CN108229683A - A kind of information processing method and device based on IRT - Google Patents
A kind of information processing method and device based on IRT Download PDFInfo
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Abstract
The embodiment of the invention discloses a kind of information processing methods and device based on IRT.This method includes：Obtain answering information sample, with the learning ability in IRT models, topic discrimination and difficulty build Bayesian network model for parameter to be estimated, wherein, parameter to be estimated meets the default prior distribution for including super ginseng, the corresponding variation distribution function of object function is determined using variation estimating method, and with the minimum principle of the degree of closeness of object function and variation distribution function, super ginseng is estimated based on Bayesian network model and answering information sample, obtain the parameter value of super ginseng, variation distribution function is updated according to the parameter value of the super ginseng of gained, it is treated based on updated variation distribution function and estimates parameter and sampled, it obtains treating the estimation for estimating parameter.The embodiment of the present invention, which can reduce, to be treated the prior estimate for estimating parameter and excessively cures influence to estimated result, effectively promotes accuracy of estimation.
Description
Technical field
The present embodiments relate to technical field of information processing more particularly to a kind of information processing method based on IRT and
Device.
Background technology
As computer technology is in the extensive use of education sector, adaptive testing and adaptive learning etc. increasingly obtain people
Concern.Adaptive and learning system is intended to provide a kind of students'autonomous study platform, and the problem solving information of student is received
Record, and pass through technological means and the topic ability of doing of student is assessed in real time, it analyzes and is most suitable for students institute subject purpose
Path is practised, and integration update at the same time is carried out to exam pool data.Adaptive and learning system have reasonably optimizing student learn schedule,
The learning initiative of mobilizing students, assisted teacher, which improve efficiency of teaching and solve educational resource, distributes unequal function.
The core of adaptive learning is how effectively to assess the problem solving information of student by computer and arrange corresponding
Learning path.The research of evaluation problem is tested about student, the classical test reason of the twentieth century proposition thirties can be traced back to
By (Classical test Theory, CTT), which regards Students ' Problem-solving result as student ability and adds random noise
Certain linear fit has huge contribution to the theory and practice of psychology and educational measurement.However, as time goes on,
Student's knowledge content is gradually abundant and diversified, and CCT theories are to the standardisation requirements of test question group and randomization skill
Art is difficult to the application and development that the factors such as repeatability implementation limit CCT theories, which has been unable to meet increasingly diversified
Teaching method and daily learning evaluation.Therefore, new theory is shown one's talent, such as Bayes's knowledge tracking (Bayesian
Knowledge tracing, BKT) model and item response theory (Item response theory, IRT) etc..
IRT models due to its ease for operation and it is flexibly embedded the features such as, become current mainstream adaptive learning platform (such as
The companies such as Knewton) used by assessment Students ' Problem-solving information analysis engine.IRT is learned using nonlinear function statement student
Relationship between habit ability and test topic.Relative to classical Error Set, item response theory can be handled preferably centainly
The data set of scale, and provide the correspondence between student ability and solved topic.In application IRT models, generally need
Parameter in model is estimated, in existing estimation scheme, such as Markov chain Monte-Carlo (Markov Chain
Monte Carlo, MCMC) method, the prior information of answer person is often what is be determined in advance, such as usually assume that all answers
The ability distribution of person is to meet normal distribution N (0,1), this just brings the curing of priori to the estimation of model, influences to estimate
Accuracy, reduce Evaluated effect.
Invention content
The purpose of the embodiment of the present invention is to provide a kind of information processing method and device based on IRT, existing to solve
Topic information estimation scheme based on IRT estimate because treating parameter prior estimate excessively cure caused by estimated result accuracy
The problem of low.
On the one hand, an embodiment of the present invention provides a kind of information processing method based on IRT, including：
Obtain answering information sample of the answer person of preset quantity about target exam pool；
It is built by parameter to be estimated of the difficulty of the learning ability of the answer person in IRT models, the discrimination of topic and topic
Bayesian network model, wherein, the parameter to be estimated meets the default prior distribution for including super ginseng；
The corresponding variation distribution function of object function is determined using variation estimating method, and with the object function and described
The minimum principle of degree of closeness of variation distribution function, based on the Bayesian network model and the answering information sample to institute
It states super ginseng to be estimated, obtains the parameter value of the super ginseng, wherein, the object function is based on the answering information sample
Posterior estimator function about the parameter to be estimated；
The variation distribution function is updated according to the parameter value of the super ginseng of gained；
The parameter to be estimated is sampled based on updated variation distribution function, obtains estimating the parameter to be estimated
Meter.
On the other hand, an embodiment of the present invention provides a kind of information processing unit based on IRT, including：
Answer sample acquisition module, for obtaining answering information sample of the answer person about target exam pool of preset quantity；
Bayesian network model builds module, for the discrimination of the learning ability of the answer person in IRT models, topic
And the difficulty of topic builds Bayesian network model for parameter to be estimated, wherein, the parameter to be estimated meets comprising the default of super ginseng
Prior distribution；
Super ginseng estimation module, for determining the corresponding variation distribution function of object function using variation estimating method, and with
The minimum principle of degree of closeness of the object function and the variation distribution function, based on the Bayesian network model and institute
State answering information sample to it is described it is super ginseng estimate, obtain the parameter value of the super ginseng, wherein, the object function be based on
The Posterior estimator function about the parameter to be estimated of the answering information sample；
Function update module is updated the variation distribution function for the parameter value of the super ginseng according to gained；
Parameter estimation module to be estimated samples the parameter to be estimated for being based on updated variation distribution function,
Obtain the estimation to the parameter to be estimated.
The information processing scheme based on IRT provided in the embodiment of the present invention, with the study energy of the answer person in IRT models
The difficulty of power, the discrimination of topic and topic builds Bayesian network model for parameter to be estimated, wherein, the parameter difference to be estimated
Meet fixed prior distribution in existing estimation scheme, but meet the default prior distribution for including super ginseng, first use and become
Point estimating method obtains the estimated value of super ginseng based on Bayesian network model and answering information sample, then treats and estimate parameter and estimated
Meter.By using above-mentioned technical proposal, it can reduce and treat the prior estimate for estimating parameter and excessively cure influence to estimated result, have
Effect promotes accuracy of estimation.
Description of the drawings
Fig. 1 is the flow diagram of a kind of information processing method based on IRT that the embodiment of the present invention one provides；
Fig. 2 a are a kind of existing Bayesian network model schematic diagram based on IRT models；
Fig. 2 b are the Bayesian network model schematic diagram based on IRT models that the embodiment of the present invention one provides；
Fig. 3 is a kind of flow diagram of the information processing method based on IRT provided by Embodiment 2 of the present invention；
Fig. 4 is the structure diagram of a kind of information processing unit based on IRT that the embodiment of the present invention three provides.
Specific embodiment
Technical solution to further illustrate the present invention below with reference to the accompanying drawings and specific embodiments.It is appreciated that
It is that specific embodiment described herein is used only for explaining the present invention rather than limitation of the invention.It further needs exist for illustrating
, part related to the present invention rather than entire infrastructure are illustrated only for ease of description, in attached drawing.
It should be mentioned that some exemplary embodiments are described as before exemplary embodiment is discussed in greater detail
The processing described as flow chart or method.Although each step is described as the processing of sequence, many of which by flow chart
Step can be implemented concurrently, concomitantly or simultaneously.In addition, the sequence of each step can be rearranged.When its operation
The processing can be terminated during completion, it is also possible to have the additional step being not included in attached drawing.The processing can be with
Corresponding to method, function, regulation, subroutine, subprogram etc..
To facilitate understanding of the present embodiment of the invention concrete scheme below first simply introduces IRT.Item Response Pattern
Theoretical IRT is also known as that latent trait theory or item characteristic curve are theoretical, it is a kind of estimation to answer person's ability, and by examinee
Certain speciality of certain reaction probability (such as answer questions probability or answer wrong probability) and the examination question to single test item (topic) is (such as
Topic discrimination and item difficulty etc.) it connects.Indicatrix contains the examination question parameter that the feature of examination question is described
The latent trait or ability parameter being described with the feature to answer person.IRT models most widely used at present are with Berne Bao
The logistic model that nurse proposes is the model of representative, and according to the difference of number of parameters, characteristic function can be divided into one-parameter IRT moulds
Type, two-parameter IRT models and three parameter IRT models, the embodiment of the present invention will be by taking most representative two-parameter IRT models as an example
Carry out subsequent explanation, but what deserves to be explained is, the scheme of the embodiment of the present invention is equally applicable to one-parameter IRT models and three ginsengs
Number IRT models, those skilled in the art can not pay creation by reading following related descriptions about two-parameter IRT models
Property labour in the case of obtain the concrete scheme for being applied to one-parameter IRT models and three parameter IRT models, therefore the present invention is implemented
It is repeated no more in example.
Embodiment one
The flow diagram of a kind of information processing method based on IRT that Fig. 1 is provided for the embodiment of the present invention one, this method
It can be performed by the information processing unit based on IRT, wherein the device can be generally integrated in by software and or hardware realization
In terminal in adaptive and learning system, which can be the terminals such as PC or server or tablet computer
Or the mobile terminals such as smart mobile phone, the embodiment of the present invention are not especially limited.As shown in Figure 1, this method includes：
Step 110 obtains answering information sample of the answer person of preset quantity about target exam pool.
In the present embodiment, target exam pool and the preset quantity of answer person can be chosen according to actual demand.For example, it can obtain
Take answering information sample of the student of a class about grade English subject exam pool in junior middle school；A cities 12-15 Sui can also be obtained
Answering information sample of the student of age bracket about olympic math exam pool；Certainly, answer person is not limited to student, can also answer
For in other field, such as B areas driving license can be obtained and be admitted to answering information sample of the personnel about subject one.Illustratively,
Answering information sample may include answer quantity, answer topic and answer situation (such as do pair or do wrong) information.
Step 120, using the difficulty of the learning ability of the answer person in IRT models, the discrimination of topic and topic to wait to estimate
Parameter builds Bayesian network model.
Wherein, the parameter to be estimated meets the default prior distribution for including super ginseng.
General based in the Bayesian network model of IRT models, the prior information of student is often determined in advance
, such as it is to meet normal distribution N (0,1) to usually assume that the ability of all students is distributed, this just brings to the estimation of model
The curing of priori, even if the parameter of normal distribution can be selected, but evolutionary process entirely to estimate that flow will be again
Perform the execution efficiency for once, seriously affecting estimation model.Therefore, the embodiment of the present invention is by introducing super ginseng (hyper-
Parameter) so that parameter to be estimated meets certain a priori assumption family of distributions, and parameter error estimation is brought so as to weaken
Analytical error.
Preferably, the learning ability of the answer person and the difficulty of the topic meet mean value and/or variance is super ginseng
Normal distribution, the logarithm normal distribution that the discrimination of the topic meets mean value and/or variance is super ginseng.This variance or very
The normal distribution all undetermined to mean value is a series of normal distyribution functions, can be referred to as normal distyribution function race.
In embodiments of the present invention, by taking classical two-parameter IRT models as an example, if θ (theta) is the study energy of answer person
Power, α (discriminination), β (difficulty) are the discrimination of topic and difficulty (coefficient) respectively, then topic is answered
Topic person do to probability be：
It should be noted that inside one-parameter IRT models, generally α is replaced with fixed D (D values 1.7).
In the embodiment of the present invention, it is assumed that it is as follows that α, β, θ meet super ginseng distribution respectively：
Wherein, τθBeing uniformly distributed in (0,100) section, τ can be metαBeing uniformly distributed in (0,100) section can be met,
τβBeing uniformly distributed in (0,100) section can be met.It is understood that above-mentioned 100 be a constant that can freely set,
Can also be other values so that the variance that any posteriority for meeting experiential fact surpasses ginseng does not all exceed this range.
Fig. 2 a are a kind of existing Bayesian network model based on IRT models, and first layer represents parameter θ to be estimated respectively,
α, β, the second layer represent sigmoid functions, and the probability to topic is done in third layer expression；Fig. 2 b are what the embodiment of the present invention one provided
Based on the Bayesian network model of IRT models, first layer represents parameter θ to be estimated, the corresponding super ginseng τ of α, β respectivelyθ(tau_
theta)、τα(tau_disc)、τβ(tau_diff), the second layer represents parameter θ to be estimated, α, β respectively, and third layer represents sigmoid
Function, the 4th layer represents to do the probability to topic.Comparison diagram 2a and Fig. 2 b can see, Bayes provided in an embodiment of the present invention
In network model, α, β, θ meet super ginseng distribution, i.e. τ respectivelyαFor the parameter of parameter alpha, τβFor the parameter of parameter beta, τθFor parameter θ
Parameter.
Step 130 determines the corresponding variation distribution function of object function using variation estimating method, and with object function and
The minimum principle of degree of closeness of variation distribution function, based on Bayesian network model and answering information sample to it is described it is super join into
Row estimation, obtains the parameter value of super ginseng.
Wherein, the object function is the Posterior estimator letter about the parameter to be estimated based on the answering information sample
Number.
It is general when being estimated based on Bayesian network model, MCMC methodology sampling can be used and carried out about a priori assumption
Integration summation, but when Bayesian network model is more complicated (such as number of student or topic quantity are more), MCMC samplers
Efficiency can very slowly, influence the execution efficiency of model.It, being capable of expanded mode well using variation estimating method in the present embodiment
The complexity of type improves sample rate, and then the execution efficiency of lift scheme.
Specifically, setting Z as parameter group to be estimated, Z=α, β, θ, α is the discrimination of topic, and β is the difficulty of topic, and θ is answers
The learning ability of topic person.The situation that the topic included in answering information sample done pair or done wrong is represented with X.If p (Z | X) it is mesh
Scalar functions, q (Z) they are the corresponding variation distribution functions of p (Z | X), wherein, q (Z)=p (α) p (β) p (θ) namely q (Z) is meet
Implicit super ginseng τα、τβAnd τθPrior density function undetermined, can obtain：
p(Z|X)≈q(Z)
With the minimum principle of the degree of closeness of object function and variation distribution function, i.e., target is corresponding to find p (Z | X)
Target variation distribution function q*(Z) (Z | X) and q (Z) closest to equal, therefore, can obtain q so that p*(Z) it is to meet to make following formula
The distribution of value minimum：
Above formula is the definition about KL divergences (Kullback-Leibler divergence).
Due to
And the true distribution p (X) of X is fixed, so the above problem can be changed into through variation lower bound (Evidence
Lower Bound, ELBO) find q*(Z) meet the maximization of following formula：
And
Therefore, optimization problem can be converted into and finds the corresponding target variation distribution function q of p (Z | X)*(Z) so that above formula
It is maximized.
P (X | Z) it is the expression formula based on IRT models：
Since q (Z) is about super ginseng τα、τβAnd τθFunction, so L (q) be also about super ginseng τα、τβAnd τθFunction,
L (q) is maximized so super ginseng meets, also the optimization problem of L (q) is converted into about τα、τβAnd τθUndetermined coefficient ask
Topic, and then realize and super ginseng is estimated and obtains the parameter value of super ginseng.
More specifically, met respectively with α, β, θ
And τα,τβ,τθAll for satisfaction (0,100) equally distributed Bayesian network.
∫q(Z)lnp(X|Z)dZ
=∫ qα(α)qβ(β)qθ(θ)[lnp(X,Z)-lnq(Z)]dZ
Now by taking α as an example, illustrate the Posterior distrbutionp for making above formula optimalFollow the example of, remember Z-αFor other than α
Other parameter (β, θ), then：
Wherein C1,C2For a certain constant.By KL divergences property it is found that above formula is made to take extreme valueIt should meet：
Wherein
P (X, Z)=p (X | Z) p (α | τα)p(β|τβ)p(θ|τθ)
P (X | Z) it is the expression formula based on IRT models, remaining is distributed as the prior distribution assumed before.It will be about qZ-α
(Z-α) optimal solutionSubstitution formula (1) and remaining parameter are similar to can be calculated following equation groups：
Above-mentioned equation group is practical only comprising super ginseng τα,τβ,τθ.Specifically, by taking (2.1) as an example
Notice that result here causesNo longer it is the density function of normal distribution, becauseInThis is not linear about α.This is because our a priori assumption normal distribution race is not
Conjugate prior function (conjugate prior) about p (X | Z).Therefore we need to carry out conjugation amendment to p (X | Z),
It is general to there is Laplce to infer that two methods are corrected in amendment and the deduction of delta methods.Obtain the amendment distribution about p (X | Z)So that：
It similarly can approximate evaluation
About above two modification method, those skilled in the art can refer to the related content in relevant document, herein
It repeats no more.The document that can refer to is such as《Variational Inference in Nonconjugate Models》, Journal
Of Machine Learning Research (2013), Chong Wang.
Step 140 is updated variation distribution function according to the parameter value of the super ginseng of gained.
In this step, obtained τ will be estimatedα、τβAnd τθIn generation, is returned in q (Z)=p (α) p (β) p (θ), so as to be carried out to q (Z)
Update, updated q (Z) is target variation distribution function q*(Z)。
Step 150 is treated based on updated variation distribution function and estimates parameter and sampled, and obtains treating and estimates estimating for parameter
Meter.
In this step, treat to estimate parameter and sampled obtain treating based on updated q (Z) and estimate parameter alpha, β, θ's
Estimation.The embodiment of the present invention is not construed as limiting specific sample mode.Preferably, updated variation is based on using MCMC methodology
Distribution function samples the parameter to be estimated.Wherein, the common technology being related to has Metropolis-Hastings
(M-H) algorithm and No-U-Turn Sampler (NUTS) algorithm etc..
The information processing method based on IRT that the embodiment of the present invention one provides, with the study energy of the answer person in IRT models
The difficulty of power, the discrimination of topic and topic builds Bayesian network model for parameter to be estimated, wherein, the parameter difference to be estimated
Meet fixed prior distribution in existing estimation scheme, but meet the default prior distribution for including super ginseng, first use and become
Point estimating method obtains the estimated value of super ginseng based on Bayesian network model and answering information sample, then treats and estimate parameter and estimated
Meter.By using above-mentioned technical proposal, it can reduce and treat the prior estimate for estimating parameter and excessively cure influence to estimated result, have
Effect promotes accuracy of estimation.
Embodiment two
Fig. 3 be a kind of flow diagram of the information processing method based on IRT provided by Embodiment 2 of the present invention, this implementation
Example is optimized based on above-described embodiment, in the present embodiment, is estimated after parameter estimated treating, and is also added to answering
Topic person pushes the correlation step of topic.
Correspondingly, the method for the present embodiment includes the following steps：
Step 310 obtains answering information sample of the answer person of preset quantity about target exam pool.
Step 320, using the difficulty of the learning ability of the answer person in IRT models, the discrimination of topic and topic to wait to estimate
Parameter builds Bayesian network model.
Wherein, the parameter to be estimated meets the default prior distribution for including super ginseng.
Step 330 determines the corresponding variation distribution function of object function using variation estimating method, and with object function and
The minimum principle of degree of closeness of variation distribution function, based on Bayesian network model and answering information sample to it is described it is super join into
Row estimation, obtains the parameter value of super ginseng.
Step 340 is updated variation distribution function according to the parameter value of the super ginseng of gained.
Step 350 samples the parameter to be estimated based on updated variation distribution function using MCMC methodology, obtains
To treating the estimation of estimating parameter.
Step 360 establishes prediction model according to the estimated result of parameter to be estimated.
Illustratively, the estimated result of parameter to be estimated is substituted into IRT models, can obtain prediction model.
Step 370, the current learning ability for obtaining current answer person.
Specifically, this step may include：Assuming that the evolution of the learning ability of answer person meets Wiener-Hopf equation, and update prediction
Model obtains the history answer data of current answer person, is determined currently according to history answer data and updated prediction model
The current learning ability of answer person.
Further, the variation of the learning ability of answer person is a process with time evolution, therefore, to answer
The answer prediction loop abridged edition inventive embodiments of person consider this factor.The evolution of the learning ability for assuming answer person meets dimension
It receives process, and updates the prediction model, including：
Assuming that meet Wiener-Hopf equation as follows for the evolution of the learning ability of answer person：
Wherein, γ is that the smoothing prior of Wiener-Hopf equation assumes parameter, θt′+τFor the current learning ability of answer person, θt′To answer
Topic person does the learning ability of topic moment t ' last time, and the time interval inscribed is done in τ=t-t ' expressions twice.
Above-mentioned hypothesis is added in prediction model, i.e., in arbitrary t moment, for the time point t ' before arbitrary t, is updated
It is as follows that the prediction model obtains updated prediction model：
Wherein,
Represent topic j in the amendment discrimination at t ' moment, θi,tRepresent the current learning ability of answer person i, Xi,j,t′
Expression answer person i inscribing to wrong situation, X at the t ' moment about topic ji,j,t′=1 expression answer person i does topic pair at the t ' moment
Topic j.
The history answer data of current answer person are then obtained, it is true according to history answer data and updated prediction model
The current learning ability of settled preceding answer person.Specifically, maximum a posteriori estimate mode, which can be used, utilizes updated prediction
Model estimates the learning ability at current answer person's current time, using this method the learning ability of answer person can be put down
Sliding processing, improves precision of prediction.
Step 380, for the candidate topic in target exam pool, according to current learning ability, candidate topic discrimination and
Difficulty and prediction model determine that current answer person answers questions the probability of candidate topic.
Step 390, when identified probability meets preset condition, to the current answer person push candidate topic.
Illustratively, preset condition can be determined according to the default setting of adaptive and learning system, also can be by answer person
It is voluntarily set according to own situation.It is in the range of default value for example, preset condition can be identified probability, it is assumed that should
Range 0.5-0.8 such as candidate topic C, when identified probability is 0.6, then pushes topic C to current answer person.
Preferably, this step may particularly include：
The entropy of the candidate topic of definition is：
H=-PFinallogPFinal-(1-PFinal)log(1-PFinal)
Wherein, PFinalTo work as identified probability, H is the entropy of candidate topic.
Work as PFinalWhen meeting so that the value of H is more than default value, candidate topic is pushed to current answer person.
It is understood that according to principle of maximum entropy, the entropy of candidate topic is bigger, then answer person, which practices the topic, to obtain
The information content taken is more, so when H values are more than certain numerical value, candidate topic is pushed to current answer person.
Information processing method provided in an embodiment of the present invention based on IRT is estimated treating after parameter estimated, according to estimating
Meter result establishes prediction model, and the current learning ability based on the prediction model and current answer person rapidly and accurately selects
Suitable topic is pushed to answer person and answers, and makes adaptive and learning system more for specific aim and personalization, maximization is answered
The learning effect of topic person avoids answer person and repeats to do too many simple topic or directly do problem to cause to do or have no harvest
Inefficient situation.
Embodiment three
Fig. 4 is the structure diagram of a kind of information processing unit based on IRT that the embodiment of the present invention three provides, which can
It by software and or hardware realization, can generally be integrated in the terminal in adaptive and learning system, which can be PC
Or the mobile terminals such as the terminals such as server or tablet computer or smart mobile phone, the embodiment of the present invention are not especially limited.
As shown in figure 4, the device includes answer sample acquisition module 41, Bayesian network model structure module 42, super ginseng estimation module
43rd, function update module 44 and parameter estimation module to be estimated 45.
Wherein, answer sample acquisition module 41, the answer person for obtaining preset quantity believe about the answer of target exam pool
Cease sample；Bayesian network model builds module 42, for the differentiation of the learning ability of the answer person in IRT models, topic
The difficulty of degree and topic builds Bayesian network model for parameter to be estimated, wherein, the parameter to be estimated meets comprising the pre- of super ginseng
If prior distribution；Super ginseng estimation module 43, for determining the corresponding variation distribution function of object function using variation estimating method,
And with the minimum principle of degree of closeness of the object function and the variation distribution function, based on the Bayesian network model
The super ginseng is estimated with the answering information sample, obtains the parameter value of the super ginseng, wherein, the object function is
The Posterior estimator function about the parameter to be estimated based on the answering information sample；Function update module 44, for basis
The parameter value of the super ginseng of gained is updated the variation distribution function；Parameter estimation module 45 to be estimated, for being based on updating
Variation distribution function afterwards samples the parameter to be estimated, and obtains the estimation to the parameter to be estimated.
Information processing unit provided in an embodiment of the present invention based on IRT, with the study energy of the answer person in IRT models
The difficulty of power, the discrimination of topic and topic builds Bayesian network model for parameter to be estimated, wherein, the parameter difference to be estimated
Meet fixed prior distribution in existing estimation scheme, but meet the default prior distribution for including super ginseng, first use and become
Point estimating method obtains the estimated value of super ginseng based on Bayesian network model and answering information sample, then treats and estimate parameter and estimated
Meter.By using above-mentioned technical proposal, it can reduce and treat the prior estimate for estimating parameter and excessively cure influence to estimated result, have
Effect promotes accuracy of estimation.
On the basis of above-described embodiment, the parameter to be estimated meets the default prior distribution comprising super ginseng and includes：
The normal state point that the learning ability of the answer person and the difficulty of the topic meet mean value and/or variance is super ginseng
Cloth, the logarithm normal distribution that the discrimination of the topic meets mean value and/or variance is super ginseng.
It is described that the parameter to be estimated is adopted based on updated variation distribution function on the basis of above-described embodiment
Sample obtains the estimation to the parameter to be estimated, including：
Updated variation distribution function is based on to the parameter to be estimated using Markov chain Monte-Carlo MCMC methodology
It is sampled, obtains the estimation to the parameter to be estimated.
It is minimum with the degree of closeness of the object function and the variation distribution function on the basis of above-described embodiment
Principle estimates the super ginseng based on the Bayesian network model and the answering information sample, obtains the super ginseng
Parameter value, including：
Being met with the super ginseng makes following formula maximum turn to principle, based on the Bayesian network model and the answering information
Sample estimates the super ginseng, obtains the parameter value of the super ginseng：
∫q(Z)lnp(X|Z)dZ
Wherein, if p (Z | X) is object function, q (Z) is the corresponding variation distribution functions of p (Z | X), p (X | Z) be based on
The probabilistic model expression formula of IRT models, X represent the situation that the topic that includes in answering information sample is done pair or done wrong, Z=α,
β, θ, α are the discrimination of topic, and β is the difficulty of topic, and θ is the learning ability of answer person.
On the basis of above-described embodiment, which further includes：
Prediction model establishes module, for after the estimation to the parameter to be estimated is obtained, according to the parameter to be estimated
Estimated result establish prediction model；
Learning ability acquisition module, for obtaining the current learning ability of current answer person；
Probability determination module, for for the candidate topic in the target exam pool, according to the current learning ability, institute
It states the discrimination of candidate topic and difficulty and the prediction model determines that the current answer person answers questions the candidate topic
Probability；
Topic pushing module, for when identified probability meets preset condition, institute to be pushed to the current answer person
State candidate topic.
On the basis of above-described embodiment, the learning ability acquisition module includes：
Prediction model updating unit, the evolution for assuming the learning ability of answer person meet Wiener-Hopf equation, and update institute
State prediction model；
Answer data capture unit, for obtaining the history answer data of current answer person；
Learning ability determination unit, for working as described in being determined according to the history answer data and updated prediction model
The current learning ability of preceding answer person.
On the basis of above-described embodiment, the prediction model updating unit is specifically used for：
Assuming that meet Wiener-Hopf equation as follows for the evolution of the learning ability of answer person：
Wherein, γ is that the smoothing prior of Wiener-Hopf equation assumes parameter, θt′+τFor the current learning ability of answer person, θt′To answer
Topic person does the learning ability of topic moment t ' last time, and the time interval inscribed is done in τ=t-t ' expressions twice；
Updating the prediction model, to obtain updated prediction model as follows：
Wherein,
Represent topic j in the amendment discrimination at t ' moment, θi,tRepresent the current learning ability of answer person i, Xi,j,t′
Expression answer person i inscribing to wrong situation, X at the t ' moment about topic ji,j,t′=1 expression answer person i does topic pair at the t ' moment
Topic j.
The information processing unit based on IRT provided in above-described embodiment can perform what any embodiment of the present invention was provided
Information processing method based on IRT has and performs the corresponding function module of this method and advantageous effect.Not in the above-described embodiments
The technical detail of detailed description, reference can be made to the information processing method based on IRT that any embodiment of the present invention is provided.
Note that it above are only presently preferred embodiments of the present invention and institute's application technology principle.It will be appreciated by those skilled in the art that
The present invention is not limited to specific embodiment described here, can carry out for a person skilled in the art various apparent variations,
It readjusts and substitutes without departing from protection scope of the present invention.Therefore, although being carried out by above example to the present invention
It is described in further detail, but the present invention is not limited only to above example, without departing from the inventive concept, also
It can include other more equivalent embodiments, and the scope of the present invention is determined by scope of the appended claims.
Claims (14)
1. a kind of information processing method based on item response theory IRT, which is characterized in that including：
Obtain answering information sample of the answer person of preset quantity about target exam pool；
Pattra leaves is built by parameter to be estimated of the difficulty of the learning ability of the answer person in IRT models, the discrimination of topic and topic
This network model, wherein, the parameter to be estimated meets the default prior distribution for including super ginseng；
The corresponding variation distribution function of object function is determined, and with the object function and the variation using variation estimating method
The minimum principle of degree of closeness of distribution function, based on the Bayesian network model and the answering information sample to described super
Ginseng estimated, obtain the parameter value of the super ginseng, wherein, the object function be based on the answering information sample about
The Posterior estimator function of the parameter to be estimated；
The variation distribution function is updated according to the parameter value of the super ginseng of gained；
The parameter to be estimated is sampled based on updated variation distribution function, obtains the estimation to the parameter to be estimated.
2. according to the method described in claim 1, it is characterized in that, the parameter to be estimated meets the default priori point for including super ginseng
Cloth includes：
The normal distribution that the learning ability of the answer person and the difficulty of the topic meet mean value and/or variance is super ginseng, institute
The discrimination for stating topic meets mean value and/or logarithm normal distribution that variance is super ginseng.
3. method according to claim 1 or 2, which is characterized in that described to be based on updated variation distribution function to institute
It states parameter to be estimated to be sampled, obtains the estimation to the parameter to be estimated, including：
Updated variation distribution function is based on using Markov chain Monte-Carlo MCMC methodology to carry out the parameter to be estimated
Sampling, obtains the estimation to the parameter to be estimated.
4. method according to claim 1 or 2, which is characterized in that with the object function and the variation distribution function
The minimum principle of degree of closeness, the super ginseng is estimated based on the Bayesian network model and the answering information sample
Meter, obtains the parameter value of the super ginseng, including：
Being met with the super ginseng makes following formula maximum turn to principle, based on the Bayesian network model and the answering information sample
The super ginseng is estimated, obtains the parameter value of the super ginseng：
∫q(Z)lnp(X|Z)dZ
Wherein, if p (Z | X) is object function, q (Z) is the corresponding variation distribution functions of p (Z | X), and p (X | Z) it is based on IRT moulds
The probabilistic model expression formula of type, X represent the situation that the topic that includes in answering information sample is done pair or done wrong, Z=α, β, θ, α
For the discrimination of topic, β is the difficulty of topic, and θ is the learning ability of answer person.
5. according to the method described in claim 1, it is characterized in that, after the estimation to the parameter to be estimated is obtained, also wrap
It includes：
Prediction model is established according to the estimated result of the parameter to be estimated；
Obtain the current learning ability of current answer person；
For the candidate topic in the target exam pool, according to the current learning ability, the candidate topic discrimination and
Difficulty and the prediction model determine that the current answer person answers questions the probability of the candidate topic；
When identified probability meets preset condition, to current answer person's push candidate topic.
6. according to the method described in claim 5, it is characterized in that, the current learning ability for obtaining current answer person, packet
It includes：
Assuming that the evolution of the learning ability of answer person meets Wiener-Hopf equation, and update the prediction model；
Obtain the history answer data of current answer person；
The current learning ability of the current answer person is determined according to the history answer data and updated prediction model.
7. according to the method described in claim 6, it is characterized in that, the evolution of the learning ability for assuming answer person meets dimension
It receives process, and updates the prediction model, including：
Assuming that meet Wiener-Hopf equation as follows for the evolution of the learning ability of answer person：
Wherein, γ is that the smoothing prior of Wiener-Hopf equation assumes parameter, θt′+τFor the current learning ability of answer person, θt′For answer person
Last time does the learning ability of topic moment t ', and the time interval inscribed is done in τ=t-t ' expressions twice；
Updating the prediction model, to obtain updated prediction model as follows：
Wherein,
Represent topic j in the amendment discrimination at t ' moment, θi,tRepresent the current learning ability of answer person i, Xi,j,t′Expression is answered
Topic person i inscribing to wrong situation, X at the t ' moment about topic ji,j,t′=1 expression answer person i is inscribed at the t ' moment to topic j.
8. a kind of information processing unit based on item response theory IRT, which is characterized in that including：
Answer sample acquisition module, for obtaining answering information sample of the answer person about target exam pool of preset quantity；
Bayesian network model builds module, for the discrimination and topic of the learning ability of the answer person in IRT models, topic
Purpose difficulty builds Bayesian network model for parameter to be estimated, wherein, the parameter to be estimated meets the default priori for including super ginseng
Distribution；
Super ginseng estimation module, for determining the corresponding variation distribution function of object function, and using variation estimating method with described
The minimum principle of degree of closeness of object function and the variation distribution function based on the Bayesian network model and described is answered
Topic message sample estimates the super ginseng, obtains the parameter value of the super ginseng, wherein, the object function is based on described
The Posterior estimator function about the parameter to be estimated of answering information sample；
Function update module is updated the variation distribution function for the parameter value of the super ginseng according to gained；
Parameter estimation module to be estimated samples the parameter to be estimated for being based on updated variation distribution function, obtains
Estimation to the parameter to be estimated.
9. device according to claim 8, which is characterized in that the parameter to be estimated meets the default priori point for including super ginseng
Cloth includes：
The normal distribution that the learning ability of the answer person and the difficulty of the topic meet mean value and/or variance is super ginseng, institute
The discrimination for stating topic meets mean value and/or logarithm normal distribution that variance is super ginseng.
10. device according to claim 8 or claim 9, which is characterized in that described to be based on updated variation distribution function to institute
It states parameter to be estimated to be sampled, obtains the estimation to the parameter to be estimated, including：
Updated variation distribution function is based on using Markov chain Monte-Carlo MCMC methodology to carry out the parameter to be estimated
Sampling, obtains the estimation to the parameter to be estimated.
11. device according to claim 8 or claim 9, which is characterized in that with the object function and the variation distribution function
The minimum principle of degree of closeness, the super ginseng is estimated based on the Bayesian network model and the answering information sample
Meter, obtains the parameter value of the super ginseng, including：
Being met with the super ginseng makes following formula maximum turn to principle, based on the Bayesian network model and the answering information sample
The super ginseng is estimated, obtains the parameter value of the super ginseng：
∫q(Z)lnp(X|Z)dZ
Wherein, if p (Z | X) is object function, q (Z) is the corresponding variation distribution functions of p (Z | X), and p (X | Z) it is based on IRT moulds
The probabilistic model expression formula of type, X represent the situation that the topic that includes in answering information sample is done pair or done wrong, Z=α, β, θ, α
For the discrimination of topic, β is the difficulty of topic, and θ is the learning ability of answer person.
12. device according to claim 8, which is characterized in that further include：
Prediction model establishes module, for after the estimation to the parameter to be estimated is obtained, according to estimating for the parameter to be estimated
Meter result establishes prediction model；
Learning ability acquisition module, for obtaining the current learning ability of current answer person；
Probability determination module, for for the candidate topic in the target exam pool, according to the current learning ability, the time
Selected topic purpose discrimination and difficulty and the prediction model determine that the current answer person answers questions the general of the candidate topic
Rate；
Topic pushing module, for when identified probability meets preset condition, the time to be pushed to the current answer person
Selected topic mesh.
13. device according to claim 12, which is characterized in that the learning ability acquisition module includes：
Prediction model updating unit, the evolution for assuming the learning ability of answer person meet Wiener-Hopf equation, and update described pre-
Survey model；
Answer data capture unit, for obtaining the history answer data of current answer person；
Learning ability determination unit, for determining described currently to answer according to the history answer data and updated prediction model
The current learning ability of topic person.
14. device according to claim 13, which is characterized in that the prediction model updating unit is specifically used for：
Assuming that meet Wiener-Hopf equation as follows for the evolution of the learning ability of answer person：
Wherein, γ is that the smoothing prior of Wiener-Hopf equation assumes parameter, θt′+τFor the current learning ability of answer person, θt′For answer person
Last time does the learning ability of topic moment t ', and the time interval inscribed is done in τ=t-t ' expressions twice；
Updating the prediction model, to obtain updated prediction model as follows：
Wherein,
Represent topic j in the amendment discrimination at t ' moment, θi,tRepresent the current learning ability of answer person i, Xi,j,t′Expression is answered
Topic person i inscribing to wrong situation, X at the t ' moment about topic ji,j,t′=1 expression answer person i is inscribed at the t ' moment to topic j.
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