Karmakar, Pratik Basu, Debabrota

We study design of black-box model extraction attacks that can send minimal number of queries from a publicly available dataset to a target ML model through a predictive API with an aim to create an informative and distributionally equivalent replica of the target. First, we define distributionally equivalent and Max-Information model extraction at...

Melbourne, James Nayar, Piotr Roberto, Cyril

We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to derive upper bounds on capacities of additive noise channels with log-concave noise. We also improve constants in the reverse entropy power inequalities for log-concave rand...

Gutiérrez-Cuevas, Rodrigo Bouchet, Dorian de Rosny, Julien Popoff, Sébastien M.

Perturbations in complex media, due to their own dynamical evolution or to external effects, are often seen as detrimental. Therefore, a common strategy, especially for telecommunication and imaging applications, is to limit the sensitivity to those perturbations in order to avoid them. Here, we instead consider crashing straight into them in order...

Ferreira Da Costa, Maxime

The Beurling--Selberg extremal approximation problems are classics in functional analysis and have found applications in numerous areas of mathematics. In this work, Vaaler's extremal approximation theory of functions of bounded variation is harnessed to frame the extremal singular values of weighted non-harmonic Fourier Matrices, where rows are sc...

Agrawal, Shubhada Mathieu, Timothée Basu, Debabrota Maillard, Odalric-Ambrym

We investigate the regret-minimisation problem in a multi-armed bandit setting with arbitrary corruptions. Similar to the classical setup, the agent receives rewards generated independently from the distribution of the arm chosen at each time. However, these rewards are not directly observed. Instead, with a fixed $\varepsilon\in (0,\frac{1}{2})$, ...

Daunas, Francisco Esnaola, Iñaki Poor, H. Vincent

This report presents the solution to the empirical risk minimization with $f$-divergence regularization, under mild conditions on $f$. Under such conditions, the optimal measure is shown to be unique and to always exist. The solution is presented as a closed-form expression of the Radon-Nikodym derivative of the optimal probability measure with res...

Khoshnoudirad, Daniel

Collatz ConjectureConjecture also called Syracuse conjectureTests have been made with Python, Java, C# programming languages

Gürpınar, Emirhan

This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy.Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games. In the former a random secret value is transformed into shares distributed among several participants in such ...

El Khalfaoui, Sabira Lhotel, Mathieu Nardi, Jade

Shi, Hui Traonmilin, Yann Aujol, J-F

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is available. Thanks to the maximum a posteriori Bayesian framework, such regularizer can be systematically linked with...