The intersection of reproducing kernel methods, dependence tests and probability metrics; where you use a clever RKHS embedding to measure differences between probability distributions.

A mere placeholder for now.

This abstract by Zoltán Szabó might serve to highlight some keywords.

Maximum mean discrepancy (MMD) and Hilbert-Schmidt independence criterion (HSIC) are among the most popular and successful approaches in applied mathematics to measure the difference and the independence of random variables, respectively. Thanks to their kernel-based foundations, MMD and HSIC are applicable on a large variety of domains such as documents, images, trees, graphs, time series, dynamical systems, sets or permutations. Despite their tremendous practical success, quite little is known about when HSIC characterizes independence and MMD with tensor kernel can discriminate probability distributions, in terms of the contributing kernel components. In this talk, I am going to provide a complete answer to this question, with conditions which are often easy to verify in practice.

Joint work with Bharath K. Sriperumbudur (PSU).

Gaël Varoquaux has a friendly illustrated introduction, Comparing distributions: Kernels estimate good representations, l1 distances give good tests based on (scetbon and Varoquaux 2019).

See the ITE toolbox (estimators).

Husain (2020)’s results connect IPMs to transport metrics and regularisation theory, and classification.

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