# Learning Graphical Model Parameters with Approximate Marginal Inference

arXiv: https://arxiv.org/abs/1301.3193 · HTML: https://mlsanity.com/paper/1301.3193/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2013.

## Built on by (most cited first, 9 of 9)

- [Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach](https://mlsanity.com/paper/2106.03188/) (2021)
- [Learning Neural Set Functions Under the Optimal Subset Oracle](https://mlsanity.com/paper/2203.01693/) (2022)
- [Relaxed Marginal Consistency for Differentially Private Query Answering](https://mlsanity.com/paper/2109.06153/) (2021)
- [Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces](https://mlsanity.com/paper/2412.01019/) (2024)
- [Combining Probabilistic Logic and Deep Learning for Self-Supervised Learning](https://mlsanity.com/paper/2107.12591/) (2021)
- [Provable Constrained Stochastic Convex Optimization with XOR-Projected Gradient Descent](https://mlsanity.com/paper/2203.11829/) (2022)
- [On Certified Generalization in Structured Prediction](https://mlsanity.com/paper/2306.09112/) (2023)
- [Monotone deep Boltzmann machines](https://mlsanity.com/paper/2307.04990/) (2023)
- [Advancing Optimal Subset Oracle via Learning Relaxation of Neural Set Functions](https://mlsanity.com/paper/2607.11555/) (2026)

## Abstract (arXiv)

Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted marginals, taking into account both model and inference approximations at training time. Experiments on imaging problems suggest marginalization-based learning performs better than likelihood-based approximations on difficult problems where the model being fit is approximate in nature.