Bayesian optimization, seeded with quasi-Monte Carlo directions for the hybrid variants, gives sliced Wasserstein estimates that are competitive with or slightly better than prior state of the art on three optimization-in-the-loop benchmarks.
Weak independence of events and the converse of the Borel--Cantelli Lemma
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abstract
The converse of the Borel-Cantelli Lemma states that if $\{A_i\}_{i=1}^\infty$ is a sequence of independent events such that $\sum P(A_i)=\infty$, then almost surely infinitely many of these events will occur. Erd\H os and R\'enyi proved that it is sufficient to weaken the condition of independence to pairwise independence. In this paper we study various conditions of weak independence that imply the conclusion of the converse of the Borel--Cantelli Lemma. We will determine the exact implicational relationship among these conditions.
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Efficient Sliced Wasserstein Distance Computation via Adaptive Bayesian Optimization
Bayesian optimization, seeded with quasi-Monte Carlo directions for the hybrid variants, gives sliced Wasserstein estimates that are competitive with or slightly better than prior state of the art on three optimization-in-the-loop benchmarks.