Description
Kernel methods are widely used in machine learning and related fields.
In this talk a comprehensive review will be given about kernel mean embeddings. The main idea of this notion is to map probability measures
into a reproducing kernel Hilbert space (RKHS) in a meaningful way and apply RKHS methods on these embedded elements. We overview the existing
theoretical results and also consider some applications of this powerful tool.
In the end of this talk I present new nonparametric hypothesis tests for the regression function of binary classification. These statistical
methods are built on conditional kernel mean embeddings.
Joint work with: Balázs Csanád Csáji, SZTAKI, ELTE
References:
Berlinet, Alain, and Christine Thomas-Agnan. Reproducing kernel Hilbert spaces in probability and statistics. Springer Science & Business Media, 2011.
Krikamol Muandet, Kenji Fukumizu, Bharath Sriperumbudur and Bernhard Schölkopf (2017), "Kernel Mean Embedding of Distributions: A Review and
Beyond", Foundations and Trends® in Machine Learning: Vol. 10: No. 1-2, pp 1-141.
Tamás, Ambrus and Csáji, Balázs Csanád (2022) Exact Distribution-Free Hypothesis Tests for the Regression Function of Binary
Classification via Conditional Kernel Mean Embeddings. IEEE CONTROL SYSTEMS LETTERS, 6. pp. 860-865. ISSN 2475-1456