Time-varying Autoregression with Low Rank Tensors
This work addresses the challenge of uncovering interpretable spatiotemporal structure in high-dimensional time-series data, though it appears incremental as it builds on existing low-rank tensor methods with specific optimizations.
The authors tackled the problem of learning parsimonious time-varying autoregressive models from multivariate time-series by proposing a windowed technique that models system matrices as a low-rank tensor, demonstrating its ability to identify true rank in synthetic examples and showing superior scalability on real-world datasets like worm behavior and monkey brain data.
We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex optimization. In each time window, we assume the data follow a linear model parameterized by a system matrix, and we model this stack of potentially different system matrices as a low rank tensor. Because of its structure, the model is scalable to high-dimensional data and can easily incorporate priors such as smoothness over time. We find the components of the tensor using alternating minimization and prove that any stationary point of this algorithm is a local minimum. We demonstrate on a synthetic example that our method identifies the true rank of a switching linear system in the presence of noise. We illustrate our model's utility and superior scalability over extant methods when applied to several synthetic and real-world example: two types of time-varying linear systems, worm behavior, sea surface temperature, and monkey brain datasets.