vertical vector) having Z _{u, 1} ^{(t) to} Z _{u, K} ^(t) as elements is expressed _{as Z u} ^(t). Z _u ^(t) is expressed as in the equation (1).

_{Z u} ^(t) for all users and all steps is collectively referred to as Z.
Hereinafter, they are referred to as user skill Z, user skill Z _u ^(t) , and user skill Z _{u, k} ^(t) .
R _m : Random variable indicating the skill required to solve the problem m Note that R _m is represented by a K-dimensional row vector (horizontal vector). Each element of R _m takes any value of 0 and 1. However, this does not apply when all the elements are 0. When the value of the k-th element is 0, it indicates that the skill k is unnecessary. When the value of the k-th element is 1, it indicates that skill k is required.

R _{m, k} : A variable indicating whether or not skill k is required to solve the problem m. R _{m, k} indicates the k-th element of _{R m.} A matrix having R _{m and k} as elements is expressed as R. In the following, it is referred to as problem skill R, problem skill R _m , and problem skill R _{m, k} .

In Figure 5, a problem skill _{R mu (t),} as a user skill ^{_{Z u, 1 (t) ~Z}} u, arrows from each of ^{K (t)} to the correctness _X ^{u (t)} is out, errata _{X u} ^(T) depends on the problem skill R _{mu (t)} and the user skills Z _{u, 1} ^{(t) to} Z _{u, K} ^(t) . Specifically, the probability of correctness X _u ^(t) under the problem skill R _{mu (t)} and the user skill Z _u ^(t) follows the Bernoulli distribution, as shown in equation (2). do.

Here, "~" in the equation (2) indicates that it follows a predetermined distribution. Bernoulli distribution is shown by Bernoulli. Specifically, on the right side of the equation (2), _{the value of correct / incorrect X u} ^(t) becomes "1" with a probability s (0 ≤ s ≤ 1) and "0" with a probability 1-s. Is shown.
The s in the equation (2) is expressed as in the equation (3).

Here, exp (x) indicates e to the x-th power. e indicates the number of Napiers. Both a and b are constant parameters. Both the value of a and the value of b are predetermined.
Equation (3) is obtained by substituting equation (4) into the logistic function.

The logistic function f (x) is expressed by Eq. (5).

FIG. 6 shows the value of the logistic function. The value of the logistic function f (x) is shown as shown in the graph of FIG. The parameter a in the equation (3) is an adjustment parameter for the slope of the graph. The larger the value of a, the steeper the slope. Parameter b is an adjustment parameter for the horizontal position of the graph. The graph is translated by the value of b in the positive direction of the x-axis.

_{The value of the user skill Z u, k} ^(t) when “t ≧ 2” depends on the skill held by the user in the previous step. Skills held in one step shall be held in the next step. That is, in the case of "Z _{u, k} ^(t-1) = 1", it is set as "Z _{u, k} ^(t) = 1".
If the skill k is not held in step t-1 (Z _{u, k} ^(t-1) = 0), _{the value of the user skill Z u, k} ^(t) is the problem solved in step t-1. It depends on whether or not skill k is required.

If the problem solved in step t-1 requires skill k (R _{mu (t-1), k} = 1), it is considered possible to acquire skill k by solving the problem. , Determine the value to 0 or 1 according to the Bernoulli distribution. In this case, it is specified as in the formula (6).

mu _k is a random variable indicating the acquisition easiness of each skill is as shown in equation (7).

Here, Beta shows a beta distribution. ξ _k and ζ _k are parameters of the beta distribution, both of which are preset for each skill.
If the problem solved in step t-1 does not require skill k (R _{mu (t-1), k} = 0), it is considered that skill k cannot be acquired by solving the problem. _{u, k} ^(t) = 0 ”.
From the above, when “t ≧ 2”, the values of Z _{u and k} ^(t) are defined as in the equation (8).

On the other hand, in the case of "t = 1", the values of Z _{u and k} ⁽¹⁾ depend on whether or not the user has possessed the skill in advance. This case is defined as in equation (9).

w _k is a random variable indicating the high possibility that the user holds the skill k in advance, and is expressed by the equation (10).

γ _k and η _k are parameters of the beta distribution, both of which are preset for each skill.
R _m shall follow a multinomial distribution and shall be defined as in equation (11).

Multi shows a multinomial distribution. v is a parameter of the multinomial distribution and is expressed as in Eq. (12).

Dir shows a Dirichlet distribution. “Α = (α ₁ , ···, α _L )” and “L = 2 ^K -1”. 2 ^K -1 is the number of all combinations of 0 and 1 for K skills, excluding the case of all 0s (when there is no required skill). α = (α ₁ , ..., α _L ) are all parameters of the Dirichlet distribution and are preset.

In the following, v, μ _{1 to μ K} , and w _{1 to w K} are referred to as θ or parameter θ.
Using this model, the problem skill R, the user skill Z, and the parameter θ that maximize the posterior probability are obtained. Assuming that the problem skill R, the user skill Z, and the parameter θ are the problem skill Rmax, the user skill Zmax, and the parameter θmax, these are expressed by the equation (13).

argmax means an argument value (Argument Of Maximum) that gives a maximum value. The right side of the equation (13) shows the values of the problem skill R, the user skill Z, and the parameter θ that maximize the posterior probability P (R, Z, θ | X).
Here, equation (13) is calculated by Gibbs sampling. When Gibbs sampling is performed from the posterior distribution of Eq. (13), Gibbs sampling is performed for each of P (R | Z, θ, X), P (Z | R, θ, X), and P (θ | R, Z, X). Is the simplest way to do this. However, with this method, the solution of equation (13) cannot be obtained in a realistic time. This is a lot of different R'and R'' at P (R, Z | θ, X), where P (Z | R', θ, X) x P (R''| Z, θ, X) Because it is so small, R is hardly updated by Gibbs sampling. Therefore, instead of sampling R and Z based on P (R, Z | θ, X), sampling is performed from the distribution P'(R) of the equation (14) in which R having the same maximum probability is used. conduct.

Here, Z _p is a normalization constant.
Z'(R) is expressed as in equation (15).

That is, Z'(R) is the user skill Z that maximizes the probability when the problem skill is R in the distribution of R and Z in the state where X and θ are given.
By using equation (14), the probability that one R is sampled by another R'is not very small as in simple Gibbs sampling, and the solution of equation (13) can be solved in a realistic time. Can be sought.
Here, consider P'(R _m | X, R ^{\ m} , θ). R ^{\ m} is _{the remainder of R minus R m} (line m). For P'(R _m | X, R ^{\ m} , θ), the relationship of Eq. (16) can be obtained.

_{The “max Z} P (Z, X | R, θ)” in parentheses in equation (16) can be efficiently calculated by the Viterbi algorithm.
Using equation (16), _{a value can be obtained for each of the cases that R m} can take (a binary vector having an element of skill number K, other than [0, ..., 0]). Normalizing this value gives the parameters of the multinomial distribution, which are the probabilities in each case. _{The value of R m} can be determined according to this multinomial distribution.
For each row of R, the above probability distribution is obtained, sampling is performed based on the obtained probability distribution, and the obtained value is put in the relevant row of R.
After sampling all the rows of _{R, Z'is calculated using "max Z} P (Z, X | R, θ)" in parentheses in equation (16).

For θ, consider equation (17).

For Z in equation (17), the user skill Z obtained by _{max Z in equation (16) is used.}
From equation (17), equation (18) can be obtained for v.

Here, nr _l indicates the number of occurrences of the line is a Binary (l) of the rows in question skill R. Binary (l) shows the binary evolution of the decimal number l. For all patterns that can be taken by the R row, the number of appearances in R is counted, and the probability distribution is set according to the obtained number of appearances.
For w, equation (19) can be obtained.

Here, nz _k1 indicates the number of occurrences of 1 in the vector Z _{:, k} ^(1). ":" Indicates a wild card. Therefore, Z _{:, k} ⁽¹⁾ indicates the presence or absence of skill k in step 1 for any user. nz _k0 indicates the number of occurrences of 0 in the vector Z _{:, k} ^(1). The number of users who held the skill k and the number of users who did not hold the skill k in step 1 are reflected in the probability that the user held the skill k in advance.
For μ, equation (20) can be obtained.

Here, nz _{k101 is defined as “R mu, k (t)} = 1”, “Z _{u, k} ^(t) = 0”, “Z _u ” for any u, t in the matrices Z _{1 to} Z _{N, R. , K} ^{(t + 1)} = 1 ”indicates the number of occurrences of the triad. That is, nz _k101 indicates the number of times the user has acquired the skill k when solving a problem that requires the skill k.

nz _{k100 is defined as “R mu, k (t)} = 1”, “Z _{u, k} ^(t) = 0”, “Z _{u, k} ” for any u, t in the matrices Z _{1 to} Z _{N, R.} ^{(T + 1)} = indicates the number of occurrences of the _triad of 0. That is, nz k100 indicates the number of times that the user who solved the problem requiring skill k did not acquire skill k. This is reflected in the ease of acquiring skill k by solving problems that require k.
The posterior probabilities are calculated based on equation (21).

FIG. 7 is a flowchart showing a procedure of processing performed by the skill estimation unit 191.
<Step S101>
The skill estimation unit 191 sets initial values for the model parameters α, ∀k (γ _k , η _k , ξ _k , ζ _k ), a, b, and K. Probability distributions are set by setting values for these model parameters. These initial values may be set in advance manually (administrator of the learning support device 100). After step S101, the process proceeds to step S102.

<Step S102>
The skill estimation unit 191 accepts the input of correct / incorrect X. Specifically, the skill estimation unit 191 reads the correct / incorrect data generated by the answer processing unit 193 from the server-side storage unit 180. After step S102, the process proceeds to step S103.
<Step S103>
The skill estimation unit 191 randomly sets the problem skill R and the parameter θ according to the probability distribution. The skill estimation unit 191 also sets the set R and θ to Rmax and θmax, respectively. After step S103, the process proceeds to step S104.

<Step S104>
The skill estimation unit 191 randomly sets the user skill Z according to the probability distribution. The skill estimation unit 191 also sets the set Z to Zmax. After step S104, the process proceeds to step S105.
<Step S105>
The skill estimation unit 191 sets an initial value −∞ in max_postier. max_postier indicates the maximum posterior probability ever obtained. After step S105, the process proceeds to step S111.

<Step S111>
The skill estimation unit 191 starts the loop L11. In loop L11, the process is repeated until a predetermined maximum number of loops is reached. After step S111, processing proceeds to step S112.
<Step S112>
The skill estimation unit 191 _{samples the problem skill R m} and updates the problem skill R. Specifically, the skill estimation unit 191 determines the distribution of the problem skill Rm for each problem (that is, for each m) based on the equation (16), and determines the value of the problem skill Rm according to the obtained distribution. .. The skill estimation unit 191 inputs the determined value of the problem skill Rm into the problem skill R. After updating the problem skill R, the skill estimation unit 191 updates the user skill Z based on the equation (16). After step S112, the process proceeds to step S113.

<Step S113>
The skill estimation unit 191 samples the parameter θ. Specifically, the skill estimation unit 191 determines the distribution of each value of _{v, w 1 to w K} , and μ _{1 to μ k} based on the equations (18) to (20), and the obtained distribution. Determine each value according to. The skill estimation unit 191 inputs the obtained values into v, w _{1 to w K} , and μ _{1 to μ k, respectively.} After step S113, the process proceeds to step S114.

<Step S114>
The skill estimation unit 191 calculates the posterior probability based on the equation (21). After step S114, the process proceeds to step S115.
<Step S115>
The skill estimation unit 191 determines whether or not the obtained posterior probability is larger than max_posterior. If it is determined to be large, the process proceeds to step S116. If it is determined that the value is not large, the process proceeds to step S117.

<Step S116>
The skill estimation unit 191 updates max_postier, Rmax, Zmax, and θmax. Specifically, the skill estimation unit 191 inputs the posterior probability (this time) calculated in step S114 to max_postier. Further, the skill estimation unit 191 inputs R obtained in step S112 to Rmax, Z obtained in step S112 is input to Zmax, and θ obtained in step S113 is input to θmax. After step S116, the process proceeds to step S117.

<Step S117>
The skill estimation unit 191 performs termination processing of the loop L11. Specifically, it is determined whether or not the number of repetitions of the loop L11 has reached the maximum number of loops. When the skill estimation unit 191 determines that the number of repetitions of loop L11 has not reached the maximum number of loops, the skill estimation unit 191 returns to step S112 and repeats the processing of loop L11. On the other hand, when the skill estimation unit 191 determines that the number of repetitions of the loop L11 has reached the maximum number of loops, the skill estimation unit 191 ends the loop L11 and proceeds to step S121.
<Step S121>
The skill estimation unit 191 outputs the obtained Rmax, Zmax, and θmax as the processing result. After step S121, the process of FIG. 7 ends.

As described above, the answer processing unit 193 acquires correct / incorrect data indicating the correctness of the answer in which the learner has solved the problem as binary data (data taking two values). The skill estimation unit 191 uses a model represented by a binary random variable (a random variable that takes two values) indicating whether or not the learner holds the skill for each skill required to solve the problem. By searching for a solution that maximizes posterior probabilities based on correct / incorrect data, the skills required to solve the problem and the skills possessed by the learner are estimated. As a result, in the learning support system 1, a human can relatively easily interpret the contents of each skill based on the estimation result of the problem skill R.

In addition, the skill estimation unit 191 searches for a solution using a model that represents the history of skills held by the learner with random variables. It is expected that the skill will be improved by the user solving the problem. The skill estimation unit 191 can estimate the skill by simulating the improvement of the skill, and in this respect, the skill can be estimated with higher accuracy.

Further, the skill estimation unit 191 is based on a function that obtains the value of a random variable indicating the skill required for solving the problem and a random variable indicating the skill held by the learner with the parameters of the model as arguments. Performs a solution search in which the random variable indicating the skill held by is excluded from the solution search space. As a result, it is possible to prevent the probability that another problem skill R'is sampled from one problem skill R becomes very small, so that a solution can be searched for in a realistic time.

The skill estimation unit 191 may have a range of steps in which the values of _{Zu and k change from 0 to 1.} There may be a plurality of step candidates in which the values of Z _{u and k change from 0 to 1.} Therefore, _{a candidate for a step in which the value of Zu, k} changes from 0 to 1 may be indicated, such as _{Zu, k} = [4,6].

Further, the skill estimation unit 191 may automatically estimate the value of K. For example, the correct / incorrect data is divided into training data and test data. Then, the skill estimation unit 191 estimates the skill for various K values using the test data, and adopts the K value having the best estimation accuracy.

Specifically, the skill estimation unit 191 estimates each K value up to "K = 2, ..., K_max" and acquires Rmax and θmax for each. K_max is an integer constant (K_max ≧ 3) that is predetermined as the upper limit value of K. Then, the skill estimation unit 191 predicts the part of X _u ^{(t> T)} _{by sampling the correct / incorrect X u of the test data.} X _u is a submatrix (vector) of correctness X, and indicates the correctness of the user u solving the problem. X _u ^{(t> T)} is a part of X _u where t> T. T is a predetermined integer constant (T ≧ 2). The skill estimation unit 191 adopts the value of K, which has the best prediction accuracy. Further, instead of sampling θ, the expected value of θ may be used.

As an application example of the embodiment of the present invention, a problem according to the skill of the user may be provided. For example, if the user's answer to the problem is incorrect, it is determined whether or not the user has all the skills necessary to solve the problem. If there is a skill that the user does not have, provide a problem that requires that skill. On the other hand, if all the problems necessary to solve the problem are held, the cause may be careless mistake or unfamiliarity with the problem, so the problem of the same skill is further provided.

Also, even if the user's answer to the problem is correct, it is determined whether or not the user has all the skills necessary to solve the problem. If there is a skill that the user does not have, it is possible to provide a problem that requires the skill and determine whether it was solved by chance or whether the skill has already been acquired. On the other hand, if you have all the skills needed to solve the problem, you provide a problem that requires other skills.

In addition, as an application example of the embodiment of the present invention, the systematization of problems may be assisted. Problems are often not systematized in the learning of empirical knowledge possessed by specialists. In such a case, by using the estimation of the problem skill according to the embodiment of the present invention, it is possible to estimate which problem and which problem have the necessary skills in common. Problems that share the same required skills may be grouped together to systematize the problems.

Next, the configuration of one embodiment of the present invention will be described with reference to FIGS. 8 and 9. FIG. 8 shows an example of the configuration of the skill estimation device according to one embodiment of the present invention. The skill estimation device 10 shown in FIG. 8 includes a correct / incorrect data acquisition unit 11 and a skill estimation unit 12.
With such a configuration, the correct / incorrect data acquisition unit 11 acquires correct / incorrect data indicating the correctness of the answer in which the learner has solved the problem as binary data. The skill estimation unit 12 uses a model in which the skills required to solve the problem and the skills held by the learner are represented by binary probability variables indicating the presence or absence of the skills for each skill, and correct / incorrect data. Search for a solution that maximizes the posterior probability based on, and estimate the skills required to solve the problem and the skills possessed by the learner. The model consists of a model represented by a binary random variable indicating whether or not the skill is necessary to solve a specific problem for each skill required to solve the problem, and a model for each skill required to solve the problem. , A model represented by a binary random variable indicating whether or not the skill is held by the learner may be included.
As a result, in the skill estimation device 10, a human can relatively easily interpret the content of each skill based on the estimation result of the problem skill.

FIG. 9 shows an example of the configuration of the learning support device according to the embodiment of the present invention. The learning support device 20 shown in FIG. 9 includes a correct / incorrect data acquisition unit 21, a skill estimation unit 22, and a problem selection unit 13. With this configuration, the correct / incorrect data acquisition unit 21 acquires correct / incorrect data indicating the correctness of the answer that the learner has solved the problem as binary data. The skill estimation unit 22 uses a model in which the skills required to solve the problem and the skills held by the learner are represented by binary probability variables indicating the presence or absence of the skills for each skill, and correct / incorrect data. By searching for a solution that maximizes the posterior probability based on, the skills required to solve the problem and the skills possessed by the learner are estimated. The question selection unit 23 selects a question to be presented to the learner based on the estimation result of the skill estimation unit 22.

As a result, in the learning support device 20, a human can relatively easily interpret the contents of each skill based on the estimation result of the problem skill. Further, the learning support device 20 can provide a problem according to the skill of the user, and can provide an appropriate problem to the user in this respect.

A program for realizing all or a part of the functions of the server-side control unit 190 is recorded on a computer-readable recording medium, and the program recorded on the recording medium is read by the computer system and executed to execute each unit. May be processed. The "computer system" here includes hardware such as an OS and peripheral devices.
The "computer system" includes a homepage providing environment (or display environment) if a WWW system is used.
The "computer-readable recording medium" refers to a storage device such as a flexible disk, a magneto-optical disk, a portable medium such as a ROM or a CD-ROM, or a hard disk built in a computer system. The above-mentioned program may be for realizing a part of the above-mentioned functions, and may be further realized by combining the above-mentioned functions with a program already recorded in the computer system.

Although the embodiments of the present invention have been described in detail with reference to the drawings, the specific configuration is not limited to this embodiment, and includes designs and the like within a range that does not deviate from the gist of the present invention.

This application claims priority on the basis of Japanese Patent Application No. 2017-1997, filed on October 13, 2017, and incorporates all of its disclosures herein.

The present invention may be applied to skill estimation devices, learning support devices, skill estimation methods and programs.

1 Learning support system 10 Skill estimation device 11, 21 Correct / incorrect data acquisition unit 12, 22, 191 Skill estimation unit 20, 100 Learning support device 23, 192 Problem selection unit 110 Server side communication unit 180 Server side storage unit 190 Server side control unit 193 Answer processing unit 200 Terminal device 210 Terminal side communication unit 220 Display unit 230 Operation input unit 280 Terminal side storage unit 290 Terminal side control unit 900 Communication network

Claims (7)

The correct / incorrect data acquisition unit that acquires correct / incorrect data that shows the correctness of the answer that the learner solved the problem with binary data,
Using a model that expresses the skills required to solve the problem and the skills held by the learner with a binary probability variable indicating the presence or absence of the skill for each skill, the posterior probability based on the correct / incorrect data is calculated. A skill estimation unit that estimates the skills required to solve the problem and the skills held by the learner by searching for the solution to be maximized.
Skill estimation device equipped with. The skill estimation unit searches for the solution using a model that represents the history of skills held by the learner with the random variables.
The skill estimation device according to claim 1. The skill estimation unit is held by the learner based on a function that obtains the value of a random variable indicating the skill required to solve the problem and a random variable indicating the skill held by the learner with the parameters of the model as arguments. Search for the solution in which the random variable indicating the skill is excluded from the solution search space.
The skill estimation device according to claim 1 or 2. The model is a model represented by a binary random variable indicating whether or not the skill is necessary to solve a specific problem for each skill required to solve the problem, and each skill required to solve the problem. The skill estimation device according to any one of claims 1 to 3, further comprising a model represented by a binary random variable indicating whether or not the skill is held by the learner. The correct / incorrect data acquisition unit that acquires correct / incorrect data that shows the correctness of the answer that the learner solved the problem with binary data,
Using a model that expresses the skills required to solve the problem and the skills held by the learner with a binary probability variable indicating the presence or absence of the skill for each skill, the posterior probability based on the correct / incorrect data is calculated. A skill estimation unit that estimates the skills required to solve the problem and the skills held by the learner by searching for the solution to be maximized.
A problem selection unit that selects a problem to be presented to the learner based on the estimation result of the skill estimation unit,
A learning support device equipped with. The device acquires correct / incorrect data that indicates the correctness of the answer that the learner solved the problem with binary data.
Using a model in which the skill required for the device to solve the problem and the skill held by the learner are represented by a binary probability variable indicating the presence or absence of the skill for each skill, the correct / incorrect data is obtained. By searching for a solution that maximizes the posterior probability based on, the skills required to solve the problem and the skills possessed by the learner can be estimated.
Skill estimation methods including. On the computer
Acquiring correct / incorrect data that shows the correctness of the answer that the learner solved the problem with binary data,
Using a model that expresses the skills required to solve the problem and the skills held by the learner with binary probability variables indicating the presence or absence of the skills for each skill, the posterior probability based on the correctness data is calculated. By searching for the solution to maximize, the skills required to solve the problem and the skills possessed by the learner can be estimated.
A program to execute.

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