# Scalable Learning of Item Response Theory Models

arXiv: https://arxiv.org/abs/2403.00680 · HTML: https://mlsanity.com/paper/2403.00680/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 74 references that are in the map.
- First posted on arXiv 1 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Coresets for Scalable Bayesian Logistic Regression](https://mlsanity.com/paper/1605.06423/) (2016)
- [On Coresets for Logistic Regression](https://mlsanity.com/paper/1805.08571/) (2018)
- [New Frameworks for Offline and Streaming Coreset Constructions](https://mlsanity.com/paper/1612.00889/) (2016)
- [Coresets for Near-Convex Functions](https://mlsanity.com/paper/2006.05482/) (2020)
- [A New Coreset Framework for Clustering](https://mlsanity.com/paper/2104.06133/) (2021)
- [Coresets for Classification -- Simplified and Strengthened](https://mlsanity.com/paper/2106.04254/) (2021)
- [Oblivious sketching for logistic regression](https://mlsanity.com/paper/2107.06615/) (2021)
- [β3-IRT: A New Item Response Model and its Applications](https://mlsanity.com/paper/1903.04016/) (2019)
- [Online Lewis Weight Sampling](https://mlsanity.com/paper/2207.08268/) (2022)
- [Generic Coreset for Scalable Learning of Monotonic Kernels: Logistic Regression, Sigmoid and more](https://mlsanity.com/paper/1802.07382/) (2018)
- [Input Sparsity and Hardness for Robust Subspace Approximation](https://mlsanity.com/paper/1510.06073/) (2015)
- [p-Generalized Probit Regression and Scalable Maximum Likelihood Estimation via Sketching and Coresets](https://mlsanity.com/paper/2203.13568/) (2022)
- [Almost Linear Constant-Factor Sketching for ℓ1 and Logistic Regression](https://mlsanity.com/paper/2304.00051/) (2023)
- [An Empirical Evaluation of k-Means Coresets](https://mlsanity.com/paper/2207.00966/) (2022)
- [Item Response Theory based Ensemble in Machine Learning](https://mlsanity.com/paper/1911.04616/) (2019)
- [Feature Space Sketching for Logistic Regression](https://mlsanity.com/paper/2303.14284/) (2023)

## Built on by (most cited first, 6 of 6)

- [Can We Trust Item Response Theory for AI Evaluation?](https://mlsanity.com/paper/2607.15190/) (2026)
- [Optimal bounds for ℓp sensitivity sampling via ℓ2 augmentation](https://mlsanity.com/paper/2406.00328/) (2024)
- [Turnstile ℓp leverage score sampling with applications](https://mlsanity.com/paper/2406.00339/) (2024)
- [Data subsampling for Poisson regression with pth-root-link](https://mlsanity.com/paper/2410.22872/) (2024)
- [Reciprocal Learning](https://mlsanity.com/paper/2408.06257/) (2024)
- [Scalable Learning of Multivariate Distributions via Coresets](https://mlsanity.com/paper/2603.19792/) (2026)

## Abstract (arXiv)

Item Response Theory (IRT) models aim to assess latent abilities of n examinees along with latent difficulty characteristics of m test items from categorical data that indicates the quality of their corresponding answers. Classical psychometric assessments are based on a relatively small number of examinees and items, say a class of 200 students solving an exam comprising 10 problems. More recent global large scale assessments such as PISA, or internet studies, may lead to significantly increased numbers of participants. Additionally, in the context of Machine Learning where algorithms take the role of examinees and data analysis problems take the role of items, both n and m may become very large, challenging the efficiency and scalability of computations. To learn the latent variables in IRT models from large data, we leverage the similarity of these models to logistic regression, which can be approximated accurately using small weighted subsets called coresets. We develop coresets for their use in alternating IRT training algorithms, facilitating scalable learning from large data.