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Preservation of log-concavity on summation
Published 2006“…We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. …”
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Infinite log-concavity: developments and conjectures
Published 2009-01-01Subjects: Get full text
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Geometry of Log-Concave Density Estimation
Published 2021“…We focus on densities on R d that are log-concave, and we study geometric properties of the maximum likelihood estimator (MLE) for weighted samples. …”
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The Minimal Perimeter of a Log-Concave Function
Published 2020-08-01Subjects: Get full text
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Entropy and Information jump for log-concave vectors
Published 2023-02-01“…We extend the result of Ball and Nguyen on the jump of entropy under convolution for log-concave random vectors. We show that the result holds for any pair of vectors (not necessarily identically distributed) and that a similar inequality holds for the Fisher information, thus providing a quantitative Blachmann–Stam inequality.…”
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An optimization perspective on log-concave sampling and beyond
Published 2023“…Some highlights include: a new analysis of the proximal sampler, taking inspiration from the proximal point algorithm in optimization; an improved and sharp analysis of the Metropolis-adjusted Langevin algorithm, yielding new state-of-the-art guarantees for high-accuracy log-concave sampling; the first lower bounds for the complexity of log-concave sampling; an analysis of mirror Langevin Monte Carlo for constrained sampling; and the development of a theory of approximate first-order stationarity in non-log-concave sampling. …”
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7
Query lower bounds for log-concave sampling
Published 2024“…Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one. …”
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Log-concavity property for some well-known distributions
Published 2011-12-01Subjects: “…Log-concavity…”
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Unimodal, log-concave and Pólya frequency sequences in combinatorics
Published 2016Get full text
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10
Flexible modeling of diversity with strongly log-concave distributions
Published 2021“…All rights reserved. Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. …”
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Flexible modeling of diversity with strongly log-concave distributions
Published 2022“…All rights reserved. Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. …”
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logcondens: Computations Related to Univariate Log-Concave Density Estimation
Published 2011-03-01Subjects: “…log-concave…”
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Maximum Likelihood Estimation for Totally Positive Log‐Concave Densities
Published 2021“…In both cases we also assume log-concavity in order to ensure boundedness of the likelihood function. …”
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A new computational framework for log-concave density estimation
Published 2024“…In statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. …”
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Maximum likelihood estimation of a multidimensional log-concave density
Published 2008“…Let X_1, ..., X_n be independent and identically distributed random vectors with a log-concave (Lebesgue) density f. We first prove that, with probability one, there exists a unique maximum likelihood estimator of f. …”
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A Lower Bound on the Differential Entropy of Log-Concave Random Vectors with Applications
Published 2018-03-01Subjects: Get full text
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Log-concavity property of the error probability with application to local bounds for wireless communications
Published 2010“…We propose an analytical framework based on the log-concavity property of the EP which we prove for a wide family of multidimensional modulation formats in the presence of Gaussian disturbances and fading. …”
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Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density
Published 2009“…We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. …”
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A study on the spectral properties of covariance type matrices with isotropic log-concave column vectors
Published 2024-01-01Get full text
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