# Parametric learning for directed graphical models

**Date:**February 24, 2022

**Time:**4:00 pm

**Room:**DBH 4011

**Speaker:**Leonard J. Schulman

**Abstract:**

The following problem has long been studied in the TCS literature: learn

a probability distribution on n bits which is known to be a mixture of k

distributions, in each of which the bits are independent. This (as a

parameter-identification problem) is intermediate in expressiveness

between the much simpler case of iid bits, and the much more ambitious

case in which the bits are not independent at all, but are related

through a Causal Bayesian Network. I’ll give an overview of a series of

works showing how to

(a) Reduce the network case to the independent case (by a conditioning

method),

(b) Reduce the independent case to the iid case (by an algorithm which

creates “synthetic bits”), and finally,

(c) Give upper and lower bounds for the iid case (the algorithm here is

the two-century-old method of Prony).

Based on joint works with Chaitanya Swamy (Waterloo), Yuval Rabani

(Hebrew U), Jian Li (Tsinghua), Spencer Gordon (Caltech) and Bijan

Mazaheri (Caltech)

**Bio:**

Bio: Leonard J. Schulman received the B.Sc. in Mathematics in 1988 and

the Ph.D. in Applied Mathematics in 1992, both from the Massachusetts

Institute of Technology. Since 2000 he has been on the faculty of the

California Institute of Technology. He has also held appointments at UC

Berkeley, the Weizmann Institute of Science, the Georgia Institute of

Technology, and the Israel Institute for Advanced Studies.