# Variational Item Response Theory: Fast, Accurate, and Expressive

arXiv: https://arxiv.org/abs/2002.00276 · HTML: https://mlsanity.com/paper/2002.00276/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2020.

## Built on by (most cited first, 29 of 29)

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- [py-irt: A Scalable Item Response Theory Library for Python](https://mlsanity.com/paper/2203.01282/) (2022)
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- [Provably Scalable Black-Box Variational Inference with Structured Variational Families](https://mlsanity.com/paper/2401.10989/) (2024)
- [Can We Trust Item Response Theory for AI Evaluation?](https://mlsanity.com/paper/2607.15190/) (2026)
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- [Training Reinforcement Learning Agents and Humans With Difficulty-Conditioned Generators](https://mlsanity.com/paper/2312.02309/) (2023)
- [Item Response Scaling Laws: A Measurement Theory Approach for Efficient and Generalizable Neural Scaling Estimation](https://mlsanity.com/paper/2606.07616/) (2026)
- [Generative Adversarial Networks for High-Dimensional Item Factor Analysis: A Deep Adversarial Learning Algorithm](https://mlsanity.com/paper/2502.10650/) (2025)
- [Just Read the Question: Enabling Generalization to New Assessment Items with Text Awareness](https://mlsanity.com/paper/2507.08154/) (2025)
- [Deep Learning-Based Estimation and Goodness-of-Fit for Large-Scale Confirmatory Item Factor Analysis](https://mlsanity.com/paper/2109.09500/) (2021)
- [Variational Factorization Machines for Preference Elicitation in Large-Scale Recommender Systems](https://mlsanity.com/paper/2212.09920/) (2022)
- [Amortised Design Optimization for Item Response Theory](https://mlsanity.com/paper/2307.09891/) (2023)
- [Introducing Flexible Monotone Multiple Choice Item Response Theory Models and Bit Scales](https://mlsanity.com/paper/2410.01480/) (2024)
- [Generative Cognitive Diagnosis](https://mlsanity.com/paper/2507.09831/) (2025)
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- [Efficient SWE Agent Benchmarking via Trajectory-Aware Evaluation](https://mlsanity.com/paper/2609.01603/) (2026)

## Abstract (arXiv)

Item Response Theory (IRT) is a ubiquitous model for understanding humans based on their responses to questions, used in fields as diverse as education, medicine and psychology. Large modern datasets offer opportunities to capture more nuances in human behavior, potentially improving test scoring and better informing public policy. Yet larger datasets pose a difficult speed / accuracy challenge to contemporary algorithms for fitting IRT models. We introduce a variational Bayesian inference algorithm for IRT, and show that it is fast and scaleable without sacrificing accuracy. Using this inference approach we then extend classic IRT with expressive Bayesian models of responses. Applying this method to five large-scale item response datasets from cognitive science and education yields higher log likelihoods and improvements in imputing missing data. The algorithm implementation is open-source, and easily usable.