Change Detection

Change point detection and localization is a classical problem in time series analysis, in which we record a series of measurements and wish to determine whether and at what time(s) the underlying generative model has changed. Such techniques are widely used in financial analysis, national security settings, and health monitoring, among other applications. In our setting, we are interested in determining times at which a sequence of signals, denoted β_ 1,β_ 2,…, exhibits a change. For instance, if there were a single change point at time t=η, then our model might be that the β_ t’s are drawn from a distribution F1 for t < η and from a different distribution F2 for t > η, and our goal is to estimate η, potentially with limited information about the distributions F1 and F2. Furthermore, in many settings we do not get to observe the β’s directly, but rather through linear projections or through their effect on an autoregressive process. Accounting for the high-dimensional nature of signals, complex observation models, and the non-parametric nature of the underlying distributions changes poses a major open problem actively being addressed by my group.

Detecting changes in visual streams:

Detecting changes in network structure: