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This paper develops bootstrap methods for practical statistical inference in panel data quantile regression models with fixed effects. We consider random-weighted bootstrap resampling and formally establish its validity for asymptotic…
Based on the property that solving the system of linear matrix equations via the column space and the row space projections boils down to an approximation in the least squares error sense, a formulation for learning the weight matrices of…
This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by…
In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of…
In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schr\"odinger equation). In this paper, we aim to reduce the generalization error without…
In this paper, we propose a novel element-wise subset selection method for the alternating least squares (ALS) algorithm, focusing on low-rank matrix factorization involving matrices with missing values, as commonly encountered in…
By amalgamating data from disparate sources, the resulting integrated dataset becomes a valuable resource for statistical analysis. In probabilistic record linkage, the effectiveness of such integration relies on the availability of linkage…
We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the…
Algebraic multigrid (AMG) is often viewed as a scalable $\mathcal{O}(n)$ solver for sparse linear systems. Yet, parallel AMG lacks scalability due to increasingly large costs associated with communication, both in the initial construction…
In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal interpolation of multidimensional analytic functions defined over a product of one dimensional bounded domains. The goal of such approach is to…
Interval-valued data receives much attention due to its wide applications in the fields of finance, econometrics, meteorology and medicine. However, most regression models developed for interval-valued data assume observations are mutually…
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on…
This paper develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated.…
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…
We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector-valued function, defined as solution of a non-homogeneous version of the eigenproblem. This approximation step is…