Publications related to Conditional mutual information

Robust Generalization via $\alpha$-Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

The aim of this work is to provide bounds connecting two probability measures of the same event using Rényi

\alpha

-Divergences and Sibson’s

\alpha

-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence and Shannon’s Mutual ...

ETHZ2020

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier, Mohamad Baker Dia

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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Given two probability measures P and Q and an event E, we provide bounds on P(E) in terms of Q(E) and f-divergences. In particular, the bounds are instantiated when the measures considered are a joint distribution and the corresponding product of marginals ...

IEEE2020

Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method

Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan

We rigorously derive a single-letter variational expression for the mutual information of the asymmetric two-groups stochastic block model in the dense graph regime. Existing proofs in the literature are indirect, as they involve mapping the model to a ran ...

IEEE2019

Strengthened Information-theoretic Bounds on the Generalization Error

Michael Christoph Gastpar, Amedeo Roberto Esposito, Ibrahim Issa

The following problem is considered: given a joint distribution P XY and an event E, bound P XY (E) in terms of P X P Y (E) (where P X P Y is the product of the marginals of P XY ) and a measure of dependence of X and Y. Such bounds have direct application ...

IEEE2019

Entropy and mutual information in models of deep neural networks

Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier, Clément Dominique Luneau

We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) we show how entropies and mutual informations can be derived from heuristic statistical physics ...

IOP PUBLISHING LTD2019

Reed-Muller codes polarize

Emmanuel Abbé, Min Ye

Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are gen ...

IEEE COMPUTER SOC2019

Theoretical foundations of forward feature selection methods based on mutual information

Francisco Santos Paredes Quartin de Macedo

Feature selection problems arise in a variety of applications, such as microarray analysis, clinical prediction, text categorization, image classification and face recognition, multi-label learning, and classification of internet traffic. Among the various ...

ELSEVIER SCIENCE BV2019

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We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its mutual information when the tensor is of even order. The proof uses the adaptive interpolation method, for which rank-on ...

IEEE2019

Measuring transient phase-amplitude coupling using local mutual information

Here we demonstrate the suitability of a local mutual information measure for estimating the temporal dynamics of cross-frequency coupling (CFC) in brain electrophysiological signals. In CFC, concurrent activity streams in different frequency ranges intera ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Conditional mutual information

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Robust Generalization via $\alpha$-Mutual Information

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method

Strengthened Information-theoretic Bounds on the Generalization Error

Entropy and mutual information in models of deep neural networks

Reed-Muller codes polarize

Theoretical foundations of forward feature selection methods based on mutual information

Measuring transient phase-amplitude coupling using local mutual information

Mutual Information for the Stochastic Block Model by the Adaptive Interpolation Method

Robust Generalization via $\alpha$-Mutual Information

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Strengthened Information-theoretic Bounds on the Generalization Error

Reed-Muller codes polarize

Measuring transient phase-amplitude coupling using local mutual information

Theoretical foundations of forward feature selection methods based on mutual information

Entropy and mutual information in models of deep neural networks