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To discretize continually: Mean shift interacting particle systems for Bayesian inference
Ayoub Belhadji, Daniel Sharp, Youssef M. Marzouk
Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating s…
One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators
Panos Tsimpos, Edoardo Calvello, Ayoub Belhadji +1
Probabilistic conditioning is concerned with the identification of a distribution of a random variable given a random variable . It is a cornerstone of scientific and engine…
Weighted quantization using MMD: From mean field to mean shift via gradient flows
Ayoub Belhadji, Daniel Sharp, Youssef Marzouk
Approximating a probability distribution using a set of particles is a fundamental problem in machine learning and statistics, with applications including clustering and quantizati…
Signal reconstruction using determinantal sampling
Ayoub Belhadji, Rémi Bardenet, Pierre Chainais
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularl…
On the design of scalable, high-precision spherical-radial Fourier features
Ayoub Belhadji, Qianyu Julie Zhu, Youssef Marzouk
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This me…
Revisiting RIP guarantees for sketching operators on mixture models
Ayoub Belhadji, Rémi Gribonval
In the context of sketching for compressive mixture modeling, we revisit existing proofs of the Restricted Isometry Property of sketching operators with respect to certain mixtures…