Explore the fascinating world of multivariate totally positive of order two (MTP2) probability distributions in this comprehensive colloquium talk. Delve into the intriguing properties of MTP2 distributions and their applications in various fields, from ferromagnetism to phylogenetics and finance. Learn about conditional independence, graphical models, and how maximum likelihood estimation for MTP2 exponential families leads to sparsity in Gaussian or Ising models without tuning parameters. Discover the challenges of non-parametric density estimation under MTP2 and its piecewise linear function solution. Gain insights into practical applications, including covariance matrix estimation for portfolio selection and learning gene regulatory networks. The talk covers motivation, theoretical foundations, examples, and concludes with an engaging Q&A session.
Your Dreams May Come True with MTP2 by Caroline Uhler
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
DATE: Mon, 22 July 2019, 15:00 to
Your Dreams May Come True with MTP2
Motivation
Positive dependence and MTP2 distributions
Properties of MTP2 distribution
No Yule-Simpson Paradox under MTP2!
Discrete MTP2 distributions
Example: EPH-gestosis
Gaussian MTP 2 distributions
Example: Stock prices
MTP2 constraints are often implicit
Example: EPH-gestosis
Remainder of this talk: Density estimation under MTP2
Negative dependence: What this talk is not about...
MTP2 exponential families
ML Estimation for Gaussian MTP2 distributions
ML estimation for ferromagnetic MTP2 Ising models
Density estimation
Shape-constrained density estimation
Log-concave density estimation
Existence, uniqueness and shape of the MLE under MTP2
Shape of the MLE
Application: Portfolio selection
Conclusions
References
I am recruiting...
Conference on Genomes and Al
Q&A
Taught by
International Centre for Theoretical Sciences
