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Wide conditions are provided to guarantee asymptotic unbiasedness and L^2-consistency of the introduced estimates of the Kullback-Leibler divergence for probability measures in R^d having densities w.r.t. the Lebesgue measure. These…

This study tackles the efficient estimation of Kullback-Leibler (KL) Divergence in Dirichlet Mixture Models (DMM), crucial for clustering compositional data. Despite the significance of DMMs, obtaining an analytically tractable solution for…

This paper studies the synthesis and mitigation of stealthy attacks in nonlinear cyber-physical systems (CPS). To quantify stealthiness, we employ the Kullback-Leibler (KL) divergence, a measure rooted in hypothesis testing and detection…

The integration of Distributed Energy Resources (DERs) into power distribution systems has made microgrids foundational to grid modernization. These DERs, connected through power electronic inverters, create power electronics dominated grid…

Power system protection schemes today rely on currents rising by several orders of magnitude when faults occur. In inverter-dominated power systems, a fault current might be just a few percent larger than normal, making fault detection more…

In the monitoring of a complex electric grid, it is of paramount importance to provide operators with early warnings of anomalies detected on the network, along with a precise classification and diagnosis of the specific fault type. In this…

Designing resilient control strategies for mitigating stealthy attacks is a crucial task in emerging cyber-physical systems. In the design of anomaly detectors, it is common to assume Gaussian noise models to maintain tractability; however,…

In this paper, we analyze the fundamental stealthiness-distortion tradeoffs of linear Gaussian dynamical systems under data injection attacks using a power spectral analysis, whereas the Kullback-Leibler (KL) divergence is employed as the…

This paper introduces a novel hybrid AI method combining H filtering and an adaptive linear neuron network for flicker component estimation in power distribution systems.The proposed method leverages the robustness of the H filter to…

In this paper, we study the strong consistency of a bias reduced kernel density estimator and derive a strongly con- sistent Kullback-Leibler divergence (KLD) estimator. As application, we formulate a goodness-of-fit test and an…

Microgrids are increasingly being utilized to improve the resilience and operational flexibility of power grids, and act as a backup power source during grid outages. However, it necessitates that the microgrid itself could provide power to…

Several scalable sample-based methods to compute the Kullback Leibler (KL) divergence between two distributions have been proposed and applied in large-scale machine learning models. While they have been found to be unstable, the…

This paper addresses the problem of distributed detection in multi-agent networks. Agents receive private signals about an unknown state of the world. The underlying state is globally identifiable, yet informative signals may be dispersed…

Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces…

This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…

Estimating Kullback Leibler (KL) divergence from samples of two distributions is essential in many machine learning problems. Variational methods using neural network discriminator have been proposed to achieve this task in a scalable…

We consider a Kullback-Leibler-based algorithm for the stochastic multi-armed bandit problem in the case of distributions with finite supports (not necessarily known beforehand), whose asymptotic regret matches the lower bound of…

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…

Gaussian random attacks that jointly minimize the amount of information obtained by the operator from the grid and the probability of attack detection are presented. The construction of the attack is posed as an optimization problem with a…

Predicting and classifying faults in electricity networks is crucial for uninterrupted provision and keeping maintenance costs at a minimum. Thanks to the advancements in the field provided by the smart grid, several data-driven approaches…