|Speaker :||Prof. Ravi Mazumdar|
|University of Waterloo|
|Time:||2:00 pm - 4:00 pm|
|Location:||LINCS Meeting Room 40|
Suppose we have N time series available where one time-series could be causally dependent on others. For example, such dependence can be found in economic data or weather data. The goal is to recover the directed causality graph that links these time series. As is well known causality and correlation are not the same and thus one of the important questions is how to address this issue. There are several frameworks such as directed information, the notion of Granger causality, etc. However working with directed information requires too much a priori knowledge about the structure of the time series that is unavailable.
In this talk I will show how the notion of Granger causality can be tied to Wiener filtering that allows us to recover a directed random graph whose edges are represented by the innovations filters. This approach as well as the directed information approach assuming Gaussianity however are not very practical and so a pairwise approach is taken. This suffers from over estimation of directed edges of the causality graph. To address this issue we show how it is possible to consider a sparse problem based on a mixed L1 – H1 norm that leads to an approach for selecting edges characterized by complex polynomials. This results in a convex optimization problem. We show that such an approach provides satisfactory results on synthetic examples and uncovers interesting causal dependencies when used on real time series data.
Joint work with S. Datta Gupta (University of Waterloo, Canada).