University of Cambridge > > Statistics > Constrained and Localized Nonparametric Estimation and Optimization

Constrained and Localized Nonparametric Estimation and Optimization

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact Quentin Berthet.

We present work on two nonstandard frameworks for minimax analysis.

For the first problem, imagine that I estimate a statistical model from data, and then want to share my model with you. But we are communicating over a resource constrained channel. By sending lots of bits, I can communicate my model accurately, with little loss in statistical risk. Sending a small number of bits will incur some excess risk. What can we say about the tradeoff between statistical risk and the communication constraints? This is a type of rate distortion and constrained minimax problem, for which we provide a sharp analysis in certain nonparametric settings.

The second problem starts with the question “how difficult is it to minimize a specific convex function?” This is tricky to formalize traditional complexity analysis is expressed in terms of the worst case over a large class of instances. We extend the classical minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. This uses a computational analogue of the modulus of continuity that is central to statistical minimax analysis, which serves as a computational analogue of Fisher information.

Joint work with Sabyasachi Chatterjee, John Duchi, and Yuancheng Zhu.

This talk is part of the Statistics series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity