5 papers
Upper and Lower Bounds on Expected Soft Maxima of Gaussian Processes
Yifeng Chu, Maxim Raginsky
We obtain upper and lower bounds for "smoothed" versions of the expected supremum of centered Gaussian processes with finite or countable index sets. These so-called soft maxima ar…
Talagrand Meets Talagrand: Upper and Lower Bounds on Expected Soft Maxima of Gaussian Processes with Finite Index Sets
Yifeng Chu, Maxim Raginsky
Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer scienc…
Majorizing Measures, Codes, and Information
Yifeng Chu, Maxim Raginsky
The majorizing measure theorem of Fernique and Talagrand is a fundamental result in the theory of random processes. It relates the boundedness of random processes indexed by elemen…
A unified framework for information-theoretic generalization bounds
Yifeng Chu, Maxim Raginsky
This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation…
A Chain Rule for the Expected Suprema of Bernoulli Processes
Yifeng Chu, Maxim Raginsky
We obtain an upper bound on the expected supremum of a Bernoulli process indexed by the image of an index set under a uniformly Lipschitz function class in terms of properties of t…