A Kernel Two-Sample Test

By Arthur Gretton, Karsten M. Borgwardt, Malte J. Rasch, Bernhard Schölkopf, Alex Smola. 2012

6,578 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Generating Sentences from a Continuous Space (2015, methodology): “Adversarial evaluation Drawing inspiration from adversarial training methods for generative models as well as non-parametric two-sample tests (Goodfellow et al., 2014; Li et al., 2015b; Denton et al., 2015; Gretton et al., 2012), we evaluate the imputed sentence completions by examining their distin”
Symbolic Music Generation with Diffusion Models (2021, methodology): “We evaluate the similarity of latent embeddings generated by each of our models using the Fréchet distance (FD) [28] and Maximum Mean Discrepancy (MMD) [29] with a polynomial kernel, which are popular evaluation metrics in the generative modeling literature.”
Learning deep representations by mutual information estimation and maximization (2018, background): “Absolute magnitude of information is only one desirable property of a representation; depending on the application, good representations can be compact (Gretton et al., 2012), independent (Hyvärinen & Oja, 2000; Hinton, 2002; Dinh et al.”
GAIT: A Geometric Approach to Information Theory (2019, methodology): “Under these circumstances, the metric structure present in the Hilbert space can be imported to define the Maximum Mean Discrepancy distance between distributions (Gretton et al., 2012).”
Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields (2017, methodology): “In a similar fashion, Generative Moment Matching Networks [30] and MMD nets [11] directly optimize a generator network to match a training distribution by using a loss function based on the maximum mean discrepancy (MMD) criterion [16].”
Generalization and Equilibrium in Generative Adversarial Nets (GANs) (2017, neutral): “We note that similar results have been shown before in study of pseudorandomness [Trevisan et al., 2009] and model criticism [Gretton et al., 2012].”
Wasserstein GAN (2017, background): “As proved on [5] we know that MMD is a proper metric and not only a pseudomet-ric when the kernel is universal.”
Generative Moment Matching Networks (2015, methodology): “In the literature there have been several alternative estimators designed to overcome this (Gretton et al., 2012a).”
Sequential Kernel Herding: Frank-Wolfe Optimization for Particle Filtering (2015, methodology): “In the context of RKHSs, MMD( p, q ) can be called the maximum mean discrepancy (Gretton et al., 2012) between the distributions p and q , and acts a pseudo-metric on the space of distributions on X .”
DeepMDP: Learning Continuous Latent Space Models for Representation Learning (2019, methodology): “Energy distance: The energy distance E was first developed to compare distributions in high dimensions via a two sample test (Székely & Rizzo, 2004; Gretton et al., 2012).”
Demystifying MMD GANs (2018, background): “…drawn i.i.d. from P , and Y = { y j } nj =1 drawn i.i.d. from Q , the empirical witness function is and an unbiased estimator of the squared MMD is (Gretton et al., 2012, Lemma 6) When the kernel is characteristic (Sriperumbudur et al., 2010; 2011), the embedding µ is injective (i.e., associated…”
Training generative neural networks via Maximum Mean Discrepancy optimization (2015, methodology): “The development here owes much to Gretton et al. [2].”
Classification Accuracy Score for Conditional Generative Models (2019, background): “Maximum Mean Discrepancy [33] is a two-sample test that has many nice theoretical properties but seems to be less used because the choice of kernels do not necessarily coincide with human judgment.”
Learning Transferable Features with Deep Adaptation Networks (2015, methodology): “The reason is that multiple kernels with different bandwidths can match both the low-order moments and high-order moments and lead to lower Type II error (Gretton et al., 2012).”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “of these difficulties, Grünewälder et al. (2012) proposes to learn transition dynamics, i.”
On the (Statistical) Detection of Adversarial Examples (2017, methodology): “In this way, we show that statistical properties of adversarial examples are essential to their detection.2”
DISCO Nets : DISsimilarity COefficients Networks (2016, background): “[8, 9]) is a statistical hypothesis test assessing if two probabilistic distributions are similar.”
Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods (2017, background): “test [7, 14], a statistical hypothesis test that answers the question “are these two sets drawn from the same underlying distribution?” The MMD is a theoretically useful technique that can be formally shown to always detect a difference if one occurs.”
Recent Progress on Generative Adversarial Networks (GANs): A Survey (2019, background): “The Wasserstein Critic [27] and Maximum Mean Discrepancy (MMD) [42] are proposed to measure the distance between the real sample distributions and the generated sample distributions.”
Path-Specific Counterfactual Fairness (2018, methodology): “We encourage ˜ p ( H m | A = a ) to have small dependence on A during training through the maximum mean discrepancy (MMD) criterion (Gretton et al., 2012).”