The Experts below are selected from a list of 2700 Experts worldwide ranked by ideXlab platform
Mokshay Madiman - One of the best experts on this subject based on the ideXlab platform.
-
An Exact Upper Bound on the L p Lebesgue Constant and The ∞-Rényi Entropy Power Inequality for Integer Valued Random Variables.
arXiv: Functional Analysis, 2018Co-Authors: Peng Xu, Mokshay Madiman, James MelbourneAbstract:In this paper, we proved an exact asymptotically sharp upper bound of the $L^p$ Lebesgue Constant (i.e. the $L^p$ norm of Dirichlet kernel) for $p\ge 2$. As an application, we also verified the implication of a new $\infty $-R\'enyi entropy Power Inequality for integer valued random variables.
-
A min-entropy Power Inequality for groups
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: Peng Xu, James Melbourne, Mokshay MadimanAbstract:We develop a general notion of rearrangement for certain metric groups, and prove a Hardy-Littlewood type Inequality. Combining this with a characterization of the extreme points of the set of probability measures with bounded densities with respect to a reference measure, we establish a general min-entropy Inequality for convolutions. Special attention is paid to the integers where a min-entropy Power Inequality is conjectured and a partial result proved.
-
ISIT - A min-entropy Power Inequality for groups
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: Peng Xu, James Melbourne, Mokshay MadimanAbstract:We develop a general notion of rearrangement for certain metric groups, and prove a Hardy-Littlewood type Inequality. Combining this with a characterization of the extreme points of the set of probability measures with bounded densities with respect to a reference measure, we establish a general min-entropy Inequality for convolutions. Special attention is paid to the integers where a min-entropy Power Inequality is conjectured and a partial result proved.
-
Reverse entropy Power inequalities for s-concave densities
2016 IEEE International Symposium on Information Theory (ISIT), 2016Co-Authors: Peng Xu, James Melbourne, Mokshay MadimanAbstract:We explore conditions under which a reverse Rényi entropy Power Inequality holds for random vectors with s-concave densities, and also discuss connections with Convex Geometry.
-
A discrete entropy Power Inequality for uniform distributions
2015 IEEE International Symposium on Information Theory (ISIT), 2015Co-Authors: Mokshay MadimanAbstract:We explore various tempting conjectures for discrete entropy Power inequalities on the integers, proving both positive results for interesting subclasses of distributions and negative results that falsify some of the conjectures in general. In particular, we show that an Inequality very similar to the usual entropy Power Inequality holds for uniform distributions over finite subsets of the integers.
Sergey G. Bobkov - One of the best experts on this subject based on the ideXlab platform.
-
variants of the entropy Power Inequality
IEEE Transactions on Information Theory, 2017Co-Authors: Sergey G. Bobkov, Arnaud MarsigliettiAbstract:An extension of the entropy Power Inequality to the form $N_{r}^\alpha (X+Y) \geq N_{r}^\alpha (X) + N_{r}^\alpha (Y)$ with arbitrary independent summands $X$ and $Y$ in $ {\mathbb {R}}^{n}$ is obtained for the Renyi entropy and Powers $\alpha \geq ~(r+1)/2$ .
-
Variants of the Entropy Power Inequality
IEEE Transactions on Information Theory, 2017Co-Authors: Sergey G. Bobkov, Arnaud MarsigliettiAbstract:An extension of the entropy Power Inequality to the form Nrα (X + Y) ≥ Nrα (X) + Nrα (Y) with arbitrary independent summands X and Y in Rn is obtained for the Rényi entropy and Powers α ≥ (r + 1)/2.
-
entropy Power Inequality for the renyi entropy
IEEE Transactions on Information Theory, 2015Co-Authors: Sergey G. Bobkov, Gennadiy P. ChistyakovAbstract:The classical entropy Power Inequality is extended to the Renyi entropy. We also discuss the question of the existence of the entropy for sums of independent random variables.
-
Entropy Power Inequality for the Rényi Entropy
IEEE Transactions on Information Theory, 2015Co-Authors: Sergey G. Bobkov, Gennadiy P. ChistyakovAbstract:The classical entropy Power Inequality is extended to the Rényi entropy. We also discuss the question of the existence of the entropy for sums of independent random variables.
-
on the problem of reversibility of the entropy Power Inequality
arXiv: Functional Analysis, 2013Co-Authors: Sergey G. Bobkov, Mokshay MadimanAbstract:As was shown recently by the authors, the entropy Power Inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved that reversibility is impossible over the whole class of convex probability distributions. Related phenomena for identically distributed summands are also discussed.
Thomas A Courtade - One of the best experts on this subject based on the ideXlab platform.
-
counterexample to the vector generalization of costa s entropy Power Inequality and partial resolution
IEEE Transactions on Information Theory, 2018Co-Authors: Thomas A Courtade, Yaochen WuAbstract:We give a counterexample to the vector generalization of Costa’s entropy Power Inequality due to Liu et al. In particular, the claimed Inequality can fail if the matrix-valued parameter in the convex combination does not commute with the covariance of the additive Gaussian noise. Conversely, the Inequality holds if these two matrices commute.
-
A Strong Entropy Power Inequality
IEEE Transactions on Information Theory, 2018Co-Authors: Thomas A CourtadeAbstract:When one of the random summands is Gaussian, we sharpen the entropy Power Inequality (EPI) in terms of the strong data processing function for Gaussian channels. Among other consequences, this `strong' EPI generalizes the vector extension of Costa's EPI to non-Gaussian channels in a precise sense. This leads to a new reverse EPI and, as a corollary, sharpens Stam's uncertainty principle relating entropy Power and Fisher information (or, equivalently, Gross' logarithmic Sobolev Inequality). Applications to network information theory are also given, including a short self-contained proof of the rate region for the two-encoder quadratic Gaussian source coding problem and a new outer bound for the one-sided Gaussian interference channel.
-
Quantitative Stability of the Entropy Power Inequality
IEEE Transactions on Information Theory, 2018Co-Authors: Thomas A Courtade, Max Fathi, Ashwin PananjadyAbstract:We establish quantitative stability results for the entropy Power Inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Kantorovich-Wasserstein distance. Furthermore, if one of the densities is Gaussian and the other is log-concave, or more generally has positive spectral gap, then the deficit in the EPI can be controlled in terms of the L1-Kantorovich-Wasserstein distance or relative entropy, respectively. As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Kantorovich-Wasserstein distance when densities are uniformly log-concave on sets of measure arbitrarily close to one. Our stability results can be extended to non-log-concave densities, provided certain regularity conditions are met. The proofs are based on mass transportation.
-
Counterexample to the Vector Generalization of Costa’s Entropy Power Inequality, and Partial Resolution
IEEE Transactions on Information Theory, 2018Co-Authors: Thomas A Courtade, Yaochen WuAbstract:We give a counterexample to the vector generalization of Costa's entropy Power Inequality due to Liu et al. In particular, the claimed Inequality can fail if the matrix-valued parameter in the convex combination does not commute with the covariance of the additive Gaussian noise. Conversely, the Inequality holds if these two matrices commute.
-
Wasserstein stability of the entropy Power Inequality for log-concave random vectors
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: Thomas A Courtade, Max Fathi, Ashwin PananjadyAbstract:We establish quantitative stability results for the entropy Power Inequality (EPI) in arbitrary dimension. Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the densities is log-concave and the other is Gaussian, then the deficit in the EPI can be controlled in terms of the L1-Wasserstein distance. As a counterpoint, an example shows that the EPI can be unstable with respect to the quadratic Wasserstein distance even if densities are uniformly log-concave on sets of measure arbitrarily close to one. The proofs are based on optimal transportation.
Olivier Rioul - One of the best experts on this subject based on the ideXlab platform.
-
Equality in the Matrix Entropy-Power Inequality and Blind Separation of Real and Complex sources
2019 IEEE International Symposium on Information Theory (ISIT), 2019Co-Authors: Olivier Rioul, Ram ZamirAbstract:The matrix version of the entropy-Power Inequality for real or complex coefficients and variables is proved using a transportation argument that easily settles the equality case. An application to blind source extraction is given.
-
ISIT - Equality in the Matrix Entropy-Power Inequality and Blind Separation of Real and Complex sources
2019 IEEE International Symposium on Information Theory (ISIT), 2019Co-Authors: Olivier Rioul, Ram ZamirAbstract:The matrix version of the entropy-Power Inequality for real or complex coefficients and variables is proved using a transportation argument that easily settles the equality case. An application to blind source extraction is given.
-
yet another proof of the entropy Power Inequality
IEEE Transactions on Information Theory, 2017Co-Authors: Olivier RioulAbstract:Yet another simple proof of the entropy Power Inequality is given, which avoids both the integration over a path of Gaussian perturbation and the use of Young’s Inequality with sharp constant or Renyi entropies. The proof is based on a simple change of variables, is formally identical in one and several dimensions, and easily settles the equality case.
-
ITA - Optimal transportation to the entropy-Power Inequality
2017 Information Theory and Applications Workshop (ITA), 2017Co-Authors: Olivier RioulAbstract:We present a simple proof of the entropy-Power Inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse Inequality involving a conditional differential entropy which has its own interest. It can also be generalized in various ways. The equality case is easily captured by this method and the proof is formally identical in one and several dimensions.
-
Optimal transportation to the entropy-Power Inequality
2017 Information Theory and Applications Workshop (ITA), 2017Co-Authors: Olivier RioulAbstract:We present a simple proof of the entropy-Power Inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse Inequality involving a conditional differential entropy which has its own interest. It can also be generalized in various ways. The equality case is easily captured by this method and the proof is formally identical in one and several dimensions.
Arnaud Marsiglietti - One of the best experts on this subject based on the ideXlab platform.
-
ISIT - A Renyi Entropy Power Inequality for Log-Concave Vectors and Parameters in [0, 1]
2018 IEEE International Symposium on Information Theory (ISIT), 2018Co-Authors: Arnaud Marsiglietti, James MelbourneAbstract:Using a sharp version of the reverse Young Inequality, and a Renyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors derive a Renyi entropy Power Inequality for log-concave random vectors when Renyi parameters belong to [0, 1]. A discussion of symmetric decreasing rearrangements of random variables strengthens the Inequality and guides the exploration as to its sharpness.
-
A Renyi Entropy Power Inequality for Log-Concave Vectors and Parameters in [0, 1]
2018 IEEE International Symposium on Information Theory (ISIT), 2018Co-Authors: Arnaud Marsiglietti, James MelbourneAbstract:Using a sharp version of the reverse Young Inequality, and a Renyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors derive a Renyi entropy Power Inequality for log-concave random vectors when Renyi parameters belong to [0, 1]. A discussion of symmetric decreasing rearrangements of random variables strengthens the Inequality and guides the exploration as to its sharpness.
-
New Connections Between the Entropy Power Inequality and Geometric Inequalities
2018 IEEE International Symposium on Information Theory (ISIT), 2018Co-Authors: Arnaud Marsiglietti, Victoria KostinaAbstract:The entropy Power Inequality (EPI) has a fundamental role in Information Theory, and has deep connections with famous geometric inequalities. In particular, it is often compared to the Brunn-Minkowski Inequality in convex geometry. In this article, we further strengthen the relationships between the EPI and geometric inequalities. Specifically, we establish an equivalence between a strong form of reverse EPI and the hyperplane conjecture, which is a long-standing conjecture in high-dimensional convex geometry. We also provide a simple proof of the hyperplane conjecture for a certain class of distributions, as a straightforward consequence of the EPI.
-
ISIT - New Connections Between the Entropy Power Inequality and Geometric Inequalities
2018 IEEE International Symposium on Information Theory (ISIT), 2018Co-Authors: Arnaud Marsiglietti, Victoria KostinaAbstract:The entropy Power Inequality (EPI) has a fundamental role in Information Theory, and has deep connections with famous geometric inequalities. In particular, it is often compared to the Brunn-Minkowski Inequality in convex geometry. In this article, we further strengthen the relationships between the EPI and geometric inequalities. Specifically, we establish an equivalence between a strong form of reverse EPI and the hyperplane conjecture, which is a long-standing conjecture in high-dimensional convex geometry. We also provide a simple proof of the hyperplane conjecture for a certain class of distributions, as a straightforward consequence of the EPI.
-
variants of the entropy Power Inequality
IEEE Transactions on Information Theory, 2017Co-Authors: Sergey G. Bobkov, Arnaud MarsigliettiAbstract:An extension of the entropy Power Inequality to the form $N_{r}^\alpha (X+Y) \geq N_{r}^\alpha (X) + N_{r}^\alpha (Y)$ with arbitrary independent summands $X$ and $Y$ in $ {\mathbb {R}}^{n}$ is obtained for the Renyi entropy and Powers $\alpha \geq ~(r+1)/2$ .