PERLAZA , Samir

Experts in data analytics and power engineering present techniques addressing the needs of modern power systems, covering theory and applications related to power system reliability, efficiency, and security. With topics spanning large-scale and distributed optimization, statistical learning, big data analytics, graph theory, and game theory,...

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Closed-form expressions are presented for the variation of the expectation of a given function due to changes in the probability measure used for the expectation. They unveil interesting connections with Gibbs probability measures, the mutual information, and the lautum information.

This paper studies an instance of zero-sum games in which one player (the leader) commits to its opponent (the follower) to choose its actions by sampling a given probability measure (strategy). The actions of the leader are observed by the follower as the output of an arbitrary channel. In response to that, the follower chooses its action...

In this paper, the method of gaps, a technique for deriving closed-form expressions in terms of information measures for the generalization error of machine learning algorithms is introduced. The method relies on two central observations: (a) The generalization error is an average of the variation of the expected empirical risk with respect to...

This report studies an instance of zero-sum games in which one player(the leader) commits to its opponent(the follower) to choose its actions by sampling a given probability measure(strategy). The actions of the leader are observed by the follower as the output of an arbitrary channel. In response to that, the follower chooses its action based...

International audience

In this paper, the fundamental limits on the rates at which information and energy can be simultaneously transmitted over an additive white Gaussian noise channel are studied under the following assumptions: (a) the channel is memoryless; (b) the number of channel input symbols (constellation size) and block length are finite; and (c) the...

International audience

Rigorous statements and formal proofs are presented for both foundational and advanced folklore theorems on the Radon-Nikodym derivative. The cases of product and marginal measures are carefully considered; and the hypothesis under which the statements hold are rigorously enumerated.

In this report, sparse stealth attack constructions that minimize the mutual information between the state variables and the observations are proposed. The attack construction is formulated as the design of a multivariate Gaussian distribution aiming to minimize the mutual information while limiting the Kullback-Leibler divergence between the...

The solution to empirical risk minimization with f-divergence regularization (ERM-fDR) is presented under mild conditions on f. Under such conditions, the optimal measure is shown to be unique. Examples of the solution for particular choices of the function f are presented. Previously known solutions to common regularization choices are...

A novel metric that describes the vulnerability of the measurements in power systems to data integrity attacks is proposed. The new metric, coined vulnerability index (VuIx), leverages information theoretic measures to assess the attack effect in terms of the fundamental limits of the disruption and detection tradeoff. The result of computing...

In this report, the fundamental limits on the rates at which information and energy can be simultaneously transmitted over an additive white Gaussian noise channel are studied under the following assumptions: (a) the channel is memoryless; (b) the number of channel input symbols (constellation size) and block length are finite; and (c) the...

The dependence on training data of the Gibbs algorithm (GA) is analytically characterized. By adopting the expected empirical risk as the performance metric, the sensitivity of the GA is obtained in closed-form. In this case, sensitivity is the performance difference with respect to an arbitrary alternative algorithm. This description enables...

Sparse stealth attack constructions that minimize the mutual information between the state variables and the observations are proposed. The attack construction is formulated as the design of a multivariate Gaussian distribution that aims to minimize the mutual information while limiting the Kullback-Leibler divergence between the distribution...

This report introduces an upper bound on the absolute difference between:$(a)$~the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables; and $(b)$~a saddlepoint approximation of such CDF.%This upper bound, which is particularly precise in the regime of large...

In this report, a formula for estimating the prevalence ratio of a disease in a population that is tested with imperfect tests is given. The formula is in terms of the fraction of positive test results and test parameters, i.e., probability of true positives (sensitivity) and the probability of true negatives (specificity). The motivation of...

In this report, the worst-case probability measure over the data is introduced as a tool for characterizing the generalization capabilities of machine learning algorithms. More specifically, the worst-case probability measure is a solution to the maximization of the expected loss under a relative entropy constraint with respect to a reference...

The effect of the relative entropy asymmetry is analyzed in the empirical risk minimization with relative entropy regularization (ERM-RER) problem. A novel regularization is introduced, coined Type-II regularization, that allows for solutions to the ERM-RER problem with a support that extends outside the support of the reference measure. The...

This paper introduces an upper-bound on the absolute difference between: (a) the cumulative distribution function (c.d.f.) of the sum of a finite number of independent and identically distributed (i.i.d) random variables; and (b) a saddlepoint approximation of such c.d.f. This upperbound is general and particularly precise in the regime of...

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...