Finite-Sample Symmetric Mean Estimation with Fisher Information Rate

Speaker: Shivam Gupta , UT Austin

Date: Wednesday, October 04, 2023

Time: 4:00 PM to 5:00 PM Note: all times are in the Eastern Time Zone

Public: Yes

Location: 32-D507

Event Type: Seminar

Room Description: 32-D507

Host: Noah Golowich, MIT

Contact: Noah Golowich, nzg@csail.mit.edu

Relevant URL:

Speaker URL: https://shivamgupta2.github.io/

Speaker Photo:
None

Reminders to: theory-seminars@csail.mit.edu, seminars@csail.mit.edu

Reminder Subject: TALK: Shivam Gupta: Finite-Sample Symmetric Mean Estimation with Fisher Information Rate

Abstract: We consider the problem of estimating the mean of a $1$-dimensional distribution $f$ given $n$ i.i.d. samples. When $f$ is known up to shift, the classical maximum-likelihood estimate (MLE) is known to be optimal in the limit as $n \to \infty$: it is asymptotically normal with variance matching the Cramer-Rao lower bound of $\frac{1}{n \mathcal I}$ where $\mathcal I$ is the Fisher information of $f$. Furthermore, [Stone; 1975] showed that the same convergence can be achieved even when $f$ is \emph{unknown} but \emph{symmetric}. However, these results do not hold for finite $n$, or when $f$ varies with $n$ and failure probability $\delta$.

In this talk, I will present two recent works that together develop a finite sample theory for symmetric mean estimation in terms of Fisher Information. We show that for arbitrary (symmetric) $f$ and $n$, one can recover finite-sample guarantees based on the \emph{smoothed} Fisher information of $f$, where the smoothing radius decays with $n$.

Based on joint works with Jasper C.H. Lee, Eric Price, and Paul Valiant.

Research Areas:
Algorithms & Theory, AI & Machine Learning

Impact Areas:
Big Data

See other events that are part of the Algorithms and Complexity Seminar 2023.

Created by Noah Golowich at Friday, September 29, 2023 at 2:16 PM.