Optimal kernel choice for large-scale two-sample tests

By Arthur Gretton, Bharath K. Sriperumbudur, Dino Sejdinovic, Heiko Strathmann, Sivaraman Balakrishnan, Massimiliano Pontil, Kenji Fukumizu. 2012

764 citations recorded by the source corpus.

Subfields: Evaluation & Benchmarks

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Citations in the corpus

Generative Moment Matching Networks (2015, methodology): “In the literature there have been several alternative estimators designed to overcome this (Gretton et al., 2012a).”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Theorem 3.5 below describes an unbiased quadratic-time estimate of the MMD, and its asymptotic distribution under an alternative hypothesis that P 6= Q. Theorem 3.6 (Gretton et al. 2012a; Lemma 6; Corollary 16).”
Kernel‐based tests for joint independence (2016, background): “ i<j o = 2σ2. This heuristic performs quite well in many practical applications. It may be possible, however, to extend alternative approaches from two-sample testing to independence testing (e.g. Gretton et al., 2012). For discrete data, we choose a trivial kernel deﬁned by k(x,y) := 1{x=y}. In ”
Interpretable Distribution Features with Maximum Testing Power (2016, methodology): “…on RKHS distances (Eric et al., 2008; Fromont et al., 2012; Gretton et al., 2012a) or energy distances (Székely and Rizzo, 2004; Baringhaus and Franz, 2004) have as their test statistic an integral probability metric, the Maximum Mean Discrepancy (Gretton et al., 2012a; Sejdinovic et al., 2013).”
Bayesian Learning of Kernel Embeddings (2016, methodology): “As noted in Gretton et al. (2012b), the choice of the kernel k is critically important for the power of the tests presented in Section 2.2.”
A Test of Relative Similarity For Model Selection in Generative Models (2015, methodology): “(Gretton et al., 2012a Let V := ( v 1 , ..., v m ) be m i.i.d. random variables, where v := ( x, y ) ∼ P x × P y .”
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “Gretton et al. [2012b] also make suggestions for choosing the bandwidth parameter, but only for the linear-time gMMD 2 l (see Section 6), and also with guarantees only in the ﬁxed d setting.”
Fast Two-Sample Testing with Analytic Representations of Probability Measures (2015, background): “The probability that all T i sit in the complement of interval ) and such an event implies that S 2 ϕ,J = 0 .”
A low variance consistent test of relative dependency (2014, background): “This kernel is sufficient to obtain good performance, although others choices exist (Gretton et al., 2012).”
On the Decreasing Power of Kernel and Distance Based Nonparametric Hypothesis Tests in High Dimensions (2014, methodology): “5A of (Gretton et al. 2012a), the authors choose the latter (veriﬁed by personal communication) and ﬁnd that the power is only very slowly affected by dimension.”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, methodology): “The maximum mean discrepancy (MMD) is the latest test statistic designed for this task by measuring the discrepancy of two distributions by embedding them in a reproducing kernel Hilbert space (Gretton et al., 2012a).”
MMD GAN: Towards Deeper Understanding of Moment Matching Network (2017, background): “Note that [18] considers the linear combination of characteristic kernels, which can also be incorporated into the discussed composition kernels.”
Revisiting Classifier Two-Sample Tests (2016, methodology): “First, two-sample tests can measure statistical dependence (Gretton et al., 2012a).”
A Comprehensive Survey on Transfer Learning (2019, background): “[62] adopt the linear-time unbiased estimation of MK-MMD to avoid numerous inner product operations.”
A Survey on Deep Transfer Learning (2018, methodology): “The MMD distance used in this work is deﬁned as and the loss function is deﬁned as [12] improved previous work by replace MMD distance with multiple kernel variant MMD (MK-MMD) distance proposed by [8].”
Deep Hashing Network for Unsupervised Domain Adaptation (2017, methodology): “) is the multi-kernel maximum mean discrepancy between the source and target representations, [24].”