# Nonparametric Bayesian Sparse Graph Linear Dynamical Systems

## TL;DR

This paper introduces a nonparametric Bayesian sparse graph linear dynamical system (SGLDS) that models multivariate sequential data using an infinite-dimensional sparse graph, effectively capturing various dynamical states.

## Contribution

It proposes a novel SGLDS framework combining Bernoulli-Poisson link and gamma process to model state transitions with sparsity and categorizes states into dynamic, non-dynamic, and different dynamical types.

## Key findings

- Demonstrates state-of-the-art performance on synthetic data
- Effectively distinguishes between different types of dynamical states
- Models complex time series with sparse, interpretable structures

## Abstract

A nonparametric Bayesian sparse graph linear dynamical system (SGLDS) is proposed to model sequentially observed multivariate data. SGLDS uses the Bernoulli-Poisson link together with a gamma process to generate an infinite dimensional sparse random graph to model state transitions. Depending on the sparsity pattern of the corresponding row and column of the graph affinity matrix, a latent state of SGLDS can be categorized as either a non-dynamic state or a dynamic one. A normal-gamma construction is used to shrink the energy captured by the non-dynamic states, while the dynamic states can be further categorized into live, absorbing, or noise-injection states, which capture different types of dynamical components of the underlying time series. The state-of-the-art performance of SGLDS is demonstrated with experiments on both synthetic and real data.