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DTSTART:20260329T010000
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DTSTART;TZID=Europe/Helsinki:20260126T140000
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SUMMARY:Eric MOULINES (EPITA & MBZUAI) - Sampling Posteriors with Implicit Priors: Diffusion Models\, Guidance Bias\, and SMC
DESCRIPTION:Statistical Seminar: Every Monday at 2:00 pm.\nTime: 2:00 pm – 3:00 pm\nDate: 26th January\nPlace: 3001 \n  \nEric MOULINES (EPITA & MBZUAI) – Sampling Posteriors with Implicit Priors: Diffusion Models\, Guidance Bias\, and SMC \n  \n Abstract:  \n  \nWe study Bayesian sampling for inverse problems where the goal is to reconstruct a signal $X$ from noisy observations $Y=A(X)+\sigma Z$ while providing uncertainty quantification. The posterior can be written as $\pi(dx)\propto g(x)\rho(dx)$\, where $g$ is a potential (typically the likelihood) and $\rho$ is an implicit prior approximated by a diffusion model (DDPM). This setting makes standard approaches that rely on evaluating the prior density intractable. We review guidance methods that modify the denoising dynamics using score-based terms (notably via Tweedie’s formula)\, and we highlight the biases introduced by approximating intermediate potentials. We then present a “sequence of distributions” viewpoint: the exact posterior path is replaced by a chain of distributions bridging a reference Gaussian to the target\, described through a Feynman–Kac representation and simulable with SMC/particle methods. Finally\, we discuss Monte Carlo guidance schemes and mixture-based approaches\, including a data-augmentation formulation and a deterministic Gibbs sampler\, and we illustrate these ideas on imaging tasks (super-resolution\, deblurring\, inpainting) and audio source separation. \n  \n  \n  \nOrganizers: \nAnna KORBA (CREST)\, Vincent DIVOL (CREST)\, Jaouad MOURTADA (CREST) \n  \n  \nSponsors:\nCREST-CMAP \n
URL:https://crest.science/event/eric-moulines-epita-mbzuai-tba/
CATEGORIES:Seminars,Statistics
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