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Quantitative Laplace-type convergence results for exponential probability measures studied

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This paper explores quantitative Laplace-type convergence results for exponential probability measures, focusing on norm-like potentials. It establishes bounds between measures $\pi_\varepsilon$ and $\pi_0$ using Wasserstein distance under a generalized Jacobian invertibility condition. The research utilizes geometric measure theory tools and applies the findings to maximum entropy models and the convergence of Stochastic Gradient Langevin Dynamics at low temperatures for non-convex minimization. AI

IMPACT Provides theoretical underpinnings for understanding the behavior of optimization algorithms like SGLD in low-temperature, non-convex settings.

RANK_REASON This is a research paper published on arXiv concerning mathematical probability and its application to algorithms.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Quantitative Laplace-type convergence results for exponential probability measures studied

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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Valentin De Bortoli, Agn\`es Desolneux ·

    On quantitative Laplace-type convergence results for some exponential probability measures, with two applications

    arXiv:2110.12922v2 Announce Type: replace-cross Abstract: Laplace-type results characterize the limit of sequence of measures $(\pi_\varepsilon)_{\varepsilon >0}$ with density w.r.t the Lebesgue measure $(\mathrm{d} \pi_\varepsilon / \mathrm{d} \mathrm{Leb})(x) \propto \exp[-U(x)…

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