Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Marsiglietti, Arnaud"'
Autor:
Marsiglietti, Arnaud, Pandey, Puja
In this note we explore how standard statistical distances are equivalent for discrete log-concave distributions. Distances include total variation distance, Wasserstein distance, and $f$-divergences.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2309.03197
A remarkable conjecture of Feige (2006) asserts that for any collection of $n$ independent non-negative random variables $X_1, X_2, \dots, X_n$, each with expectation at most $1$, $$ \mathbb{P}(X < \mathbb{E}[X] + 1) \geq \frac{1}{e}, $$ where $X = \
Externí odkaz:
http://arxiv.org/abs/2208.12702
Autor:
Marsiglietti, Arnaud, Melbourne, James
We utilize and extend a simple and classical mechanism, combining log-concavity and majorization in the convex order to derive moments, concentration, and entropy inequalities for certain classes of log-concave distributions.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2205.08293
Autor:
Marsiglietti, Arnaud, Pandey, Puja
We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total variation distance, Wasserstein distance, Kullback-Leibler distance and mor
Externí odkaz:
http://arxiv.org/abs/2112.09009
We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration bounds. As an application, we derive concentration bounds for the intri
Externí odkaz:
http://arxiv.org/abs/2104.05054
Two-sided bounds are explored for concentration functions and R\'enyi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.
Comment: 21 pages
Comment: 21 pages
Externí odkaz:
http://arxiv.org/abs/2007.11030
Autor:
Marsiglietti, Arnaud, Melbourne, James
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the integers. A functional analogue of this geometric inequality is derive
Externí odkaz:
http://arxiv.org/abs/2004.12005
We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/1903.03666
We investigate the role of convexity in R\'enyi entropy power inequalities. After proving that a general R\'enyi entropy power inequality in the style of Bobkov-Chistyakov (2015) fails when the R\'enyi parameter $r\in(0,1)$, we show that random vecto
Externí odkaz:
http://arxiv.org/abs/1901.10616
We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.
Comment: 20 pages
Comment: 20 pages
Externí odkaz:
http://arxiv.org/abs/1901.02984