Learning Temporal Dependence from Time-Series Data with Latent Variables
This work addresses the challenge of modeling temporal dependencies with latent memory and variable lags for applications in time-series analysis, representing an incremental advance over existing methods.
The paper tackles the problem of learning causal graphs from time-series data with latent variables and random lags, developing an estimator that achieves consistent parameter learning under genericity assumptions and shows significant performance gains in synthetic and real-world datasets.
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.