Related papers: Geometric View of Measurement Errors
In this note we consider the optimal design problem for estimating the slope of a polynomial regression with no intercept at a given point, say z. In contrast to previous work, which considers symmetric design spaces we investigate the…
Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations.…
Three methods of least squares are examined for fitting a line to points in the plane. Two well known methods are to minimize sums of squares of vertical or horizontal distances to the line. Less known is to minimize sums of squares of…
The paper studies a geometrically robust least-squares problem that extends classical and norm-based robust formulations. Rather than minimizing residual error for fixed or perturbed data, we interpret least-squares as enforcing approximate…
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…
Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatics…
Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their…
Birg{\'e} and Massart proposed in 2001 the slope heuristics as a way to choose optimally from data an unknown multiplicative constant in front of a penalty. It is built upon the notion of minimal penalty, and it has been generalized since…
This paper presents the asymptotic behavior of a linear instrumental variables (IV) estimator that uses a ridge regression penalty. The regularization tuning parameter is selected empirically by splitting the observed data into training and…
In an attempt to provide an answer to the increasing criticism against p-values and to bridge the gap between statistical inference and prediction modelling, we introduce the probability of improved prediction (PIP). In general, the PIP is…
For a probability measure on a real separable Hilbert space, we are interested in "volume-based" approximations of the d-dimensional least squares error of it, i.e., least squares error with respect to a best fit d-dimensional affine…
We consider drawings of graphs in the plane in which vertices are assigned distinct points in the plane and edges are drawn as simple curves connecting the vertices and such that the edges intersect only at their common endpoints. There is…
The multivariate errors-in-variables regression model is applicable when both dependent and independent variables in a multivariate regression are subject to measurement errors. In such a scenario it is long established that the traditional…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
This paper introduces a number of new techniques in the study of the famous question from numerical linear algebra: what is the largest possible growth factor when performing Gaussian elimination with complete pivoting? This question is…
We investigate mismatched estimation in the context of the distance geometry problem (DGP). In the DGP, for a set of points, we are given noisy measurements of pairwise distances between the points, and our objective is to determine the…
Constant gain least-mean-squares (LMS) algorithms have a wide range of applications in trajectory tracking problems, but the formal convergence of LMS in mean square is not yet fully established. This work provides an upper bound on the…
Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model…