December 13, 2023 by alkhwarizmi

Rim Hariss

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$\begin{quote} \begin{center} \textbf{Use case of ML for Optimization} \end{center} \medskip In this work, we examine a data-driven optimization approach to making optimal decisions as evaluated by a trained random forest, where these decisions can be constrained by an arbitrary polyhedral set. We model this optimization problem as a mixed-integer linear program. We show this model can be solved to optimality efficiently using pareto-optimal Benders cuts for ensembles containing a modest number of trees. We consider a random forest approximation that consists of sampling a subset of trees and establish that this gives rise to near-optimal solutions by proving analytical guarantees. In particular, for axis-aligned trees, we show that the number of trees we need to sample is sublinear in the size of the forest being approximated. Motivated by this result, we propose heuristics inspired by cross-validation that optimize over smaller forests rather than one large forest and assess their performance on synthetic datasets. We present two case studies on a property investment problem and a jury selection problem. We show this approach performs well against other benchmarks while providing insights into the sensitivity of the algorithm's performance for different parameters of the random forest. \end{quote}$

December 11, 2023December 11, 2023 by alkhwarizmi

Lolo Jones

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$\begin{quote} \begin{center} \textbf{Diffusion geometry for data analysis} \end{center} \medskip We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the theory of Markov diffusion operators to define an exterior calculus on certain probability spaces, which allows many objects from Riemannian geometry to be constructed in this very general setting. Given a finite sample of data, we can define estimators for all these constructions, including vector fields and differential forms, wedge product, exterior derivative, Lie bracket, Levi-Civita connection, Hodge Laplacian and Riemann curvature tensor. Compared with existing approaches like persistent homology and local principal component analysis, diffusion geometry is explicitly related to existing theory in geometry, is significantly more robust to noise, significantly faster to compute, provides a richer topological description with the cup product on cohomology, and is naturally vectorised for statistics and machine learning. \end{quote}$

December 11, 2023December 11, 2023 by alkhwarizmi

Irem Portakal

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$\begin{quote} \begin{center} \textbf{Game Theory of undirected graphical models} \end{center} \medskip Game theory is an area that has historically benefited greatly from outside ideas. In 1950, Nash published a very influential two-page paper proving the existence of Nash equilibria for any finite game. The proof uses an elegant application of the Kakutani fixed-point theorem from the field of topology. This opened a new horizon not only in game theory, but also in areas such as economics, computer science, evolutionary biology, and social sciences. In this talk, we model different notions of equilibria in terms of undirected graphical models.The vertices of the underlying graph of the graphical model represent the players of the game and the dependencies of the choices of the players are depicted with an edge in the graph.This approach brings game theory in contact with the field of algebraic statistics for the first time, which offers a strong foundation for utilizing algebro-geometric tools to solve interesting problems in game theory. This is joint work with Javier Sendra-Arranz and Bernd Sturmfels. \end{quote}$

December 6, 2023December 8, 2023 by alkhwarizmi

Mouad Elhamdi

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$\begin{quote} \begin{center} \textbf{Optimization Techniques for Neighbor Embedding Methods} \end{center} \medskip Neighbor embedding methods are crucial in machine learning and data analysis, capturing the intricate structures of complex datasets by mapping high-dimensional data into lower-dimensional spaces while preserving local relationships among points. The success of neighbor embedding hinges on effective optimization. This discussion concisely reviews advanced optimization techniques designed to enhance the performance of neighbor embedding algorithms. \end{quote}$

December 6, 2023December 6, 2023 by alkhwarizmi

Lhoucine Ben Hssain

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$\begin{quote} \begin{center} \textbf{Portfolio selection based on Spectral Gini Shortfall risk measures} \end{center} \medskip In this paper, we conducted a comprehensive examination of the Extended Gini Shortfall (EGS) as a flexible risk measure for portfolio selection, employing various approaches. The EGS measure possesses desirable properties, such as coherence, risk and variability measurement, and risk aversion. Additionally, we introduced the Reward Risk Ratio induced from EGS and explored its associated properties. Our main focus centered on a convex optimization problem, where the objective was to minimize portfolio risk while adhering to reward and budget constraints. We demonstrated the effectiveness of the obtained theoretical results through a practical application. \end{quote}$

December 6, 2023December 6, 2023 by alkhwarizmi

Wafaa El Hannoun

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$\begin{quote} \begin{center} \textbf{Vine copula quantile regression for a multidimensional water expenditures analysis} \end{center} \medskip Water expenditures are one of the main indicators of water consumption which makes them an ideal tool for addressing water policies. Many studies have approached water expenditures analysis through several factors, including social, space and climate factors mainly by modelling tools which can be considered as black boxes. In this work, we try to analyze water expenditures using D-vine copula quantile regression. This method has proven its efficiency in predicting quantiles in different areas, including hydrology. An illustration of the proposed methodology is presented for Morocco and results show different relationships between water expenditures and social factors (geographical area, sex and educational level of the householder) and also the quantiles variability at the regional scale. \end{quote}$

December 6, 2023December 6, 2023 by alkhwarizmi

Salah-Eddine Chorfi

Uncategorized

$\begin{quote} \begin{center} \textbf{Impulsive control for parabolic equations with various boundary conditions} \end{center} \medskip We present a comparative study to numerically compute impulse approximate controls for parabolic equations with various boundary conditions. Theoretical controllability results have been recently investigated using a logarithmic convexity estimate at a single time based on a Carleman commutator approach. We propose a numerical algorithm for computing the impulse controls with minimal $L^2$-norms by adapting a penalized Hilbert Uniqueness Method (HUM) combined with a Conjugate Gradient (CG) method. We consider static boundary conditions (Dirichlet and Neumann) as well as dynamic boundary conditions. Some numerical experiments are given to validate and compare the theoretical impulse controllability results. \end{quote}$

December 6, 2023December 6, 2023 by alkhwarizmi

Maryam Boubekraoui

Uncategorized

$\begin{quote} \begin{center} \textbf{Extrapolation methods for multilinear PageRank} \end{center} \medskip Multilinear PageRank stands as an innovative rendition of the Google PageRank algorithm, designed to consider a network's diverse web of connections. This algorithm promises heightened efficiency and precision in the ranking of web pages by simultaneously accounting for multiple relationship types. For the computation of the multilinear PageRank vector, the higher-order power method is commonly employed due to its practical implementation, minimal storage requirements, and its organic extension from the traditional power method employed in the classic Google PageRank algorithm. Nonetheless, the convergence of this method does not always come with a guarantee, and even when it does, its pace can be sluggish. In this presentation, we introduce an acceleration approach for computing fixed-point multilinear PageRank. We achieve this by harnessing vector extrapolation techniques, specifically the minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE). These methods promise to enhance the efficiency of the computation process, a development that could have significant implications for web ranking systems. \end{quote}$

December 6, 2023December 6, 2023 by alkhwarizmi

Amal Machtalay

Uncategorized

$\begin{quote} \begin{center} \textbf{Mean-field game: application to traffic} \end{center} \medskip The theory of mean-field game to study complex systems in which many agents interact strategically in an evolving stochastic environment was introduced by Lasry and Lions in 2007 and Huang, Caines, and Malhame in 2006. The first mathematical traffic model called the kinematic wave model was introduced in 1955, as was focusing on the propagation of waves in traffic. Since then, various models have been developed to understand traffic dynamics, predict road capacity, and describe significant transportation phenomena described as shock waves and phase transitions. Indeed, the mean-field game approach provides an attractive mathematical framework that can contribute to a better understanding of traffic's complex dynamics. \end{quote}$

December 6, 2023December 6, 2023 by alkhwarizmi

Ismail Oubarka

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$\begin{quote} \begin{center} \textbf{A robust and well-balanced finite volume solver for investigating the effects of tides on water renewal timescale in semi-enclosed environments} \end{center} \medskip In this study, we utilize the Constituent-oriented Age and Residence Time Theory to investigate timescales associated with water renewal in semi-enclosed domains, with a particular focus on the Nador Lagoon. Our modeling approach adopts an Eulerian framework and integrates two interconnected components: (i) the shallow-water equations for hydrodynamics and (ii) a transport equation for passive tracers. These components are seamlessly integrated into a high-order finite volume solver that operates on unstructured meshes. To accurately account for advection processes and accommodate topographic variations, we employ a Non-Homogeneous Riemann Solver (SRNH). Our primary objective is to explore recirculation phenomena within the Nador Lagoon and, more specifically, to quantify the residence time of water within this unique coastal environment. Through a comprehensive numerical investigation, we aim to ascertain the need for, and potential locations of, additional channels con- necting the lagoon to the Mediterranean Sea. Such channels, if deemed necessary, can potentially reduce the residence time of specific tracers within the lagoon. This study contributes valuable insights into the dynamic behavior of semi-enclosed coastal domains and provides a scientific basis for informed decision making regarding the management and conservation of these fragile ecosystems. \end{quote}$