OxCSML seminar this week: Georgios Batzolis

[Hai Dang Dau]

Dear all,

This week we'll welcome Georgios Batzolis from University of Cambridge at our OxCSML seminar. Please find the details of his talk below. Looking forwards to seeing you there.

Kind regards,

Saif & Hai-Dang.

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Speaker: Georgios Batzolis (University of Cambridge)

Time and date: 14.00 to 15.00 Friday 27 October
Place: Room LG.03 (Small lecture theatre), Department of Statistics, Oxford

Zoom: https://zoom.us/j/92566824256?pwd=L0NFSk1MdkczTEJMNSt2VnhrTXBNdz09

Title: Your diffusion model secretly knows the dimension of the data manifold

Abstract: In this work, we propose a novel framework for estimating the dimension of the data manifold using a trained diffusion model. A diffusion model approximates the score function i.e. the gradient of the log density of a noise-corrupted version of the target distribution for varying levels of corruption. We prove that, if the data concentrates around a manifold embedded in the high-dimensional ambient space, then as the level of corruption decreases, the score function points towards the manifold, as this direction becomes the direction of maximal likelihood increase. Therefore, for small levels of corruption, the diffusion model provides us with access to an approximation of the normal bundle of the data manifold. This allows us to estimate the dimension of the tangent space, thus, the intrinsic dimension of the data manifold. To the best of our knowledge, our method is the first estimator of the data manifold dimension based on diffusion models and it outperforms well established statistical estimators in controlled experiments on both Euclidean and image data.