# Information Theoretic Structured Generative Modeling

arXiv: https://arxiv.org/abs/2110.05794 · HTML: https://mlsanity.com/paper/2110.05794/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Nonlinear Information Bottleneck](https://mlsanity.com/paper/1705.02436/) (2017)
- [Uncertainty in the Variational Information Bottleneck](https://mlsanity.com/paper/1807.00906/) (2018)
- [Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences](https://mlsanity.com/paper/1609.00978/) (2016)

## Abstract (arXiv)

R'enyi's information provides a theoretical foundation for tractable and data-efficient non-parametric density estimation, based on pair-wise evaluations in a reproducing kernel Hilbert space (RKHS). This paper extends this framework to parametric probabilistic modeling, motivated by the fact that R'enyi's information can be estimated in closed-form for Gaussian mixtures. Based on this special connection, a novel generative model framework called the structured generative model (SGM) is proposed that makes straightforward optimization possible, because costs are scale-invariant, avoiding high gradient variance while imposing less restrictions on absolute continuity, which is a huge advantage in parametric information theoretic optimization. The implementation employs a single neural network driven by an orthonormal input appended to a single white noise source adapted to learn an infinite Gaussian mixture model (IMoG), which provides an empirically tractable model distribution in low dimensions. To train SGM, we provide three novel variational cost functions, based on R'enyi's second-order entropy and divergence, to implement minimization of cross-entropy, minimization of variational representations of f-divergence, and maximization of the evidence lower bound (conditional probability). We test the framework for estimation of mutual information and compare the results with the mutual information neural estimation (MINE), for density estimation, for conditional probability estimation in Markov models as well as for training adversarial networks. Our preliminary results show that SGM significantly improves MINE estimation in terms of data efficiency and variance, conventional and variational Gaussian mixture models, as well as the performance of generative adversarial networks.