Learning Temporal Dependence from Time-Series Data with Latent Variables

TL;DR

This paper introduces a method to learn the causal graph of time-series data with hidden states and variable lags, demonstrating consistent estimation and practical effectiveness on synthetic and real data.

Contribution

It develops a novel estimator for latent-variable time-series models with variable lags, proving its consistency and showing practical improvements.

Findings

Estimator achieves consistent parameter recovery under generic conditions.

Practical adaptation improves performance on synthetic datasets.

Method demonstrates effectiveness on real-world time-series data.

Abstract

We consider the setting where a collection of time series, modeled as random processes, evolve in a causal manner, and one is interested in learning the graph governing the relationships of these processes. A special case of wide interest and applicability is the setting where the noise is Gaussian and relationships are Markov and linear. We study this setting with two additional features: firstly, each random process has a hidden (latent) state, which we use to model the internal memory possessed by the variables (similar to hidden Markov models). Secondly, each variable can depend on its latent memory state through a random lag (rather than a fixed lag), thus modeling memory recall with differing lags at distinct times. Under this setting, we develop an estimator and prove that under a genericity assumption, the parameters of the model can be learned consistently. We also propose a practical adaption of this estimator, which demonstrates significant performance gains in both synthetic and real-world datasets.