arXiv Machine Learning By Patrick Forr\'e

A Direct Route to Markov Chain Convergence via Asymptotic Equivalence with the Target

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arXiv:2608. 03353v1 Announce Type: cross Abstract: For a Markov kernel $T$ with an invariant probability measure $\pi$, we give a self-contained proof of the Markov chain convergence theorem via a criterion called asymptotic equivalence with the target.

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arXiv Machine Learning
1d ago

Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run

arXiv:2608. 16878v1 Announce Type: cross Abstract: For any convex body $\mathcal{K}\subset\mathbb{R}^{n}$ containing a unit ball, the spectral gap of Hit-and-Run is $\Omega(1/(n^2 C_{\mathsf{PI}}))$, where $C_{\mathsf{PI}}$ is the Poincar\'e constant of the uniform distribution $\pi$ over $\mathcal{K}$.

By Yunbum Kook, Santosh S. Vempala