# Inferring Parameters and Structure of Latent Variable Models by Variational Bayes

arXiv: https://arxiv.org/abs/1301.6676 · HTML: https://mlsanity.com/paper/1301.6676/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2013.

## Built on by (most cited first, 11 of 11)

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- [Structured Recognition for Generative Models with Explaining Away](https://mlsanity.com/paper/2209.05212/) (2022)
- [Semantic Variational Bayes Based on Semantic Information G Theory for Solving Latent Variables](https://mlsanity.com/paper/2408.13122/) (2024)
- [Quantile deep learning models for multi-step ahead time series prediction](https://mlsanity.com/paper/2411.15674/) (2024)
- [Flat-topped Probability Density Functions for Mixture Models](https://mlsanity.com/paper/2203.17027/) (2022)
- [Choosing the number of factors in factor analysis with incomplete data via a hierarchical Bayesian information criterion](https://mlsanity.com/paper/2204.09086/) (2022)
- [Empirical Bayes Linked Matrix Decomposition](https://mlsanity.com/paper/2408.00237/) (2024)
- [Amortized Variational Inference for Partial-Label Learning: A Probabilistic Approach to Label Disambiguation](https://mlsanity.com/paper/2510.21300/) (2025)

## Abstract (arXiv)

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior distributions over the parameters remains a difficult problem. Moreover, learning the structure of models with latent variables, for which the Bayesian approach is crucial, is yet a harder problem. In this paper I present the Variational Bayes framework, which provides a solution to these problems. This approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner without resorting to sampling methods. Unlike in the Laplace approximation, these posteriors are generally non-Gaussian and no Hessian needs to be computed. The resulting algorithm generalizes the standard Expectation Maximization algorithm, and its convergence is guaranteed. I demonstrate that this algorithm can be applied to a large class of models in several domains, including unsupervised clustering and blind source separation.