Kernel methods and the exponential family

By Stéphane Canu, Alex Smola. 2006

111 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Control and Systems Engineering

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Citations in the corpus

Density Estimation in Infinite Dimensional Exponential Families (2013, background): “In this paper, we consider the following inﬁnite dimensional generalization [7, 14] of (1) as where the function space F is deﬁned as A ( f ) is the cumulant generating function and ( H , h· , ·i H ) is a reproducing kernel Hilbert space (RKHS) [1] with k as its reproducing kernel (see Section 2…”
Sliced Score Matching: A Scalable Approach to Density and Score Estimation (2019, methodology): “Here, q 0 is a ﬁxed function and f belongs to a reproducing kernel Hilbert space H , with kernel k (Canu & Smola, 2006; Sriperumbudur et al., 2017).”
KALE: When Energy-Based Learning Meets Adversarial Training (2020, methodology): “Examples of non-parametric spaces are Reproducing Kernel Hilbert Spaces (RKHS) as considered in (Canu & Smola, 2006; Fukumizu, 2009; Sriperumbudur et al., 2017).”
Causal reasoning by evaluating the complexity of conditional densities with kernel methods (2008, background): “A general framework for applying the kernel approach to exponential families can be found in [15].”
On the calibration of sensor arrays for pattern recognition using the minimal number of experiments (2014, background): “For example, Adaboost, Support Vector Machines, Neural Networks, Least Squares Support Vector Machines or Logistic Regression can be formulated as Large Margin algorithms [62,63] and Support Vector Machines are related to probabilistic exponential models [64,65,39].”
Entropy and Margin Maximization for Structured Output Learning (2010, background): “The connections between SVMs and exponential families have been indicated in [11], and our work makes the link between the log-loss and max-margin loss more explicit through the inverse temperature and also extends to structured classifiers and latent variables.”
Information, Divergence and Risk for Binary Experiments (2009, background): “…distance minimisation (Borwein and Lewis, 1991; Altun and Smola, 2006; Broniatowski, 2004), and more narrowly focussed “unifying frameworks” such as information geometry (Dawid, 2007; Eguchi, 2005), exponential families (Canu and Smola, 2006) and the information bottleneck (Tishby et al., 2000).”
Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition (2017, methodology): “In this experiment, OC-SVM was applied because it was a kind of de facto standard for novelty/change-point detection, and RuLSIF ws used because it had achieved the best performance among methods based on density-ratio estimation [47].”
Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “…normalisation constant exp ( a ( 𝜃 )), used in statistical applications such as random graph estimation (Yang et al., 2015), spin glass 2 For maximum clarity, the vector calculus notation is expanded as follows: models (Besag, 1974) and the kernel exponential family model (Canu & Smola, 2006).”
Kernel Exponential Family Estimation via Doubly Dual Embedding (2018, methodology): “It is natural to consider generalizing the richness and ﬂexibility of the exponential family to an inﬁnite - dimensional parameterization via reproducing kernel Hilbert spaces (RKHS) (Canu and Smola, 2006).”
Learning structured densities via infinite dimensional exponential families (2015, methodology): “We consider probabilities that are members of an infinite dimensional exponential family [4], which is parametrized by a reproducing kernel Hilbert space (RKHS) H and its kernel k.”
Learning deep kernels for exponential family densities (2018, methodology): “One promising approach for incorporating this necessary structure is the kernel exponential family (Canu and Smola 2006; Fukumizu 2009; Sriperumbudur et al. 2017).”