# Stochastic Collapsed Variational Inference for Structured Gaussian Process Regression Network

arXiv: https://arxiv.org/abs/2106.00719 · HTML: https://mlsanity.com/paper/2106.00719/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 48 references that are in the map.
- First posted on arXiv 1 Jun 2021.

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

- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [Non-Stationary Spectral Kernels](https://mlsanity.com/paper/1705.08736/) (2017)
- [Structured Variational Learning of Bayesian Neural Networks with Horseshoe Priors](https://mlsanity.com/paper/1806.05975/) (2018)
- [Doubly Stochastic Variational Inference for Neural Processes with Hierarchical Latent Variables](https://mlsanity.com/paper/2008.09469/) (2020)
- [Nonstationary Multivariate Gaussian Processes for Electronic Health Records](https://mlsanity.com/paper/1910.05851/) (2019)
- [Deep learning as a tool for neural data analysis: speech classification and cross-frequency coupling in human sensorimotor cortex](https://mlsanity.com/paper/1803.09807/) (2018)
- [Semiparametric Estimation of Cross-covariance Functions for Multivariate Random Fields](https://mlsanity.com/paper/1911.02258/) (2019)

## Abstract (arXiv)

This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and jointly treats both the distributions of the inducing variables and hyper-parameters as variational parameters. Then we propose structured variable distributions and marginalize latent variables, which enables the decomposability of a tractable variational lower bound and leads to stochastic optimization. Our inference approach is able to model data in which outputs do not share a common input set with a computational complexity independent of the size of the inputs and outputs and thus easily handle datasets with missing values. We illustrate the performance of our method on synthetic data and real datasets and show that our model generally provides better imputation results on missing data than the state-of-the-art. We also provide a visualization approach for time-varying correlation across outputs in electrocoticography data and those estimates provide insight to understand the neural population dynamics.