Fourier analysis and applications: filtering, numerical computation, wavelets
Fourier analysis and applications: filtering, numerical computation, wavelets
On the influence of the kernel on the consistency of support vector machines
The Journal of Machine Learning Research
Kernel independent component analysis
The Journal of Machine Learning Research
Dimensionality Reduction for Supervised Learning with Reproducing Kernel Hilbert Spaces
The Journal of Machine Learning Research
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Kernel Methods for Measuring Independence
The Journal of Machine Learning Research
The Journal of Machine Learning Research
A Hilbert Space Embedding for Distributions
ALT '07 Proceedings of the 18th international conference on Algorithmic Learning Theory
Support Vector Machines
Fast kernel-based independent component analysis
IEEE Transactions on Signal Processing
On Divergences and Informations in Statistics and Information Theory
IEEE Transactions on Information Theory
Comparing distributions and shapes using the kernel distance
Proceedings of the twenty-seventh annual symposium on Computational geometry
Universality, Characteristic Kernels and RKHS Embedding of Measures
The Journal of Machine Learning Research
The Journal of Machine Learning Research
On minimum distribution discrepancy support vector machine for domain adaptation
Pattern Recognition
Gaussianity measures for detecting the direction of causal time series
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Batch mode active sampling based on marginal probability distribution matching
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Feature selection via dependence maximization
The Journal of Machine Learning Research
Querying discriminative and representative samples for batch mode active learning
Proceedings of the 19th ACM SIGKDD international conference on Knowledge discovery and data mining
Batch Mode Active Sampling Based on Marginal Probability Distribution Matching
ACM Transactions on Knowledge Discovery from Data (TKDD) - Special Issue on ACM SIGKDD 2012
Moving heaven and earth: distances between distributions
ACM SIGACT News
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). A pseudometric on the space of probability measures can be defined as the distance between distribution embeddings: we denote this as γk, indexed by the kernel function k that defines the inner product in the RKHS. We present three theoretical properties of γk. First, we consider the question of determining the conditions on the kernel k for which γk is a metric: such k are denoted characteristic kernels. Unlike pseudometrics, a metric is zero only when two distributions coincide, thus ensuring the RKHS embedding maps all distributions uniquely (i.e., the embedding is injective). While previously published conditions may apply only in restricted circumstances (e.g., on compact domains), and are difficult to check, our conditions are straightforward and intuitive: integrally strictly positive definite kernels are characteristic. Alternatively, if a bounded continuous kernel is translation-invariant on ℜd, then it is characteristic if and only if the support of its Fourier transform is the entire ℜd. Second, we show that the distance between distributions under γk results from an interplay between the properties of the kernel and the distributions, by demonstrating that distributions are close in the embedding space when their differences occur at higher frequencies. Third, to understand the nature of the topology induced by γk, we relate γk to other popular metrics on probability measures, and present conditions on the kernel k under which γk metrizes the weak topology.