Related papers: Parsimonious Mahalanobis Kernel for the Classifica…
Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…
Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…
This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides…
Radial Basis Function (RBF), or Gaussian, kernels are among the most widely used parametric kernels in machine learning, particularly in methods such as Support Vector Machines (SVM) and kernel-based subspace approaches. The kernel…
Linear mixed models (LMMs) are used extensively to model dependecies of observations in linear regression and are used extensively in many application areas. Parameter estimation for LMMs can be computationally prohibitive on big data.…
The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…
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…
This paper focuses on the problem of kernelizing an existing supervised Mahalanobis distance learner. The following features are included in the paper. Firstly, three popular learners, namely, "neighborhood component analysis", "large…
Most metric learning algorithms, as well as Fisher's Discriminant Analysis (FDA), optimize some cost function of different measures of within-and between-class distances. On the other hand, Support Vector Machines(SVMs) and several Multiple…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…
Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…
We propose a novel class of kernels to alleviate the high computational cost of large-scale nonparametric learning with kernel methods. The proposed kernel is defined based on a hierarchical partitioning of the underlying data domain, where…
We undertake Bayesian learning of the high-dimensional functional relationship between a system parameter vector and an observable, that is in general tensor-valued. The ultimate aim is Bayesian inverse prediction of the system parameters,…
The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…
Kernel methods have been successfully applied to the areas of pattern recognition and data mining. In this paper, we mainly discuss the issue of propagating labels in kernel space. A Kernel-Induced Label Propagation (Kernel-LP) framework by…
Sequence classification has numerous applications in various fields. Despite extensive studies in the last decades, many challenges still exist, particularly in pattern-based methods. Existing pattern-based methods measure the…
We study change-point detection for high-dimensional data in regimes where inference must be performed from small batches of observations. Our primary focus is the high-dimensional, low sample size (HDLSS) regime, where the sequence length…
Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…