Learning Graphical Models with Mercer Kernels

By Francis R. Bach, Michael I. Jordan. 2002

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Citations in the corpus

Nonparametric Independence Testing for Small Sample Sizes (2014, methodology): “ing. The long list of applications includes kernel PCA [1], dimension reduction [2], structure discovery [3], independence testing [4], Granger causality in time series [5], learning graphical models [6], feature learning [7], target or conditional shift [8] and kernel Bayes’ rule [9]. All the above”
Generalized Score Functions for Causal Discovery (2018, methodology): “More recently, some other score-based methods [2, 4, 18, 19, 26] and hybrid methods [9, 31] have been proposed; they exploit some assumptions of the model class.”
From sample similarity to ensemble similarity: probabilistic distance measures in reproducing kernel Hilbert space (2006, methodology): “Therefore a regularized covariance matrix is needed in [9], [10], [11].”
Learning Bayesian Networks with the bnlearn R Package (2009, background): “Other distributional assumptions lead to more complex learning algorithms (such as the non-parametric approach proposed by Bach and Jordan (2003)) or present various limitations due to the diﬃculty of specifying the distribution functions in closed form (such as the approach to learn Bayesian…”
Learning Bayesian networks: approaches and issues (2011, methodology): “Bach and Jordan (2003) also use kernels, of the Mercer variety. Slightly different is the work of Monti and Cooper (1997a, 1997b), who use neural networks to represent the density function. A different approach, based on the CI testing paradigm is used by Margaritis (2004). In the discrete case, the”
Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery (2005, methodology): “In fact, the Gaussian distribution has previously been assumed in the feature space, generating satisfactory experimental results in image segmentation and graphical model learning [18], [26], [27].”
Learning Sparse Nonparametric DAGs (2019, methodology): “Comparisons with other score-based methods (KGV score (Bach and Jordan, 2003), Spearman correlation (Sokolova et al.”