Related papers: Optimal kernel selection for density estimation
We establish a new concentration result for regularized risk minimizers which is similar to an oracle inequality. Applying this inequality to regularized least squares minimizers like least squares support vector machines, we show that…
A problem of statistical estimation of a Hermitian nonnegatively definite matrix of unit trace (for instance, a density matrix in quantum state tomography) is studied. The approach is based on penalized least squares method with a…
This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…
We emphasize that it is possible to improve the principle of unbiased risk estimation for model selection by addressing excess risk deviations in the design of penalization procedures. Indeed, we propose a modification of Akaike's…
By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…
We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
In the framework of computational complexity and in an effort to define a more natural reduction for problems of equivalence, we investigate the recently introduced kernel reduction, a reduction that operates on each element of a pair…
We establish sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups.
We consider a finite mixture of Gaussian regression model for high- dimensional data, where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by a maximum…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown…
This paper addresses the problem of distributed learning under communication constraints, motivated by distributed signal processing in wireless sensor networks and data mining with distributed databases. After formalizing a general model…
In this paper, we study the Nystr{\"o}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nystr{\"o}m type subsampling which is…
We propose a simple yet effective multiple kernel clustering algorithm, termed simple multiple kernel k-means (SimpleMKKM). It extends the widely used supervised kernel alignment criterion to multi-kernel clustering. Our criterion is given…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
It is common, in deconvolution problems, to assume that the measurement errors are identically distributed. In many real-life applications, however, this condition is not satisfied and the deconvolution estimators developed for…