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With network data becoming ubiquitous in many applications, many models and algorithms for network analysis have been proposed. Yet methods for providing uncertainty estimates in addition to point estimates of network parameters are much…
The problem of efficient approximation of a linear operator induced by the Gaussian or softmax kernel is often addressed using random features (RFs) which yield an unbiased approximation of the operator's result. Such operators emerge in…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
Feature selection plays a pivotal role in learning, particularly in areas were parsimonious features can provide insight into the underlying process, such as biology. Recent approaches for non-linear feature selection employing greedy…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…
Kernel ridge regression (KRR) is a well-known and popular nonparametric regression approach with many desirable properties, including minimax rate-optimality in estimating functions that belong to common reproducing kernel Hilbert spaces…
This article focuses on estimating relative transfer functions (RTFs) for beamforming applications. Traditional methods often assume that spectra are uncorrelated, an assumption that is often violated in practical scenarios due to factors…
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…
We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference…
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…
We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space,…
Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…
We give the first algorithm for kernel Nystr\"om approximation that runs in *linear time in the number of training points* and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions. The…
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…
The Fast Fourier Transform (FFT), as a core computation in a wide range of scientific applications, is increasingly threatened by reliability issues. In this paper, we introduce TurboFFT, a high-performance FFT implementation equipped with…
Empirical Risk Minimization (ERM) algorithms are widely used in a variety of estimation and prediction tasks in signal-processing and machine learning applications. Despite their popularity, a theory that explains their statistical…
We provide uniform confidence bands for kernel ridge regression (KRR), a widely used nonparametric regression estimator for nonstandard data such as preferences, sequences, and graphs. Despite the prevalence of these data--e.g., student…
Time series data analytics has been a problem of substantial interests for decades, and Dynamic Time Warping (DTW) has been the most widely adopted technique to measure dissimilarity between time series. A number of global-alignment kernels…