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Michael Christoph Gastpar

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Related publications (132)

On Sibson’s α-Mutual Information

Michael Christoph Gastpar, Adrien Vandenbroucque, Amedeo Roberto Esposito

2022

From Generalisation Error to Transportation-cost Inequalities and Back

Michael Christoph Gastpar, Amedeo Roberto Esposito

In this work, we connect the problem of bounding the expected generalisation error with transportation-cost inequalities. Exposing the underlying pattern behind both approaches we are able to generalise them and go beyond Kullback- Leibler Divergences/Mutu ...

2022

Private Retrieval, Computing, and Learning: Recent Progress and Future Challenges

Michael Christoph Gastpar

Most of our lives are conducted in the cyberspace. The human notion of privacy translates into a cyber notion of privacy on many functions that take place in the cyberspace. This article focuses on three such functions: how to privately retrieve informatio ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

A Johnson-Lindenstrauss Framework for Randomly Initialized CNNs

Michael Christoph Gastpar, Jan Hazla, Ido Nachum

How does the geometric representation of a dataset change after the application of each randomly initialized layer of a neural network? The celebrated Johnson-Lindenstrauss lemma answers this question for linear fully-connected neural networks (FNNs), stat ...

2022

Shannon Bounds on Lossy Gray-Wyner Networks

Michael Christoph Gastpar, Erixhen Sula

The Gray-Wyner network subject to a fidelity criterion is studied. Upper and lower bounds for the trade-offs between the private sum-rate and the common rate are obtained for arbitrary sources subject to mean-squared error distortion. The bounds meet exact ...

2022

Information Measures of Redundancy and Synergy in Neural Activity

Michael Christoph Gastpar

Springer Science And Business Media2022

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise

Michael Christoph Gastpar, Alper Köse, Ahmet Arda Atalik

The conditional mean is a fundamental and important quantity whose applications include the theories of estimation and rate-distortion. It is also notoriously difficult to work with. This paper establishes novel bounds on the differential entropy of the co ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Lower-bounds on the Bayesian Risk in Estimation Procedures via f–Divergences

Michael Christoph Gastpar, Adrien Vandenbroucque, Amedeo Roberto Esposito

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of f-Divergences. The results are then applied to specific settings of interest and compared to other notable results i ...

2022

The Gray-Wyner Network and Wyner's Common Information for Gaussian Sources

Michael Christoph Gastpar, Erixhen Sula

This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, ou ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

The Price of Distributed: Rate Loss in the CEO Problem

Michael Christoph Gastpar, Alper Köse, Ahmet Arda Atalik

In the distributed remote (CEO) source coding problem, many separate encoders observe independently noisy copies of an underlying source. The rate loss is the difference between the rate required in this distributed setting and the rate that would be requi ...

2022

Lower bound on relaxed Wyner's Common Information

Michael Christoph Gastpar, Erixhen Sula

An important notion of common information between two random variables is due to Wyner. In this paper, we derive a lower bound on a relaxed variant of Wyner's common information for continuous random variables. The new bound reduces to the lower bound on W ...

IEEE2021

On conditional Sibson's alpha-Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito

In this work, we analyse how to define a conditional version of Sibson's alpha-Mutual Information. Several such definitions can be advanced and they all lead to different information measures with different (but similar) operational meanings. We will analy ...

IEEE2021

Common Information Components Analysis

Michael Christoph Gastpar, Erixhen Sula

Wyner's common information is a measure that quantifies and assesses the commonality between two random variables. Based on this, we introduce a novel two-step procedure to construct features from data, referred to as Common Information Components Analysis ...

2021

Learning, compression, and leakage: Minimising classification error via meta-universal compression principles

Michael Christoph Gastpar, Fernando Rosas de Andraca

Learning and compression are driven by the common aim of identifying and exploiting statistical regularities in data, which opens the door for fertile collaboration between these areas. A promising group of compression techniques for learning scenarios is ...

IEEE2021

Lower-bounds on the Bayesian Risk in estimation procedures via Sibson's alpha-Mutual Information

Michael Christoph Gastpar, Amedeo Roberto Esposito

In this work, we consider the problem of parameter estimation in a Bayesian setting. We propose a new approach to lower-bounding the Bayesian risk, based on Sibson's alpha-Mutual Information. The results are then applied to specific settings of interest. A ...

IEEE2021

A Discretization Approach to Compute-Forward

Michael Christoph Gastpar, Adriano Pastore, Sung Hoon Lim, Chen Feng

We present a novel unified framework of compute- forward achievable rate regions for simultaneous decoding of multiple linear codeword combinations. This framework covers a wide class of discrete and continuous-input channels, and computation over finite f ...

IEEE2021

Differential Entropy of the Conditional Expectation under Gaussian Noise

Michael Christoph Gastpar, Alper Köse, Ahmet Arda Atalik

This paper considers an additive Gaussian noise channel with arbitrarily distributed finite variance input signals. It studies the differential entropy of the minimum mean-square error (MMSE) estimator and provides a new lower bound which connects the diff ...

IEEE2021

On Calculating the Minimum Rate for the Cooperative Data Exchange Problem Over Fully Connected Networks

Michael Christoph Gastpar, Su Li

We study the cooperative data exchange problem for fully connected networks. In this problem, nodes make broadcast transmissions to recover a file consisting of K independent packets. Each node initially only possesses a subset of the packets. We propose ( ...

2021

Locally Differentially-Private Randomized Response for Discrete Distribution Learning

Michael Christoph Gastpar, Adriano Pastore

We consider a setup in which confidential i.i.d. samples X1, . . . , Xn from an unknown finite-support distribution p are passed through n copies of a discrete privatization chan- nel (a.k.a. mechanism) producing outputs Y1, . . . , Yn. The channel law gua ...

2021

Generalization Error Bounds Via Rényi-, f-Divergences and Maximal Leakage

Michael Christoph Gastpar, Ibrahim Issa, Amedeo Roberto Esposito

In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two random variables. ...

2021

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