Integrating structured biological data by Kernel Maximum Mean Discrepancy

By Karsten M. Borgwardt, Arthur Gretton, Malte J. Rasch, Hans-Peter Kriegel, Bernhard Schölkopf, Alex Smola. 2006

1,690 citations recorded by the source corpus.

Subfields: Molecular Biology, Computational Biology & Bioinformatics

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “On a discrete domain X = {x1, . . . ,xn}, any strictly positive definite kernel, e.g., k(x,x′) = 1{x=x′}, is universal (Borgwardt et al. 2006; Section 2.3).”
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.”
Fast Two-Sample Testing with Analytic Representations of Probability Measures (2015, methodology): “These include data integration in bioinformatics [6], benchmarking for steganography [20] and automated model checking [19].”
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test (2014, background): “…(Smola et al., 2008; Sriperumbudur et al., 2010; 2011; Sejdinovic et al., 2013) and successful applications including biological data test (Borgwardt et al., 2006), data integration and attribute matching (Gretton et al., 2009), outlier detection, data classifiability (Sriperumbudur et…”
Kernel Adaptive Metropolis-Hastings (2013, methodology): “In these examples, exact quantile regions of the targets can be computed analytically, so we can directly assess performance without the need to estimate distribution distances on the basis of samples (i.e., by estimating MMD to the benchmark sample).”
Hilbert Space Embeddings and Metrics on Probability Measures (2009, background): “• Structured domains: Since γk is dependent only on the kernel (see Theorem 1) and kernels can be defined on arbitrary domains M (Aronszajn, 1950), choosing F = Fk provides the flexibility of measuring the distance between probability measures defined on structured domains (Borgwardt et al., 2006) l”
A Kernel Method for the Two-Sample-Problem (2006, positive): “These results build on o ur earlier work in [6] on MMD for the two sample problem, which addresses only the second kind of t est.”
Simultaneous Deep Transfer Across Domains and Tasks (2015, background): “In fact, the size of a domain shift is often measured by the distance between the source and target subspace representations [5, 11, 21, 25, 27].”
Deep Domain Confusion: Maximizing for Domain Invariance (2014, methodology): “In fact, the size of a domain shift is often measured by the distance between the source and target subspace representations [6, 13, 23, 26, 28].”
Kernel methods in machine learning (2007, neutral): “The corresponding distance d(p, q) := ‖μ[p]− μ[q]‖ leads to a U -statistic which allows one to compute empirical estimates of distances between distributions efficiently [22].”
A Comprehensive Survey on Transfer Learning (2019, methodology): “The measurement termed maximum mean discrepancy (MMD) is widely used in the field of transfer learning, which is formulated as follows [35]:”
Return of Frustratingly Easy Domain Adaptation (2015, background): “Others minimize the distance between the target and source domains, either by re-weighting the domains or by changing the feature representation according to some explicit distribution distance metric (Borgwardt et al. 2006).”
Domain Adaptive Neural Networks for Object Recognition (2014, methodology): “By deﬁning F as the set of functions of the unit ball in a universal Reproducing Kernel Hilbert Space (RKHS), denoted by H , it was shown that MMD ( F , p, q ) = 0 will detect any discrepancy between p and q (Borgwardt et al., 2006).”