Bhattacharyya and Expected Likelihood Kernels

By Tony Jebara, Risi Kondor. 2003

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Citations in the corpus

Super-Samples from Kernel Herding (2010, background): “The central result of this paper is now that the pseudosamples generated by kernel herding inherit the fast O(T−1) decrease in error.”
Generative and Latent Mean Map Kernels (2010, background): “Hence, the Gaussian convolution is critical to the exponential decay; in contrast, the Fourier spectrum of the PPK depends on the Fourier transforms of the distributions [10].”
Kernel methods in machine learning (2007, neutral): “Smola and Kondor [125] suggest kernels K = r(L) or K = r(L̃), which have desirable smoothness properties.”
The Multiscale Laplacian Graph Kernel (2016, methodology): “Speciﬁcally, we use the Bhattacharyya kernel because for Gaussian distributions it can be computed in closed form (Jebara & Kondor, 2003), giving If some of the eigenvalues of L − 1 1 or L − 1 2 are zero or very close to zero, along certain directions in space the two distributions in (2) become…”
Image Classification Using Super-Vector Coding of Local Image Descriptors (2010, methodology): “A well-known example is the Bhattacharyya kernel [15]: Here p ( x ) and q ( x ) represent two images as distributions over local descriptor vectors, and µ ( x ) is the image independent background measure.”
A Hilbert Space Embedding for Distributions (2007, result): “This notion was subsequently extended to deal with intermediate density estimates by [63].”
A Kernel Between Sets of Vectors (2003, background): “For more general applications of kernels of the form (1) see (Jebara & Kondor, 2003).”
A Kernel Two-Sample Test (2012, background): “Jebara and Kondor (2003) later extended this setting by smoothing the empirical densities before computing inner products.”
Support Measure Data Description A One-Class Classifier for Group Anomaly Detection (2017, methodology): “Other related kernels on distributions which assume probabilistic models for observations are the Fisher kernel [13], the kernel based on the symmetrized Kullback-Leibler (KL) divergence on distributions [17], the Bhaacharyya kernel [16], and the probability product kernel [14].”
A Discriminative Kernel-Based Approach to Rank Images from Text Queries (2008, background): “Among the three kernels evaluated, the visterm kernel is clearly yielding the best performance, followed by the match kernel and then the ELK.”
Hilbertian Metrics and Positive Definite Kernels on Probability Measures (2005, methodology): “• Given a statistical model for the data one can first fit the model to the data and then use the kernel to compare two fits, see [8, 7].”
Large-scale image categorization with explicit data embedding (2010, methodology): “In section 6, we systematically compare the accuracy of the additive kernels with their exponential counterparts and confirm the superiority of exponential kernels.”