Kernel Embeddings of Conditional Distributions: A Unified Kernel Framework for Nonparametric Inference in Graphical Models

By Le Song, Kenji Fukumizu, Arthur Gretton. 2013

251 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Biophysics, Probabilistic & Bayesian Methods, Statistical Learning Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “The kernel Bayes’ rule is given by µΠY |x = CΠY |Xφ(x) = CΠYX(CΠXX )−1φ(x) (4.22) where the operators CΠ YX and CΠ XX are given by CΠYX = (CX |YCΠYY )⊤, CΠXX = C(XX)|Y µΠY , where the former uses the kernel product rule (4.19), and the latter uses the kernel sum rule (4.16).”
Domain Generalization via Conditional Invariant Representations (2018, methodology): “Before introducing the proposed method, we brieﬂy review the kernel mean embedding of distributions, which is an important mathematical tool to represent and compare distributions (Song, Fukumizu, and Gretton 2013; Sriperum-budur et al. 2010).”
K2-ABC: Approximate Bayesian Computation with Infinite Dimensional Summary Statistics via Kernel Embeddings (2015, methodology): “…et al., 2007; Sriperumbudur et al., 2010) offer a flexible representation of probability measures and have been used in nonparametric hypothesis testing (Gretton et al., 2012), inference in graphical models (Song et al., 2013) and constructing proposals in adaptive MCMC (Sejdinovic et al., 2014).”
Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “There is a good review paper on Bayesian inference with the kernel mean (Song et al., 2013).”
Filtering with State-Observation Examples via Kernel Monte Carlo Filter (2013, methodology): “For details, we refer to the tutorial papers (Smola et al., 2007; Song et al., 2013).”
Smooth Operators (2013, methodology): “…include the sum rule for marginalising out a random variable in a multivariate distribution (Song, Huang, Smola, and Fukumizu, 2009), and kernel-based approximations to Bayes' rule for inference without parametric models (Fukumizu, Song, and Gretton, 2011; Song, Fukumizu, and Gretton, 2013).”
Recycling Privileged Learning and Distribution Matching for Fairness (2017, methodology): “To generalize this to any type and multiple dependence of protected characteristics, we can use the Hilbert Space embedding of conditional distributions framework of [44, 45].”
Non-parametric Policy Search with Limited Information Loss (2017, background): “Using such embeddings avoids estimating the joint density and leads to good results even for high-dimensional data, and renders calculations of expected values over a function in F straightforward without numerical integration (Song et al., 2013).”
Monte Carlo Filtering Using Kernel Embedding of Distributions (2014, methodology): “In general, the embedding mP is estimated in the form of a weighted sum of feature vectors φ(Xi) of the data m̂P = n∑ i=1 wiφ(Xi), (2) where the (possibly negative) weights wi ∈ R are computed by an estimator ofmP (Song, Fukumizu, and Gretton 2013).”
Learning Program Embeddings to Propagate Feedback on Student Code (2015, methodology): “From the kernel methods literature, there has also been recent work on representations of conditional probability distributions as operators on a Hilbert space (Song et al., 2013; 2009).”
Non-linear Causal Inference using Gaussianity Measures (2014, methodology): “We note that the estimate obtained in (21) coincides with the kernel conditional embedding operator described by Song et al. (2013) for mapping conditional distributions into infinite dimensional feature spaces using kernels.”
Learning of Non-Parametric Control Policies with High-Dimensional State Features (2015, methodology): “They also render calculations of expected values over a function in F straightfoward without numerical integration [Song et al., 2013].”
Variational Approach for Learning Markov Processes from Time Series Data (2017, background): “As shown in [28], this approximation becomes exact in the limit of infinitely-sized feature transformations with f = g, and a similar conclusion can also be obtained when f ,g are infinite-dimensional feature functions deduced from a characteristic kernel [56].”
Recovering Distributions from Gaussian RKHS Embeddings (2014, methodology): “The RKHS embedding approach for nonparametric statistical inference has been developed in the machine learning community as a recent advance of kernel methods (Smola et al., 2007; Sriperumbudur et al., 2010; Song et al., 2013).”