On Pairwise Kernels: An Efficient Alternative and Generalization Analysis

Kashima, Hisashi; Oyama, Satoshi; Yamanishi, Yoshihiro; Tsuda, Koji

doi:10.1007/978-3-642-01307-2_110

Cited by 20 publications

(18 citation statements)

References 11 publications

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“…. , T } [34], [35]. Cartesian graphs have been considered in the graph signal processing literature for graph filtering and Fourier transforms of time-varying functions [35], but not for signal reconstruction.…”

Section: A Doubly-selective Space-time Kernelsmentioning

confidence: 99%

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Romero

Ioannidis

Giannakis

2017

IEEE J. Sel. Top. Signal Process.

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Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the cost of sampling. Alleviating the limited flexibility of existing approaches, the present paper broadens the existing kernel-based graph function reconstruction framework to accommodate time-evolving functions over possibly time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-time kernels with complementary strengths. The first facilitates judicious control of regularization on a space-time frequency plane, whereas the second can afford time-varying topologies. Batch and online estimators are also put forth, and a novel kernel Kalman filter is developed to obtain these estimates at affordable computational cost. Numerical tests with real data sets corroborate the merits of the proposed methods relative to competing alternatives.

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Section: A Doubly-selective Space-time Kernelsmentioning

confidence: 99%

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Romero

Ioannidis

Giannakis

2017

IEEE J. Sel. Top. Signal Process.

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“…This kernel has been introduced in [68] for modelling protein-protein interactions. We consider this kernel because of its universal approximation property, but also other pairwise kernels exist, such as the cartesian pairwise kernel [69], the metric learning pairwise kernel [70] and the transitive pairwise kernel [71,64]. Nonetheless, it is probably not very surprising that such kernels only yield an improvement if the concepts to be learned satisfy the restrictions that are imposed by the kernels [67].…”

Section: Supervised Rankingmentioning

confidence: 99%

Identification of Functionally Related Enzymes by Learning-to-Rank Methods

Stock

Fober

Hüllermeier

et al. 2014

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Enzyme sequences and structures are routinely used in the biological sciences as queries to search for functionally related enzymes in online databases. To this end, one usually departs from some notion of similarity, comparing two enzymes by looking for correspondences in their sequences, structures or surfaces. For a given query, the search operation results in a ranking of the enzymes in the database, from very similar to dissimilar enzymes, while information about the biological function of annotated database enzymes is ignored. In this work, we show that rankings of that kind can be substantially improved by applying kernel-based learning algorithms. This approach enables the detection of statistical dependencies between similarities of the active cleft and the biological function of annotated enzymes. This is in contrast to search-based approaches, which do not take annotated training data into account. Similarity measures based on the active cleft are known to outperform sequence-based or structure-based measures under certain conditions. We consider the Enzyme Commission (EC) classification hierarchy for obtaining annotated enzymes during the training phase. The results of a set of sizeable experiments indicate a consistent and significant improvement for a set of similarity measures that exploit information about small cavities in the surface of enzymes.

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“…An alternative approach known as the Cartesian kernel has been proposed by Kashima et al [2009b] for overcoming the computational challenges associated with the Kronecker product kernels. This kernel indeed exhibits interesting computational properties, but it can be solely employed in selected applications, because it cannot make predictions for (couples of) objects that are not observed in the training dataset, that is, in setting 4 (see for further discussion and experimental results).…”

Section: Learning Setting and Related Workmentioning

confidence: 99%

Efficient regularized least-squares algorithms for conditional ranking on relational data

et al. 2013

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In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational data, where rankings can be conditioned on unseen data objects. We propose efficient algorithms for conditional ranking by optimizing squared regression and ranking loss functions. We show theoretically, that learning with the ranking loss is likely to generalize better than with the regression loss. Further, we prove that symmetry or reciprocity properties of relations can be efficiently enforced in the learned models. Experiments on synthetic and real-world data illustrate that the proposed methods deliver state-of-the-art performance in terms of predictive power and computational efficiency. Moreover, we also show empirically that incorporating symmetry or reciprocity properties can improve the generalization performance.

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On Pairwise Kernels: An Efficient Alternative and Generalization Analysis

Cited by 20 publications

References 11 publications

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

Identification of Functionally Related Enzymes by Learning-to-Rank Methods

Efficient regularized least-squares algorithms for conditional ranking on relational data

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