Related papers: Optimal kernel selection for density estimation
Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum…
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of…
Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…
We study Nystr\"om type subsampling approaches to large scale kernel methods, and prove learning bounds in the statistical learning setting, where random sampling and high probability estimates are considered. In particular, we prove that…
The accuracy and complexity of kernel learning algorithms is determined by the set of kernels over which it is able to optimize. An ideal set of kernels should: admit a linear parameterization (tractability); be dense in the set of all…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.
Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through…
Learning linear combinations of multiple kernels is an appealing strategy when the right choice of features is unknown. Previous approaches to multiple kernel learning (MKL) promote sparse kernel combinations to support interpretability and…
There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…
The problem of assessing the performance of algorithms used for the minimization of an $\ell_1$-penalized least-squares functional, for a range of penalty parameters, is investigated. A criterion that uses the idea of `approximation…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
We present a number of new piecewise-polynomial kernels for image interpolation. The kernels are constructed by optimizing a measure of interpolation quality based on the magnitude of anisotropic artifacts. The kernel design process is…
Many statistical estimation procedures lead to nonconvex optimization problems. Algorithms to solve these are often guaranteed to output a stationary point of the optimization problem. Oracle inequalities are an important theoretical…
To cluster data that are not linearly separable in the original feature space, $k$-means clustering was extended to the kernel version. However, the performance of kernel $k$-means clustering largely depends on the choice of kernel…
We derive oracle inequalities for the problems of isotonic and convex regression using the combination of $Q$-aggregation procedure and sparsity pattern aggregation. This improves upon the previous results including the oracle inequalities…
Kernel density estimation is a technique for approximating probability distributions. Here, it is applied to the calculation of mutual information on a metric space. This is motivated by the problem in neuroscience of calculating the mutual…
A framework of M-estimation based fuzzy C-means clustering (MFCM) algorithm is proposed with iterative reweighted least squares (IRLS) algorithm, and penalty constraint and kernelization extensions of MFCM algorithms are also developed.…
We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned…