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Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…
Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian…
Spatial range joins have many applications, including geographic information systems, location-based social networking services, neuroscience, and visualization. However, joins incur not only expensive computational costs but also too large…
Because of the recent advances of genome sequences, a large number of human genome sequences are available for the study of human genetics. Genome-wide association studies typically focus on associations between single-nucleotide…
We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…
Kernel methods have produced state-of-the-art results for a number of NLP tasks such as relation extraction, but suffer from poor scalability due to the high cost of computing kernel similarities between natural language structures. A…
Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…
Kernel approximation is widely used to scale up kernel SVM training and prediction. However, the memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices such as…
Structured kernel interpolation (SKI) accelerates Gaussian process (GP) inference by interpolating the kernel covariance function using a dense grid of inducing points, whose corresponding kernel matrix is highly structured and thus…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD…
Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs…
A well-recognized limitation of kernel learning is the requirement to handle a kernel matrix, whose size is quadratic in the number of training examples. Many methods have been proposed to reduce this computational cost, mostly by using a…
This paper discusses the problem of marrying structural similarity with semantic relatedness for Information Extraction from text. Aiming at accurate recognition of relations, we introduce local alignment kernels and explore various…
The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…
Suppose an oracle knows a string $S$ that is unknown to us and that we want to determine. The oracle can answer queries of the form "Is $s$ a substring of $S$?". In 1995, Skiena and Sundaram showed that, in the worst case, any algorithm…
Due to its promising classification performance, sparse representation based classification(SRC) algorithm has attracted great attention in the past few years. However, the existing SRC type methods apply only to vector data in Euclidean…
The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…
We propose a sparse algebra for samplet compressed kernel matrices, to enable efficient scattered data analysis. We show the compression of kernel matrices by means of samplets produces optimally sparse matrices in a certain S-format. It…