2000 character limit reached
On Generalized Sub-Gaussian Canonical Processes and Their Applications
Published 27 Jan 2024 in math.PR | (2401.15314v2)
Abstract: We obtain the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d case, and we further get a tighter bound of concentration inequality through uniformly randomized techniques. A concentration inequality for general functions involving independent random variables is also derived as an extension. As for applications, we derive convergence results for principal component analysis and the Rademacher complexities method.
- V.V. Buldygin and Y. Kozachenko. Metric characterization of random variables and random processes, volume 188. American Mathematical Soc,2000.
- Y. Kozachenko and A. Olenko. Aliasing-truncation Errors in Sampling Approximations of sub-Gaussian Signals. IEEE Transactions on Information Theory. 5831 - 5838, 2016.
- R. Latała. Bounding suprema of canonical processes via convex hull. arXiv:2204.09463v1, 2022.
- S. Mendelson. Empirical processes with a bounded ψ1subscript𝜓1\psi_{1}italic_ψ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT diameter. Geom. Funct. Anal. 20 988– 1027, 2010
- S. Mendelson. Upper bounds on product and multiplier empirical processes. Stochastic Process. Appl. 126 3652–3680, 2016.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.