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The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
Deep neural networks have recently achieved state of the art performance thanks to new training algorithms for rapid parameter estimation and new regularization methods to reduce overfitting. However, in practice the network architecture…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
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…
As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…
This paper introduces a new and effective algorithm for learning kernels in a Multi-Task Learning (MTL) setting. Although, we consider a MTL scenario here, our approach can be easily applied to standard single task learning, as well. As…
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…
Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…
Kernels for structured data are commonly obtained by decomposing objects into their parts and adding up the similarities between all pairs of parts measured by a base kernel. Assignment kernels are based on an optimal bijection between the…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
Kernels ensuing from tree ensembles such as random forest (RF) or gradient boosted trees (GBT), when used for kernel learning, have been shown to be competitive to their respective tree ensembles (particularly in higher dimensional…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…
Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…