##### Department of Mathematics,

University of California San Diego

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### Math 278B

## Amir Sagiv

#### Columbia University

## Sampling by Transport and the Approximation of Measures

##### Abstract:

Transportation of measure underlies many contemporary methods in machine learning and statistics. Sampling, which is a fundamental building block in computational science, can be done efficiently given an appropriate measure-transport map. We ask: what is the effect of using approximate maps in such algorithms?

We propose a new framework to analyze the approximation power of measure transport. This framework applies to existing algorithms, but also suggests new ones. At the core of our analysis is the theory of optimal transport regularity, approximation theory, and an emerging class of inequalities, previously studied in the context of uncertainty quantification (UQ).

### June 1, 2023

### 11:00 AM

APM 2402

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