Novel PDMPs using mirror maps enable unbiased sampling from distributions on convex sets while allowing exact subsampling and outperforming SDE methods.
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General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
LGD reaches Bayes optimality at optimal hyperparameters and admits an O(dh) pseudo-dimension bound for meta-learning hyperparameters on convex regression tasks.
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Piecewise Deterministic Sampling for Constrained Distributions
Novel PDMPs using mirror maps enable unbiased sampling from distributions on convex sets while allowing exact subsampling and outperforming SDE methods.
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Convergence rate of the occupation measure of classes of ergodic processes toward their invariant distribution in mean Wasserstein distance
General criteria extend L^p-mean Wasserstein convergence rates of occupation measures to non-stationary or non-Markovian ergodic processes under conditional convergence to equilibrium, with applications to Brownian diffusions and fractional Brownian driven SDEs.
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Generalization Guarantees on Data-Driven Tuning of Gradient Descent with Langevin Updates
LGD reaches Bayes optimality at optimal hyperparameters and admits an O(dh) pseudo-dimension bound for meta-learning hyperparameters on convex regression tasks.