Probability Product Kernels

By Tony Jebara, Risi Kondor, Andrew G. Howard. 2004

581 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods, Statistical Learning Theory

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Citations in the corpus

Discriminative Embeddings of Latent Variable Models for Structured Data (2016, neutral): “The Fisher kernel (Jaakkola & Haussler, 1999) and probability product kernel (Jebara et al., 2004) are two representative instances within the family.”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “For intractable models, Jebara et al. (2004) suggested approximating (3.48) by using structured mean-field approximations.”
Word Representations via Gaussian Embedding (2014, background): “This idea seems very natural, and indeed has appeared before – the idea of mapping data casesw into probability distributions (often over their contexts), and comparing them via integrals has a history under the name of the expected likelihood or probability product kernel (Jebara et al., 2004).”
Learning Theory for Distribution Regression (2014, methodology): “Methods based on parametric assumption in a RKHS: A heuristic related to the parametric approach is to assume that the training distributions are Gaussians in a reproducing kernel Hilbert space (see for example Jebara et al., 2004; Zhou and Chellappa, 2006, and references therein).”
Fast Distribution To Real Regression (2013, methodology): “Perhaps the most clear-cut of these methods is to ﬁt a parametric model to distributions for estimating ker-Junier nels [5, 4, 10].”
Nonparametric kernel estimators for image classification (2012, methodology): “We first fit the density to each group, and then compute the KLdivergence (G-KL, GMM-KL) [19] and product probability kernels (G-PPK, GMM-PPK) [11] with α = 0.”
Generative and Latent Mean Map Kernels (2010, methodology): “For the GMMK and PPK, we adopted a heuristic formula [11] to choose the number of states n in the HMM learned for a particular sequence: n = b 12 √ k2 + 4(Tγ + k + 1)− 12kc+1, for k symbols and a constant γ set to 0.”
Propagation kernels: efficient graph kernels from propagated information (2014, background): “Finally, propagation kernels mark another connection, namely between graph kernels and kernels between probability distributions (Jaakkola andHaussler 1998; Lafferty and Lebanon 2002; Moreno et al. 2003; Jebara et al. 2004) and between sets (Kondor and Jebara 2003; Shi et al.”
Tensor Representations via Kernel Linearization for Action Recognition from 3D Skeletons (2016, methodology): “To obtain these maps, we use a fast approximation method based on probability product kernels [35].”
The Vendi Score: A Diversity Evaluation Metric for Machine Learning (2022, methodology): “We adapt this approach and we calculate vs using the probability product kernel (Jebara et al., 2004): , where the class likelihoods are given by the classiﬁer.”
Towards a Learning Theory of Cause-Effect Inference (2015, background): “In a separate strand of research, there has been several attempts to learn from probability distributions in a principled manner (Jebara et al., 2004; Hein & Bousquet, 2004; Cuturi et al., 2005; Martins et al., 2009; Muandet et al., 2012).”
Generative Kernels for Tree-Structured Data (2018, methodology): “In [33], it has been discussed an alternative feature space obtained by concatenating the sufficient HTMM statistics, as well as a tree kernel based on the probability product approach in [34].”
Learning from Conditional Distributions via Dual Kernel Embeddings (2016, methodology): “, the probability product kernel [15], can be also used in incorporating invariance.”
Hybrid Models with Deep and Invertible Features (2019, background): “Perhaps there are even deeper connections to be made via Fisher kernels (Jaakkola & Haussler, 1999) or probability product kernels (Jebara et al., 2004)—kernel functions derived from generative models—but we leave this investigation to future work.”
Mean Map Kernel Methods for Semisupervised Cloud Classification (2010, methodology): “measure is computed in the Hilbert space between the Gaussians obtained after mapping the set of vectors into H; in [37], kernel machines are combined with generative modeling”
Probabilistic Face Embeddings (2019, background): “onally independent (given the latent code z). It can be shown that: p(zjx 1;x 2;:::;x n+1) = p(zjx n+1) p(z) p(zjx 1;x 2;:::;x n); (5) 5also known as expected likelihood or probability product kernel [14]. where is a normalization factor. To simplify the notations, let us only consider a one-dimensi”
A Survey of Vision-Based Trajectory Learning and Analysis for Surveillance (2008, methodology): “In a similar spirit, kernel methods have been derived from large-margin research to account for nonlinear clusters yet preserve structure and the ordering constraints of tracks [63], [64].”