318 Hanes Hall, CB #3260 Chapel Hill, NC 27599-3260
919-962-1329
Loading Events

STOR Colloquium: Elina Robeva, MIT

February 15, 2019 @ 3:30 pm - 4:30 pm

Elina Robeva
Massachusetts Institute of Technology


Maximum likelihood estimation under total positivity

 

Nonparametric density estimation is a challenging statistical problem — in general the maximum likelihood estimate (MLE) does not even exist! Introducing shape constraints allows a path forward. In this talk I will discuss non-parametric density estimation under total positivity (i.e. log-supermodularity). Though they possess very special structure, totally positive random variables are quite common in real world data and exhibit appealing mathematical properties. Given i.i.d. samples from a totally positive and log-concave distribution, we prove that the MLE exists with probability one if there are at least 3 samples. We characterize the domain of the MLE, and give algorithms to compute it. If the observations are 2-dimensional or binary, we show that the logarithm of the MLE is a piecewise linear function and can be computed via a certain convex program. Finally, I will discuss statistical guarantees for the convergence of the MLE, and will conclude with a variety of further research directions.

 

Share This Event

  • This event has passed.

Details

Date:
February 15, 2019
Time:
3:30 pm - 4:30 pm
Event Categories:
,

Venue

120 Hanes Hall
Hanes Hall
Chapel Hill, NC 27599 United States