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Posts
An Alternative to the Log-Likelihood with Entropic Optimal Transport
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.
Discrete Morse Theory for Relative Cosheaf Homology
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.
Robustness in Neural ODEs and SDEs
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.
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.
Pixel Art
Published:
Small project using C++ and SFML to depixelize pixel art.
Forest Classification - Kaggle Challenge
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.
3D Graphics with OpenGL
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Small project using the OpenGL library to draw a complex 3D scene.
Elliptic Curve Cryptography
Published:
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.
portfolio
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publications
Piecewise Deterministic Generative Models
Published in The Thirty-Eighth Conference on Neural Information Processing Systems (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. NeurIPS 2024
See paper | GitHub Repository
Denoising Levy Probabilistic Models (DLPM)
Published in The Thirteenth International Conference on Learning Representations (ICLR), 2025
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. (2025). Denoising Lévy Probabilistic Models. ICLR 2025
See paper | See slides | GitHub Repository
Denoising Markov Probabilistic Models (DMPM)
Published in Arxiv, 2025
This paper introduces a novel framework for discrete data generation on the hypercube ${0, 1}^d$. We establish theoretical and methodological alignment with classical continuous score-based modesls. We demonstrate the effectiveness of this approach on low and high dimensional datasets (Binary MNIST), beating other state-of-the-art methods like Discrete Flow Matching
Shariatian D., Pham L.T.N., Ocello A., Conforti G., Durmus A.O. (2025). Denoising Markov Probabilistic Models. ArXiv, abs/2502.07939.
See paper | GitHub Repository
talks
Denoising Levy Probabilistic Model (DLPM)
Published:
Denoising Levy Probabilistic Model (DLPM)
Published:
Denoising Markov Probabilistic Model (DMPM)
Published:
Denoising Levy Probabilistic Model (DLPM)
Published:
teaching
Master X-HEC Data Science and AI for Business/Finance
Admission procedure, Ecole Polytechnique - HEC, 2024
Assisting the admission team during the multiple rounds of the selection process by conducting the mathematical interviews.
Numerical Analysis MAA106
Undergraduate course, Ecole Polytechnique, CMAP, 2024
TA’d a 4 months course for 1st year students on numerical analysis.
Master X-HEC Data Science and AI for Business/Finance
Admission procedure, Ecole Polytechnique - HEC, 2025
Assisting the admission team during the multiple rounds of the selection process by conducting the mathematical interviews.