Preservation of log-concavity on summation by Johnson, O, Goldschmidt, C

“…We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. …”

Infinite log-concavity: developments and conjectures by Peter R. W. McNamara, Bruce E. Sagan

Subjects: Get full text

Geometry of Log-Concave Density Estimation by Robeva, Elina, Sturmfels, Bernd, Uhler, Caroline

“…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. …”
Get full text

The Minimal Perimeter of a Log-Concave Function by Niufa Fang, Zengle Zhang

Subjects: Get full text

Entropy and Information jump for log-concave vectors by Bizeul, Pierre

“…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.…”
Get full text

An optimization perspective on log-concave sampling and beyond by Chewi, Sinho

“…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. …”
Get full text

Query lower bounds for log-concave sampling by Chewi, Sinho, de Dios Pont, Jaume, Li, Jerry, Lu, Chen, Narayanan, Shyam

“…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. …”
Get full text

Log-concavity property for some well-known distributions by G. R. Mohtashami Borzadaran, H. A. Mohtashami Borzadaran

Subjects: “…Log-concavity…”
Get full text

Unimodal, log-concave and Pólya frequency sequences in combinatorics by Brenti, Francesco, 1960-

Get full text

Flexible modeling of diversity with strongly log-concave distributions by Robinson, J, Sra, S, Jegelka, S

“…All rights reserved. Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. …”
Get full text

Flexible modeling of diversity with strongly log-concave distributions by Robinson, Joshua, Sra, Suvrit, Jegelka, Stefanie Sabrina

“…All rights reserved. Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. …”
Get full text

logcondens: Computations Related to Univariate Log-Concave Density Estimation by Lutz Dümbgen, Kaspar Rufibach

Subjects: “…log-concave…”
Get full text

Maximum Likelihood Estimation for Totally Positive Log‐Concave Densities by Robeva, Elina, Uhler, Caroline

“…In both cases we also assume log-concavity in order to ensure boundedness of the likelihood function. …”
Get full text

A new computational framework for log-concave density estimation by Chen, Wenyu, Mazumder, Rahul, Samworth, Richard J.

“…In statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. …”
Get full text

The f-vector of a representable-matroid complex is log-concave by Lenz, M

Maximum likelihood estimation of a multidimensional log-concave density by Cule, M, Samworth, R, Stewart, M

“…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. …”

A Lower Bound on the Differential Entropy of Log-Concave Random Vectors with Applications by Arnaud Marsiglietti, Victoria Kostina

Subjects: Get full text

Log-concavity property of the error probability with application to local bounds for wireless communications by Tralli, V., Sidenko, S., Panchenko, Dmitry A., Conti, Andrea

“…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. …”
Get full text
Get full text

Theoretical properties of the log-concave maximum likelihood estimator of a multidimensional density by Cule, M, Samworth, R

“…We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. …”

A study on the spectral properties of covariance type matrices with isotropic log-concave column vectors by Shaojia Jin, Zhanwen Shi

Get full text