Convolution kernels on discrete structures

By David Haussler. 1999

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Citations in the corpus

Learning Convolutional Neural Networks for Graphs (2016, background): “…to (Yanardag & Vish-wanathan, 2015) and graph invariant kernels (Orsini et al., 2015) compare graphs based on the existence or count of small substructures such as shortest paths (Borgwardt & Kriegel, 2005), graphlets, subtrees, and other graph invariants (Haussler, 1999; Orsini et al., 2015).”
Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, background): “Moreover, the empirical version of (3.49) and (3.40) coincides with that of classical set kernel of Haussler (1999) and Gärtner et al. (2002) (see also Kondor and Jebara (2003)).”
Learning Theory for Distribution Regression (2014, methodology): “As a special case of our results, we proved the consistency of regression for set kernels (Haussler, 1999; Gärtner et al., 2002), which was a 17-year-old open problem, and for a recent kernel family (Christmann and Steinwart, 2010), which we have expanded upon (Table 1).”
Fastfood: Approximate Kernel Expansions in Loglinear Time (2014, background): “(25) This is a locally weighted variant of the conventional Gaussian RBF kernel, e.g. as described by Haussler (1999).”
On the Schoenberg Transformations in Data Analysis: Theory and Illustrations (2010, neutral): “3 Some properties of the Schoenberg transformations”
An End-to-End Deep Learning Architecture for Graph Classification (2018, methodology): “A pioneering work was introduced as the convolution kernel in (Haussler 1999), which decomposes graphs into small substructures and computes kernel functions by adding up the pair-wise similarities between these components.”
A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, background): “Graph kernel is an instance of R-convolution kernels [136], which is a generic way of defining kernels on discrete compound objects by recursively decomposing structured objects into “atomic” substructures and comparing all pairs of them [93].”
A simple yet effective baseline for non-attribute graph classification (2018, background): “nomial time [Bab16]. The subgraph isomorphism, on the other hand, is NP-complete. 2 2 Related Work 2.1 Graph Kernel There are various graph kernels, many of which explore the R-convolutional framework[Hau99]. The key ideaistodecompose awholegraph into smallsubstructures andbuild graph kernels based ”
Graph Kernels (2008, neutral): “Haussler (1999) implicitly assumed this sum to be well-defined, and hence did not use a measure µ in his definition.”
Kernel methods in machine learning (2007, positive): “In this case, it can be shown that the R-convolution is a valid kernel (Haussler [62]).”
On Valid Optimal Assignment Kernels and Applications to Graph Classification (2016, background): “Most kernels for structured data decompose both objects and add up the pairwise similarities between their parts following the seminal concept of convolution kernels proposed by Haussler [12].”
Kernel Methods for Relation Extraction (2002, background): “They are yet to be experimentally validated for information extraction problems.”
Propagation kernels: efficient graph kernels from propagated information (2014, background): “As for a given graph G(i) the number of nodes is finite, K (G t ,G ( j) t ) is a convolution kernel (Haussler 1999).”
Ordered Decompositional DAG kernels enhancements (2015, background): “ning algorithm. A popular strategy for dening kernel functions for structured data is to decompose the structures into their constituent parts, and then, for each pair of parts, apply a local kernel [12]. While this strategy has been proved successful for strings and trees [13, 14, 15, 16, 17, 18], ”
Marginalized kernels for biological sequences (2002, methodology): “Since the number of parameters of the second-order HMM is much When there is one-to-one correspondence between two parameter spaces around and , the Fisher kernel is invariant to parametrization because of the Fisher information matrix (Jaakkola & Haussler, 1999).”
Probability Product Kernels (2004, background): “, 2002), convolutional kernels (Haussler, 1999; Collins and Duffy, 2002), alignment kernels (Watkins, 2000), rational kernels (Cortes et al.”