# Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo

arXiv: https://arxiv.org/abs/2406.04796 · HTML: https://mlsanity.com/paper/2406.04796/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 79 references that are in the map.
- First posted on arXiv 7 Jun 2024.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)](https://mlsanity.com/paper/1503.01057/) (2015)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Approximate Inference for Fully Bayesian Gaussian Process Regression](https://mlsanity.com/paper/1912.13440/) (2019)
- [Langevin diffusions and the Metropolis-adjusted Langevin algorithm](https://mlsanity.com/paper/1309.2983/) (2013)
- [Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors](https://mlsanity.com/paper/2006.12335/) (2020)
- [Marginalizing Gaussian Process Hyperparameters using Sequential Monte Carlo](https://mlsanity.com/paper/1502.01908/) (2015)
- [Scalable Bayesian dynamic covariance modeling with variational Wishart and inverse Wishart processes](https://mlsanity.com/paper/1906.09360/) (2019)
- [Stochastic Differential Equations with Variational Wishart Diffusions](https://mlsanity.com/paper/2006.14895/) (2020)
- [Generalized Wishart processes for interpolation over diffusion tensor fields](https://mlsanity.com/paper/1606.07968/) (2016)
- [Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes](https://mlsanity.com/paper/2207.06544/) (2022)

## Abstract (arXiv)

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics on covariance