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Regularization is a popular technique to solve the overfitting problem of machine learning algorithms. Most regularization technique relies on parameter selection of the regularization coefficient. Plug-in method and cross-validation…
This paper addresses the problem of finding the closest generalized essential matrix from a given $6\times 6$ matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
In this work, we use rational approximation to improve the accuracy of spectral solutions of differential equations. When working in the vicinity of solutions with singularities, spectral methods may fail their propagated spectral rate of…
We present a constructive approach for approximating the conformal map (uniformization) of a polyhedral surface to a canonical domain in the plane. The main tool is a characterization of convex spaces of quasiconformal simplicial maps and…
We present pairwise fairness metrics for ranking models and regression models that form analogues of statistical fairness notions such as equal opportunity, equal accuracy, and statistical parity. Our pairwise formulation supports both…
The paper proposes a novel calibration approach for the Orthoglide-type mechanisms based on observations of the manipulator leg parallelism during mo-tions between the prespecified test postures. It employs a low-cost measuring system…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
This article advocates the use of conformal prediction (CP) methods for Gaussian process (GP) interpolation to enhance the calibration of prediction intervals. We begin by illustrating that using a GP model with parameters selected by…
Image prediction methods often struggle on tasks that require changing the positions of objects, such as video prediction, producing blurry images that average over the many positions that objects might occupy. In this paper, we propose a…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Image harmonization aims to adjust the foreground illumination in a composite image to make it harmonious. The existing harmonization methods can only produce one deterministic result for a composite image, ignoring that a composite image…
We discuss efficient conversion algorithms for orthogonal polynomials. We describe a known conversion algorithm from an arbitrary orthogonal basis to the monomial basis, and deduce a new algorithm of the same complexity for the converse…
Orthogonal systems in $\mathrm{L}_2(\mathbb{R})$, once implemented in spectral methods, enjoy a number of important advantages if their differentiation matrix is skew-symmetric and highly structured. Such systems, where the differentiation…
Statistical matching methods are widely used in the social and health sciences to estimate causal effects using observational data. Often the objective is to find comparable groups with similar covariate distributions in a dataset, with the…
Estimating a depth map from multiple views of a scene is a fundamental task in computer vision. As soon as more than two viewpoints are available, one faces the very basic question how to measure similarity across >2 image patches.…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
In text classification, the problem of overfitting arises due to the high dimensionality, making regularization essential. Although classic regularizers provide sparsity, they fail to return highly accurate models. On the contrary,…
Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…
We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the…