Dario Shariatian

Dario Shariatian

PhD Student, working on generative models

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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

Pages

Posts

An Alternative to the Log-Likelihood with Entropic Optimal Transport

less than 1 minute read

Published:

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.

See paper | GitHub Repository

Discrete Morse Theory for Relative Cosheaf Homology

less than 1 minute read

Published:

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.

See paper

Robustness in Neural ODEs and SDEs

less than 1 minute read

Published:

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

less than 1 minute read

Published:

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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Forest Classification - Kaggle Challenge

less than 1 minute read

Published:

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.

See paper

portfolio

publications

Denoising Levy Probabilistic Models (DLPM)

Published in arxiv, 2024

This paper introduces a novel framework to use heavy-tailed noise in the denoising diffusion paradigm, which constitutes a generalization of the original DDPM method. Using heavy-tailed noise is shown to bring benefits in various contexts: heavy-tailed data distributions, better robustness to class imbalance, and smaller computational time.

Shariatian, D., Simsekli, U., & Durmus, A.O. (2024). Denoising Lévy Probabilistic Models. ArXiv, abs/2407.18609.
See paper | See slides | GitHub Repository

Piecewise deterministic generative models

Published in Neurips, 2024

We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), which combine deterministic motion with random jumps. Like diffusions, PDMPs can be reversed in time. We derive explicit expressions for jump rates and kernels in the time-reversed processes and propose efficient training methods and approximate simulation techniques. Additionally, we provide bounds on the total variation distance between the data and model distributions, supported by promising numerical simulations.

Bertazzi, A., Shariatian, D., Durmus, A.O., Simsekli, U., & Moulines, É. (2024). Piecewise deterministic generative models. Neurips24
See paper | GitHub Repository

talks

teaching

Numerical Analysis MAA106

Undergraduate course, Ecole Polytechnique, CMAP, 2024

TA’d a 4 months course for 1st year students on numerical analysis.