Dario Shariatian

Dario Shariatian

PhD Student, working on generative models

Discrete Morse Theory for Relative Cosheaf Homology

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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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An Alternative to the Log-Likelihood with Entropic Optimal Transport

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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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Robustness in Neural ODEs and SDEs

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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.

See paper | GitHub Repository

Spectral Methods for Clustering in Finance

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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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