Abstract Gaussian processes are well-established Bayesian machine learning algorithms with significant merits, despite a strong limitation: lack of scalability. Clever solutions address this issue by inducing sparsity through low-rank approximations, often based on the Nystrom method. Here, we propose different method to achieve better scalability and higher accuracy using quantum computing, ou...

Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly unrelated topic pure and applied mathematics, is class of stochastic point processes with probability distribution characterized by sub-determinants kernel matri...

We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a matrix n data points requires Omega(n^2) computations. This quadratic scaling is significant bottleneck, especially when similarities are computed via expensive functions, e.g., transformer models. Approximation methods reduce this complexity, often by using small...

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Several numerical methods for approximating the solution of Hammerstein integral equations are known. For Fredholm-Hammerstein integral equations, the classical method of successive approximations was introduced in [16]. A variation of the Nystrom method was presented in [11]. A collocation-type method was developed in [9]. In [3], Brunner applied a collocation-type method to nonlinear Volterra...

One-bit matrix completion is an important class of positive-unlabeled (PU) learning problems where the observations consist only positive examples, e.g., in top-N recommender systems. For first time, we show that 1-bit can be formulated as problem recovering clean graph signals from noise-corrupted hypergraphs. This makes it possible to enjoy recent advances signal learning. Then, propose spect...

INTRODUCTION: A high level of muscle strength is regarded as a prerequisite for success in many sporting activities, especially in combat sports (Janiak & Krawczyk, 1995). Maximal muscle torque measurements under static conditions have been widely used in evaluating the strength of athletes practicing diverse sports (Buœko, 1998; Bober & Pietraszewski, 1996; Janiak & Krawczyk, 1995; Trzaskoma, ...

Kernel Logistic Regression (KLR) is a powerful classification technique that has been applied successfully in many classification problems. However, it is often not found in large-scale data classification problems and this is mainly because it is computationally expensive. In this paper, we present a new KLR algorithm based on Truncated Regularized Iteratively Reweighted Least Squares(TR-IRLS)...