SNE and t-SNE perform dimensionality reduction by minimizing relative entropy (KL) between high and low dimensional spaces. t-SNE improves over SNE by replacing Gaussians with students’ t-distributions in the low dimensional space. en.wikipedia.org/wiki/T-distrib…

Oldies but goldies: I.M. Sobol, Distribution of points in a cube and approximate evaluation of integrals, 1967. Introduces the most well-known low-discrepancy quasi-random sequence. en.wikipedia.org/wiki/Sobol_seq…

Oldies but goldies: Hastings, Monte Carlo Sampling Methods Using Markov Chains and Their Applications, 1970. Metropolis-Hasting is a simple way to sample from a density known only up to a constant. en.wikipedia.org/wiki/Metropoli…

The Fourier slice theorem relates the 1D Fourier transform of Radon projections to the 2D transform of the image. Useful to analyze and invert scanner medical imaging. en.wikipedia.org/wiki/Projectio…

Excited to be in Aistats 🇪🇸🇪🇸🇪🇸

I will present:

- Enhancing Hypergradients Estimation: A Study of Preconditioning and Reparameterization
arxiv.org/abs/2402.16748
- A Lower Bound and a Near-Optimal Algorithm for Bilevel Empirical Risk Minimization
arxiv.org/abs/2302.08766

Oldies but goldies: L Kantorovich, On translocation of masses, 1942. Nobel Prize in Economy in 1975 for a description of optimal transport as a linear program. en.wikipedia.org/wiki/Leonid_Ka…

HAN Solo drops by Valencia for AISTATS24!
I’ll present my paper arxiv.org/abs/2304.08061.
We prove that our cognitive network HAN Solo effectively learns. It provides insights on how local learning rules lead to global learning in the brain.
Joint work w. Samuel Vaiter & Patricia Reynaud-Bouret.

The Fast Marching algorithm is a generalization of Dijkstra’s algorithm. Computes the geodesic distance in O(n*log(n)) operation. Equivalently solves the non-linear Eikonal equation in a non-iterative way by front propagation. en.wikipedia.org/wiki/Fast_marc… nbviewer.jupyter.org/github/gpeyre/…

Oldies but goldies: Eugene Wigner, Characteristic Vectors of Bordered Matrices with Infinite Dimensions, 1955. The empirical distribution of eigenvalues of random symmetric matrices converges to a half-circle density. en.wikipedia.org/wiki/Wigner_se…

Subdivision curves exist in two flavors: interpolating and approximating. numerical-tours.com/matlab/meshwav… ibiblio.org/e-notes/Spline… en.wikipedia.org/wiki/Spline_(m…

Oldies but goldies: Andrew Berry, The Accuracy of the Gaussian Approximation to the Sum of Independent Variates, 1941. Provides a quantitative estimation of the convergence speed of the central limit theorem. en.wikipedia.org/wiki/Berry%E2%…

The Fisher metric defines the unique Riemannian structure of parametric densities invariant by re-parameterization. For 1D Gaussians, corresponds to the Poincaré hyperbolic half plane. en.wikipedia.org/wiki/Fisher_in…

In case you are wondering, this paper proves that, in general, diffusion models do not define optimal transport maps. The proof is not straightforward though (diffusion maps are optimal maps in 1D, for radial measure and for Gaussians ...) cvgmt.sns.it/media/doc/pape…

Any pair of planar triangulations of n vertices can be connected by O(n) edge flips (despite the exponential number of such triangulations!). en.wikipedia.org/wiki/Klaus_Wag… eudml.org/doc/146109

Oldies but goldies: Martial Agueh and Guillaume Carlier, Barycenters in the Wasserstein Space, 2011. Defines a notion of averaging of probability distributions which is the solution of a convex program involving optimal transport distances. ceremade.dauphine.fr/~carlier/AC_ba…