# Bayesian Nonparametric Kernel-Learning

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Junier B. Oliva,
Avinava Dubey,
Andrew G. Wilson,
Barnabas Poczos,
Jeff Schneider,
Eric P. Xing
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Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:1078-1086, 2016.

#### Abstract

Kernel methods are ubiquitous tools in machine learning. They have proven to be effective in many domains and tasks. Yet, kernel methods often require the user to select a predefined kernel to build an estimator with. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample estimator may be greatly affected by the choice of kernel. Furthermore, when directly applying kernel methods, one typically needs to compute a N \times N Gram matrix of pairwise kernel evaluations to work with a dataset of N instances. The computation of this Gram matrix precludes the direct application of kernel methods on large datasets, and makes kernel learning especially difficult. In this paper we introduce Bayesian nonparmetric kernel-learning (BaNK), a generic, data-driven framework for scalable learning of kernels. BaNK places a nonparametric prior on the spectral distribution of random frequencies allowing it to both learn kernels and scale to large datasets. We show that this framework can be used for large scale regression and classification tasks. Furthermore, we show that BaNK outperforms several other scalable approaches for kernel learning on a variety of real world datasets.

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