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Algorithmic Approaches to Statistical Estimation under Structural Constraints

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The area of inference under structural (or shape) constraints— that is, inference about a probability distribution under the constraint that its density function satisfies certain qualitative properties—is a classical topic in statistics and machine learning. Shape restricted inference has seen a recent surge of research activity, in part due to the ubiquity of structured distributions in the natural sciences. The hope is that, under such structural constraints, the quality of the resulting estimators may dramatically improve, both in terms of sample size and in terms of computational efficiency.

In this talk, we will describe a framework that yields new, provably efficient estimators for several natural and well-studied classes of distributions. Our approach relies on a single, unified algorithm that provides a fairly complete picture of the sample and computational complexities for fundamental inference tasks. The focus of the talk will be on density estimation (learning), but we may also discuss applications of these ideas to hypothesis testing.

This talk is part of the Statistics series.

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