Reduced-Rank Linear Dynamical Systems

Linear Dynamical Systems are widely used to study the underlying patterns of multivariate time series. A basic assumption of these models is that high-dimensional time series can be characterized by some underlying, low-dimensional and time-varying latent states. However, existing approaches to LDS modeling mostly learn the latent space with a prescribed dimensionality. When dealing with short-length high-dimensional time series data, such models would be easily overfitted. We propose Reduced-Rank Linear Dynamical Systems (RRLDS), to automatically retrieve the intrinsic dimensionality of the latent space during model learning. Our key observation is that the rank of the dynamics matrix of LDS captures the intrinsic dimensionality, and the variational inference with a reduced-rank regularization finally leads to a concise, structured, and interpretable latent space. To enable our method to handle count-valued data, we introduce the dispersion-adaptive distribution to accommodate over-/ equal- / and under-dispersion nature of such data. Results on both simulated and experimental data demonstrate our model can robustly learn latent space from short-length, noisy, count-valued data and significantly improve the prediction performance over the state-of-the-art methods.