This talk is concerned with probability measures in high dimension that satisfy certain geometric convexity assumptions. Probability distributions on high ...

Maxwell's observation: The sphere's marginals are approximately gaussian (n → ∞). • What other distributions in high dimension.

Apr 24, 2010 · Abstract. We review recent advances in the understanding of probability measures with geometric characteristics on Rn , for large n.

PDF | We discuss metric, algorithmic and geometric issues related to broadly understood complexity of high dimensional convex sets. The specific topics.

We shall see that convexity conditions fit very well with the high dimensionality. Uniform measures on convex domains.

Duration: 1:05:37
Posted: Nov 1, 2022

and, since these geometric parameters of random convex bodies are random variables, their expectation, variance, or whether their value is of some order ...

Mar 25, 2019 · Theoretical analysis implies that convex penalization schemes have nearly optimal estimation properties in certain settings. However, in general ...

Description: This course will address the design of provably efficient algorithms for data processing that leverage prior information. We will focus on the ...

However, in general the gaps between statistically optimal estimation (with unbounded computational resources) and convex methods are poorly understood. We show ...