# US 10,706,188 B1 · Parallel computing for data analysis using generalized latent variable models > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,706,188 B1 - Document ID: US10706188B1 - Status: Granted - Kind: B1 - Application number: 15/348,083 - Filed: 2016-11-10 - Granted: 2020-07-07 - Earliest claimed: 2015-11-12 - Assignees: Educational Testing Service - Applicants: Educational Testing Service - Inventors: Matthias von Davier - Web page: https://patentgrep.com/patent/US10706188B1 ## CPC - G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} - G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30) - G06N 20/00: Machine learning - G09B 7/02: of the type wherein the student is expected to construct an answer to the question which is presented or wherein the machine gives an answer to the question presented by a student - G06N 7/01: Probabilistic graphical models, e.g. probabilistic networks - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - G06N: COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS - G09B: EDUCATIONAL OR DEMONSTRATION APPLIANCES; APPLIANCES FOR TEACHING, OR COMMUNICATING WITH, THE BLIND, DEAF OR MUTE; MODELS; PLANETARIA; GLOBES; MAPS; DIAGRAMS (devices for psychotechnics or for testing reaction times A61B5/16; games, sports, amusements A63; projectors, projector screens G03B) ## Abstract Systems and methods are provided for implementing a parallel Expectation Minimization algorithm for generalized latent variable models. Item response data that is based on responses to items from multiple respondents is accessed. The item response data includes data for multiple response variables. The item response data is analyzed using a generalized latent variable model, and the analysis includes an application of a Parallel-E Parallel-M (PEPM) algorithm. In a parallel Expectation step of the PEPM algorithm, the respondents are subdivided into N groups of respondents, and computations for the N groups are performed in parallel using the N processor cores. In a parallel Maximization step of the PEPM algorithm, the response variables are subdivided into N groups of response variables, and computations for the N groups of response variables are performed in parallel using the N processor cores. ## Claims ### Claim 1 A computer-implemented method performed in a computer system including N processor cores, where N is greater than one, the method comprising: accessing response data that is based on responses to test questions from multiple test-takers, the response data including data for multiple response variables; and analyzing the response data using a generalized latent variable model, the analysis including an application of a parallel Expectation parallel Maximization (PEPM) algorithm, wherein a parallel Expectation step of the PEPM algorithm includes: subdividing the test-takers into N groups of test-takers, and performing computations for the N groups in parallel using the N processor cores, data for each of the N groups being processed by a respective core of the N processor cores, wherein the computations include, for each of the multiple test-takers, calculating the posterior of the latent variable given responses; and wherein a parallel Maximization step of the PEPM algorithm includes: subdividing the response variables into N groups of response variables, and performing computations for the N groups of response variables in parallel using the N processor cores, data for each of the N groups being processed by a respective core of the N processor cores, wherein the computations include, for each response variable of the multiple response variables, updating parameters associated with the response variable, wherein results of the PEPM algorithm are utilized to provide a score to a new response received from a new test-taker, the score estimating a skill of the new test-taker. ### Claim 2 (depends on 1) The method of claim 1, wherein the response data includes no data or an indication of no data for certain response variables for certain test-takers. ### Claim 3 (depends on 1) The method of claim 1, further comprising: selecting the value N based on a number of processor cores available for performing the method. ### Claim 4 (depends on 3) The method of claim 3, wherein N is selected based on a number of processor cores present on a computing machine. ### Claim 5 (depends on 1) The method of claim 1, further comprising: computing a convergence criteria value; comparing the convergence criteria value to a threshold; and re-performing the parallel Expectation step and the parallel Maximization step based on said comparing. ### Claim 6 (depends on 1) The method of claim 1, wherein the PEPM algorithm is performed using a graphics processing unit (GPU). ### Claim 7 (depends on 1) The method of claim 1, wherein the score is used to estimate the skill of the new test-taker based on an item response theory analysis. ### Claim 8 (depends on 7) The method of claim 7, wherein the score is provided such that each of a plurality of new responses does not have an identical contribution to the score because each of the plurality of new responses does not have an identical relevance to the score. ### Claim 9 A system comprising: a processing system including N processor cores, N being greater than one; and one or more non-transitory computer-readable storage mediums in communication with the processing system and encoded with instructions for commanding the processing system to execute steps comprising: accessing response data that is based on responses to test questions from multiple test-takers, the response data including data for multiple response variables; and analyzing the response data using a generalized latent variable model, the analysis including an application of a parallel Expectation parallel Maximization (PEPM) algorithm, wherein a parallel Expectation step of the PEPM algorithm includes: subdividing the test-takers into N groups of test-takers, and performing computations for the N groups in parallel using the N processor cores, data for each of the N groups being processed by a respective core of the N processor cores, wherein the computations include, for each of the multiple test-takers, calculating the posterior of the latent variable given responses; and wherein a parallel Maximization step of the PEPM algorithm includes: subdividing the response variables into N groups of response variables, and performing computations for the N groups of response variables in parallel using the N processor cores, data for each of the N groups being processed by a respective core of the N processor cores, wherein the computations include, for each response variable of the multiple response variables, updating parameters associated with the response variable, wherein results of the PEPM algorithm are utilized to provide a score to a new response received from a new test-taker, the score estimating a skill of the new test-taker. ### Claim 10 (depends on 9) The system of claim 9, wherein the response data includes no data or an indication of no data for certain response variables for certain test-takers. ### Claim 11 (depends on 9) The system of claim 9, wherein the steps further include: selecting the value N based on a number of processor cores available for performing the method. ### Claim 12 (depends on 11) The system of claim 11, wherein N is selected based on a number of processor cores present on a computing machine. ### Claim 13 (depends on 9) The system of claim 9, wherein the steps further include: computing a convergence criteria value; comparing the convergence criteria value to a threshold; and re-performing the parallel Expectation step and the parallel Maximization step based on said comparing. ### Claim 14 (depends on 9) The system of claim 9, wherein the PEPM algorithm is performed using a graphics processing unit (GPU). ### Claim 15 (depends on 9) The system of claim 9, wherein the score is used to estimate the skill of the new test-taker based on an item response theory analysis. ### Claim 16 (depends on 15) The system of claim 15, wherein the score is provided such that each of a plurality of new responses does not have an identical contribution to the score because each of the plurality of new responses does not have an identical relevance to the score. ### Claim 17 A non-transitory computer-readable storage medium comprising computer executable instructions which, when executed, cause a processing system including N processor cores to execute steps comprising: accessing response data that is based on responses to test questions from multiple test-takers, the response data including data for multiple response variables; and analyzing the response data using a generalized latent variable model, the analysis including an application of a parallel Expectation parallel Maximization (PEPM) algorithm, wherein a parallel Expectation step of the PEPM algorithm includes: subdividing the test-takers into N groups of test-takers, N being greater than one, and performing computations for the N groups in parallel using the N processor cores, data for each of the N groups being processed by a respective core of the N processor cores, wherein the computations include, for each of the multiple test-takers, calculating the posterior of the latent variable given responses; and wherein a parallel Maximization step of the PEPM algorithm includes: subdividing the response variables into N groups of response variables, and performing computations for the N groups of response variables in parallel using the N processor cores, data for each of the N groups being processed by a respective core of the N processor cores, wherein the computations include, for each response variable of the multiple response variables, updating parameters associated with the response variable, wherein results of the PEPM algorithm are utilized to provide a score to a new response received from a new test-taker, the score estimating a skill of the new test-taker.