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The minimum sum-of-squares clustering problem (MSSC), also known as $k$-means clustering, refers to the problem of partitioning $n$ data points into $k$ clusters, with the objective of minimizing the total sum of squared Euclidean distances…
In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations (BSDEs). The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte…
Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…
In the wake of the highly electrified future ahead of us, the role of energy storage is crucial wherever distributed generation is abundant, such as in microgrid settings. Given the variety of storage options that are becoming more and more…
This paper proposes a new convex model predictive control strategy for dynamic optimal power flow between battery energy storage systems distributed in an AC microgrid. The proposed control strategy uses a new problem formulation, based on…
This paper deals with distributed control of microgrids composed of storages, generators, renewable energy sources, critical and controllable loads. We consider a stochastic formulation of the optimal control problem associated to the…
Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…
The AMIAS/RISE framework formulates emission tomography as a probabilistic inverse problem in which reconstructed images are sampled from a distribution defined by the measurement model and counting statistics. In this work we present a…
Stochastic convex optimization algorithms are the most popular way to train machine learning models on large-scale data. Scaling up the training process of these models is crucial, but the most popular algorithm, Stochastic Gradient Descent…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
First of all, this paper presents some improvements of DSMC method in the form of new schemes and approaches, that, for a wide class of problems, increase performance and reduce the demands on computer resources. The most important…
Microgrids are local energy systems that integrate energy production, demand, and storage units. They are generally connected to the regional grid to import electricity when local production and storage do not meet the demand. In this…
Modern signal processing (SP) methods rely very heavily on probability and statistics to solve challenging SP problems. SP methods are now expected to deal with ever more complex models, requiring ever more sophisticated computational…
The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination…
Elementary cellular automata (ECA) is a widely studied one-dimensional processing methodology where the successive iteration of the automaton may lead to the recreation of a rich pattern dynamic. Recently, cellular automata have been…
Derivation of the probability density evolution provides invaluable insight into the behavior of many stochastic systems and their performance. However, for most real-time applica-tions, numerical determination of the probability density…
In this paper we propose robust efficiency scores for the scenario in which the specification of the inputs/outputs to be included in the DEA model is modelled with a probability distribution. This proba- bilistic approach allows us to…
We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…
Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…
This paper deals with the optimization of industrial asset management strategies, whose profitability is characterized by the Net Present Value (NPV) indicator which is assessed by a Monte Carlo simulator. The developed method consists in…