Related papers: Learning the kernel matrix by resampling
This study proposes a data condensation method for multivariate kernel density estimation by genetic algorithm. First, our proposed algorithm generates multiple subsamples of a given size with replacement from the original sample. The…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…
A limitation of many clustering algorithms is the requirement to tune adjustable parameters for each application or even for each dataset. Some techniques require an \emph{a priori} estimate of the number of clusters while density-based…
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion…
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…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
The paper addresses the problem to estimate the power spectral density of an ARMA zero mean Gaussian process. We propose a kernel based maximum entropy spectral estimator. The latter searches the optimal spectrum over a class of high order…
This paper develops a nonparametric density estimator with parametric overtones. Suppose $f(x,\theta)$ is some family of densities, indexed by a vector of parameters $\theta$. We define a local kernel smoothed likelihood function which for…
Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and…
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
In this paper we refine the procedure proposed by Lin et al. (2015) to estimate the density at a given quantile based on a resampling method. The approach consists on generating multiple samples of the zero-mean Gaussian variable from which…
Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large…
Decision forests are widely used for classification and regression tasks. A lesser known property of tree-based methods is that one can construct a proximity matrix from the tree(s), and these proximity matrices are induced kernels. While…
Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…
Kernel-based K-means clustering has gained popularity due to its simplicity and the power of its implicit non-linear representation of the data. A dominant concern is the memory requirement since memory scales as the square of the number of…