# Inferring Latent dimension of Linear Dynamical System with Minimum Description Length

## TL;DR

This paper introduces a minimum description length-based criterion for automatically inferring the optimal latent dimension of linear dynamical systems, addressing the challenge of manual specification and improving model selection.

## Contribution

It extends the minimum description length principle to explicitly incorporate latent structure in linear dynamical systems for better model selection.

## Key findings

- Effective in selecting latent dimensions for univariate sequences
- Demonstrates improved model training performance
- Validates approach on multivariate data

## Abstract

Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability needs to be manually specified. It can be demonstrated that a lower-order model class could be totally nested into a higher-order class, and the corresponding likelihood is nondecreasing. Hence, criterion built on the likelihood is not appropriate for model selection. This paper addresses the issue and proposes a criterion for linear dynamical system based on the principle of minimum description length. The latent structure, which is omitted in previous work, is explicitly considered in this newly proposed criterion. Our work extends the principle of minimum description length and demonstrates its effectiveness in the tasks of model training. The experiments on both univariate and multivariate sequences confirm the good performance of our newly proposed method.