Time-Varying Causal Inference
We consider the questions:
- Do two observed time series have a causal influence on one another?
- How do these influences change over time?
Using a Granger causality viewpoint, at every time t, the causal influence from X to Y is meant to represent how much better we can predict Y given its past and the past of X than if we were given the past of Y alone. To actually acquire these measures, we leverage tools in sequential prediction and directed information.
Non-Linear / Non-Markov Latent Time-Series Estimation
We consider the problem of estimating a latent multi-dimensional time-series given noisy measurements and knowledge of the dynamics of the signal. In the case of a Markov signal with linear dynamics and Gaussian measurements, the problem can be solved using the Kalman filter.
We consider the class of problems where the underlying signal is non-Markov and/or the measurements obey and arbitrary log-concave likelihood model. We propose a framework that uses the Alternating Direction Method of Multipliers to decompose problems of this nature into smaller, easy to solve subproblems.
An application of this method to acquire low-rank spectrotemporal decompositions was published at the IEEE Workshop on Statistical Signal Processing in 2016 and can be found here.