# Structured Recognition for Generative Models with Explaining Away

arXiv: https://arxiv.org/abs/2209.05212 · HTML: https://mlsanity.com/paper/2209.05212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 56 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [DRAW: A Recurrent Neural Network For Image Generation](https://mlsanity.com/paper/1502.04623/) (2015)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Composing graphical models with neural networks for structured representations and fast inference](https://mlsanity.com/paper/1603.06277/) (2016)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [Gradient Estimation with Stochastic Softmax Tricks](https://mlsanity.com/paper/2006.08063/) (2020)
- [The Variational Gaussian Process](https://mlsanity.com/paper/1511.06499/) (2015)
- [Approximate Inference with Amortised MCMC](https://mlsanity.com/paper/1702.08343/) (2017)
- [Structured Stochastic Variational Inference](https://mlsanity.com/paper/1404.4114/) (2014)
- [Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains](https://mlsanity.com/paper/1604.03053/) (2016)
- [Sparse Gaussian Process Variational Autoencoders](https://mlsanity.com/paper/2010.10177/) (2020)
- [Variational Message Passing with Structured Inference Networks](https://mlsanity.com/paper/1803.05589/) (2018)
- [The Gaussian Process Autoregressive Regression Model (GPAR)](https://mlsanity.com/paper/1802.07182/) (2018)
- [Inferring Parameters and Structure of Latent Variable Models by Variational Bayes](https://mlsanity.com/paper/1301.6676/) (2013)
- [Efficient non-conjugate Gaussian process factor models for spike count data using polynomial approximations](https://mlsanity.com/paper/1906.03318/) (2019)
- [Training VAEs Under Structured Residuals](https://mlsanity.com/paper/1804.01050/) (2018)
- [Graphical Generative Adversarial Networks](https://mlsanity.com/paper/1804.03429/) (2018)
- [tvGP-VAE: Tensor-variate Gaussian Process Prior Variational Autoencoder](https://mlsanity.com/paper/2006.04788/) (2020)

## Built on by (most cited first, 1 of 1)

- [Provably Scalable Black-Box Variational Inference with Structured Variational Families](https://mlsanity.com/paper/2401.10989/) (2024)

## Abstract (arXiv)

A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent variables captured through a probabilistic graphical model. Although the learning of structured graphical models has a long history, much recent work in unsupervised modelling has instead emphasised flexible deep-network-based generation, either transforming independent latent generators to model complex data or assuming that distinct observed variables are derived from different latent nodes. Here, we extend amortised variational inference to incorporate structured factors over multiple variables, able to capture the observation-induced posterior dependence between latents that results from ``explaining away'' and thus allow complex observations to depend on multiple nodes of a structured graph. We show that appropriately parametrised factors can be combined efficiently with variational message passing in rich graphical structures. We instantiate the framework in nonlinear Gaussian Process Factor Analysis, evaluating the structured recognition framework using synthetic data from known generative processes. We fit the GPFA model to high-dimensional neural spike data from the hippocampus of freely moving rodents, where the model successfully identifies latent signals that correlate with behavioural covariates.