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This paper explores the entropic optimal transport (EOT) loss and its estimator in parameter estimation, comparing its advantages over traditional likelihood methods, such as improved robustness, faster convergence, and resilience to bad local optima, with a focus on theoretical justification and experimental validation in Gaussian Mixture Models.
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This paper aims to generalize discrete Morse theory in the context of relative cosheaf homology on filtrations of finite simplicial complexes, enabling faster computations. These methods are extended to persistent cosheaf homology for longer filtrations.
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Recent studies show that Neural ODEs are more robust against adversarial attacks than traditional DNNs, but as complexity increases, concerns about robustness and expressivity arise, prompting exploration of stochastic noise regularization.
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This report gathers tools from spectral graph theory to analyze stock market relation graphs, focusing on spectral embedding for positioning companies in Euclidean space and exploring graph entropy to classify graphs and detect regime changes, with a generalization to directed weighted graphs and in-depth explanations of the underlying concepts and algorithms.
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Small project using C++ and SFML to depixelize pixel art.
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This Kaggle challenge involved a classification problem (with 7 different classes) based on a dataset of forest parcels. The data consisted of 55 columns, including 11 numerical variables and 2 categorical variables (with 4 and 40 classes, respectively). To tackle this problem, we employed strategies detailed chronologically in this report. After an initial data exploration phase and attempts at dimensionality reduction, we tested several classic algorithms and proceeded with optimizations where possible.
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Small project using the OpenGL library to draw a complex 3D scene.
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Mini project studying elliptic curves on finite field, from basic properties to Hasse theorem and Schoof’s algorithm. Accompanying C++ library with GMP implementing these results.