Kernel Choice and Classifiability for RKHS Embeddings of Probability Distributions

By Bharath K. Sriperumbudur, Kenji Fukumizu, Arthur Gretton, Gert R. G. Lanckriet, Bernhard Schölkopf. 2009

247 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning, Probabilistic & Bayesian Methods

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Citations in the corpus

Generative Moment Matching Networks (2015, methodology): “A good heuristic is to perform a line search to obtain the bandwidth that produces the maximal distance (Sriperumbudur et al., 2009), other more advanced heuristics are also available (Gretton et al.”
Learning Transferable Features with Deep Adaptation Networks (2015, methodology): “By choosing η as a (kernel) Parzen window classifier (Sriperumbudur et al., 2009), dH(p, q) can be bounded by the empirical estimate”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Hence, it cannot be a universal kernel in the sense of Steinwart (2002) for probability distributions.”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, methodology): “In some situations, MMD with a kernel family is preferred (Sriperumbudur et al., 2009).”
Testing Hypotheses by Regularized Maximum Mean Discrepancy (2013, background): “An investigation of the effect of kernel selection and tuning parameters [22] showed that best results for MMD can be achieved by those kernels and parameters that obtain supreme value for MMD.”
Hypothesis testing using pairwise distances and associated kernels (2012, background): “Such tests can further be generalized to structured and non-Euclidean domains, such as text strings, graphs or groups (Fukumizu et al., 2009).”
Universality, Characteristic Kernels and RKHS Embedding of Measures (2010, methodology): “We also show that the converse to the result by Gretton et al. (2007) is not true, i.e., if a kernel is characteristic , it need not be c-universal (see Sriperumbudur et al., 2009b, Corollary 15).”
Hilbert Space Embeddings and Metrics on Probability Measures (2009, background): “In Section 3.1, we present the simple characterization that integrally strictly positive definite (pd) kernels (see Section 1.2 for the definition) are characteristic, i.e., the induced RKHS is characteristic (also see Sriperumbudur et al., 2009a, Theorem 4).”
MMD GAN: Towards Deeper Understanding of Moment Matching Network (2017, background): “We refer interested readers to [16] for more rigorous discussions about testing power and increasing MMD distances.”
A Permutation-Based Kernel Conditional Independence Test (2014, background): “Other strategies existing for selecting σ to improve the power of the test statistic (Sriperumbudur et al., 2009; Gretton et al., 2012b).”
Learning Deep Kernels for Non-Parametric Two-Sample Tests (2020, methodology): “Theorem 7 of Sriperumbudur et al. (2009) gives a similar bound in terms of Rademacher chaos complexity, but for ease of combination with our bound on convergence of the variance estimator, we use a simple (cid:15) -net argument instead.”
Domain Generalization with Adversarial Feature Learning (2018, background): “It has been proven that if the kernel k(·, ·) is characteristic, then the mapping μ : P → H is injective [32].”
Universality , Characteristic Kernels and RKHS Embedding of Measures (2011, background): “…(to universality) notion of characteristic kernel has been proposed and characterized (Fukumizu et al., 2004, 2008, 2009; Gretton et al., 2007; Sriperumbudur et al., 2008, 2009, 2010b), which has found applications in testing for homogeneity (Gretton et al., 2007), independence (Gretton et…”
Feature-based transfer learning with real-world applications (2010, unknown): “Research issues include: (1) how to determine the number of the reduced dimensionalities adaptively? (2) How to get a generalization error bound of the proposed framework? (3) How to develop an efficient algorithm for kernel choice of TCA and SSTCA based on the recent theoretic study in [176].”