相关论文: Minimizing Squared Perpendicular Errors

We give a short and easy upper bound on the worst-case size of fault tolerant spanners, which improves on all prior work and is fully optimal at least in the setting of vertex faults.

In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…

In this work, we study the problem of finding approximate, with minimum support set, solutions to matrix max-plus equations, which we call sparse approximate solutions. We show how one can obtain such solutions efficiently and in polynomial…

In this paper we find the optimal error bound (smallest possible estimate, independent of the starting point) for the linear convergence rate of the simultaneous projection method applied to closed linear subspaces in a real Hilbert space.…

We study the problem of finding a triangulation T of a planar point set S such as to minimize the expected distance between two points x and y chosen uniformly at random from S. By distance we mean the length of the shortest path between x…

Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…

We consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon $P$ with $n$ vertices. We give a randomized near-linear-time $(1-\varepsilon)$-approximation algorithm for…

The weighted region problem is the problem of finding the weighted shortest path on a plane consisting of polygonal regions with different weights. For the case when the plane is tessellated by squares, we can solve the problem…

This paper focuses on optimal unimodal transformation of the score outputs of a univariate learning model under linear loss functions. We demonstrate that the optimal mapping between score values and the target region is a rectangular…

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth. In this paper, we introduce a general class of approximate proximal splitting (APS) methods for solving such minimization…

The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…

The three-dimensional cylindrical regression problem is a problem of finding a cylinder best fitting a group of points in three-dimensional Euclidean space. The words best fitting are usually understood in the sense of the minimum root mean…

Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined in a restricted space. It can also be…

This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…

Using linear projections one gets new inequalities for the successive minima of the lattice of sections of an hermitian line bundle on an arithmetic surface.

A new error bound which is better than the current exponential-type error bound is presented in this paper.

We consider the piecewise linear approximation of saddle functions of the form $f(x,y)=ax^2-by^2$ under the L-infinity error norm. We show that interpolating approximations are not optimal. One can get slightly smaller errors by allowing…

We consider the two-line fitting problem. True points lie on two straight lines and are observed with Gaussian perturbations. For each observed point, it is not known on which line the corresponding true point lies. The parameters of the…

We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of…

We seek for lines of minimal distance to finitely many points in the plane. The distance between a line and a set of points is defined by the L^p-norm, 1\leq p\leq \infty, of the vector of vertical or orthogonal distances from the single…