Estimation and Inference for Differential Networks




Siegel Hall, Room 118

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Department of Applied Mathematics




Mladen Kolar
Booth School of Business, University of Chicago







We present a recent line of work on estimating differential networks
and conducting statistical inference about parameters in a
high-dimensional setting. First, we consider a Gaussian setting and
show how to directly learn the difference between the graph
structures. A debiasing procedure will be presented for construction
of an asymptotically normal estimator of the difference. Next,
building on the first part, we show how to learn the difference
between two graphical models with latent variables. Linear convergence
rate is established for an alternating gradient descent procedure with
correct initialization. Simulation studies illustrate performance of
the procedure. We also illustrate the procedure on an application in
neuroscience. Finally, we will discuss how to do statistical inference
on the differential networks when data are not Gaussian.