相关论文: Geometric View of Measurement Errors
The slope of the best fit line from minimizing the sum of both the squared vertical errors and the squared horizontal errors is shown to be the root of a fourth degree polynomial.
Pose-Graph optimization is a crucial component of many modern SLAM systems. Most prominent state of the art systems address this problem by iterative non-linear least squares. Both number of iterations and convergence basin of these…
The geometric-mean method is often used to estimate the spatial resolution of a position-sensitive detector probed by tracks. It calculates the resolution solely from measured track data without using a detailed tracking simulation and…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…
We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…
We propose generalized resubstitution error estimators for regression, a broad family of estimators, each corresponding to a choice of empirical probability measures and loss function. The usual sum of squares criterion is a special case…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…
The best fit line from minimizing the sum of the squared perpendicular error is given.
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is…
We investigate the estimation of the perimeter of a set by a graph cut of a random geometric graph. For $\Omega \subset D = (0,1)^d$, with $d \geq 2$, we are given $n$ random i.i.d. points on $D$ whose membership in $\Omega$ is known. We…
Ridge estimator is an alternative to ordinary least square estimator when there is multicollinearity problem. There are many proposed estimators in literature. In this paper, we propose new estimators which are modifications of the…
In this paper, I show that classic two-stage least squares (2SLS) estimates are highly unstable with weak instruments. I propose a ridge estimator (ridge IV) and show that it is asymptotically normal even with weak instruments, whereas 2SLS…
We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown $d$-dimensional $\mathcal{C}^k$-smooth submanifold of $\mathbb{R}^D$, we…
This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…
This paper is devoted to the statistical and numerical properties of the geometric median, and its applications to the problem of robust mean estimation via the median of means principle. Our main theoretical results include (a) an upper…
We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in…
While the P vs NP problem is mainly approached form the point of view of discrete mathematics, this paper proposes reformulations into the field of abstract algebra, geometry, fourier analysis and of continuous global optimization - which…
In this paper, we address the problem of reconstruction of support of a measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure…