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B0992
**Title: **Functional differential graph estimation
**Authors: **Boxin Zhao - University of Chicago (United States)

Y Samuel Wang - Cornell University (United States)**[presenting]**

Mladen Kolar - University of Chicago (United States)

**Abstract: **The problem of estimating the difference between two functional undirected graphical models with shared structures is considered. In many applications, data are naturally regarded as a vector of random functions rather than a vector of scalars. For example, electroencephalography (EEG) data are more appropriately treated as functions of time. In these problems, not only can the number of functions measured per sample be large, but each function is itself an infinite-dimensional object, making estimation of model parameters challenging. This is further complicated by the fact that the curves are usually only observed at discrete time points. We first define a functional differential graph that captures differences between two functional graphical models and formally characterize when the functional differential graph is well defined. We then propose a method, FuDGE, that directly estimates the functional differential graph without first estimating each individual graph. This is particularly beneficial in settings where the individual graphs are dense, but the differential graph is sparse. We show that FuDGE consistently estimates the functional differential graph even in a high-dimensional setting for both discretely observed and fully observed function paths.

Y Samuel Wang - Cornell University (United States)

Mladen Kolar - University of Chicago (United States)