# A moment-matching metric for latent variable generative models

arXiv: https://arxiv.org/abs/2111.00875 · HTML: https://mlsanity.com/paper/2111.00875/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 45 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Towards a Definition of Disentangled Representations](https://mlsanity.com/paper/1812.02230/) (2018)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Testing Goodness of Fit of Conditional Density Models with Kernels](https://mlsanity.com/paper/2002.10271/) (2020)
- [A Kernel Stein Test for Comparing Latent Variable Models](https://mlsanity.com/paper/1907.00586/) (2019)

## Abstract (arXiv)

It can be difficult to assess the quality of a fitted model when facing unsupervised learning problems. Latent variable models, such as variation autoencoders and Gaussian mixture models, are often trained with likelihood-based approaches. In scope of Goodhart's law, when a metric becomes a target it ceases to be a good metric and therefore we should not use likelihood to assess the quality of the fit of these models. The solution we propose is a new metric for model comparison or regularization that relies on moments. The concept is to study the difference between the data moments and the model moments using a matrix norm, such as the Frobenius norm. We show how to use this new metric for model comparison and then for regularization. It is common to draw samples from the fitted distribution when evaluating latent variable models and we show that our proposed metric is faster to compute and has a smaller variance that this alternative. We conclude this article with a proof of concept of both applications and we discuss future work.