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 , the causal influence from to is meant to represent how much better we can predict given its past and the past of than if we were given the past of 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.
- “A Modularized Efficient Framework for Non-Markov Time Series Estimation”, IEEE Transactions on Signal Processing, In Press. [arXiv] [Code Ocean]
- “Efficient Low-Rank Spectrotemporal Decomposition using ADMM”, IEEE Statistical Signal Processing Workshop, June 2016. [IEEE Xplore]