|
Activity Number:
|
146
- Statistical Physics, Information Theory, and Statistics
|
|
Type:
|
Invited
|
|
Date/Time:
|
Monday, July 30, 2018 : 10:30 AM to 12:20 PM
|
|
Sponsor:
|
IMS
|
|
Abstract #326639
|
|
|
Title:
|
Additivity of Information in Multilayer Networks via Additive Gaussian Noise Transforms
|
|
Author(s):
|
Galen Reeves*
|
|
Companies:
|
Duke University
|
|
Keywords:
|
mulitlayer networks;
phase transitions;
statistical physics;
information theory
|
|
Abstract:
|
Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear functions are defined by information channels. These models have gained great popularity due to their ability to characterize complex probabilistic relationships arising in a wide variety of inference problems. In this talk, we will describe a new method for analyzing the fundamental limits of statistical inference in settings where the model is known. The validity of our method can be established in a number of settings and is conjectured to hold more generally. A key assumption made throughout is that the matrices are drawn randomly from orthogonally invariant distributions. Our method yields explicit formulas for 1) the mutual information; 2) the minimum mean-squared error (MMSE); 3) the existence and locations of certain phase-transitions with respect to the problem parameters; and 4) the stationary points for the state evolution of approximate message passing algorithms.
|
Authors who are presenting talks have a * after their name.
Back to the full JSM 2018 program
|
