Related papers: Doubly stochastic large scale kernel learning with…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…
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…
Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors,…
A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…
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…
Kernel methods are fundamental in machine learning, and faster algorithms for kernel approximation provide direct speedups for many core tasks in machine learning. The polynomial kernel is especially important as other kernels can often be…
We consider the problem of learning functions within the $\mathcal{F}_{p,\pi}$ and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer neural networks, as well as kernel methods. Leveraging tools…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques,…
Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
In recent years, non-parametric methods utilizing random walks on graphs have been used to solve a wide range of machine learning problems, but in their simplest form they do not scale well due to the quadratic complexity. In this paper, a…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…