Appears in collection : 2016 - T1 - WS4 - Inference problems theme

In this talk, I will focus on the problem of density estimation, i. e. , how to estimate (learn) a probability distribution based on random samples. I will describe a sample-optimal and computationally efficient algorithm to learn univariate distributions that are well-approximated by piecewise polynomial density functions. As a consequence of this algorithm, we obtain the first (near-)sample optimal andear-linear time density estimators for a wide range of well-studied structured distribution families. If time permits, I will mention applications of the underlying algorithmic ideas to other inference tasks (e. g. , regression). (Joint work with J. Acharya, J. Li, and L. Schmidt. )