Feb. 9, 2024, 5:43 a.m. | Ingvar Ziemann Stephen Tu George J. Pappas Nikolai Matni

cs.LG updates on arXiv.org arxiv.org

In this work, we study statistical learning with dependent ($\beta$-mixing) data and square loss in a hypothesis class $\mathscr{F}\subset L_{\Psi_p}$ where $\Psi_p$ is the norm $\|f\|_{\Psi_p} \triangleq \sup_{m\geq 1} m^{-1/p} \|f\|_{L^m} $ for some $p\in [2,\infty]$. Our inquiry is motivated by the search for a sharp noise interaction term, or variance proxy, in learning with dependent data. Absent any realizability assumption, typical non-asymptotic results exhibit variance proxies that are deflated \emph{multiplicatively} by the mixing time of the underlying covariates process. …

beta class cs.lg data hypothesis loss norm sample search square statistical stat.ml study theory work

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