# Modeling Item Response Theory with Stochastic Variational Inference

arXiv: https://arxiv.org/abs/2108.11579 · HTML: https://mlsanity.com/paper/2108.11579/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 64 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [A Conceptual Introduction to Hamiltonian Monte Carlo](https://mlsanity.com/paper/1701.02434/) (2017)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Multimodal Generative Models for Scalable Weakly-Supervised Learning](https://mlsanity.com/paper/1802.05335/) (2018)
- [Dynamic Key-Value Memory Networks for Knowledge Tracing](https://mlsanity.com/paper/1611.08108/) (2016)
- [Neural Variational Inference and Learning in Belief Networks](https://mlsanity.com/paper/1402.0030/) (2014)
- [Sylvester Normalizing Flows for Variational Inference](https://mlsanity.com/paper/1803.05649/) (2018)
- [Deep-IRT: Make Deep Learning Based Knowledge Tracing Explainable Using Item Response Theory](https://mlsanity.com/paper/1904.11738/) (2019)
- [Improving Variational Auto-Encoders using Householder Flow](https://mlsanity.com/paper/1611.09630/) (2016)
- [Faithful Inversion of Generative Models for Effective Amortized Inference](https://mlsanity.com/paper/1712.00287/) (2017)
- [Enhancing Item Response Theory for Cognitive Diagnosis](https://mlsanity.com/paper/1905.10957/) (2019)
- [The Stanford Acuity Test: A Precise Vision Test Using Bayesian Techniques and a Discovery in Human Visual Response](https://mlsanity.com/paper/1906.01811/) (2019)

## Built on by (most cited first, 3 of 3)

- [Raising the Bar: Investigating the Values of Large Language Models via Generative Evolving Testing](https://mlsanity.com/paper/2406.14230/) (2024)
- [Foundation Posteriors for Approximate Probabilistic Inference](https://mlsanity.com/paper/2205.09735/) (2022)
- [Introducing Flexible Monotone Multiple Choice Item Response Theory Models and Bit Scales](https://mlsanity.com/paper/2410.01480/) (2024)

## Abstract (arXiv)

Item Response Theory (IRT) is a ubiquitous model for understanding human behaviors and attitudes based on their responses to questions. Large modern datasets offer opportunities to capture more nuances in human behavior, potentially improving psychometric modeling leading to improved scientific understanding and public policy. However, while larger datasets allow for more flexible approaches, many contemporary algorithms for fitting IRT models may also have massive computational demands that forbid real-world application. To address this bottleneck, we introduce a variational Bayesian inference algorithm for IRT, and show that it is fast and scalable without sacrificing accuracy. Applying this method to five large-scale item response datasets from cognitive science and education yields higher log likelihoods and higher accuracy in imputing missing data than alternative inference algorithms. Using this new inference approach we then generalize IRT with expressive Bayesian models of responses, leveraging recent advances in deep learning to capture nonlinear item characteristic curves (ICC) with neural networks. Using an eigth-grade mathematics test from TIMSS, we show our nonlinear IRT models can capture interesting asymmetric ICCs. The algorithm implementation is open-source, and easily usable.