An Approximation Algorithm for Least Median
نویسنده
چکیده
Least median of squares (LMS) regression is a robust method to t equations to observed data (typically in a linear model). This paper describes an approximation algorithm for LMS regression. The algorithm generates a regression solution with median residual no more than twice the optimal median residual. Random sampling is used to provide a simple O(n log 2 n) expected time algorithm in the two-dimensional case that is successful with high probability. This algorithm is also extended to arbitrary dimension d with O(n d?1 logn) worst-case complexity for xed d > 2.
منابع مشابه
An approximation algorithm and FPTAS for Tardy/Lost minimization with common due dates on a single machine
This paper addresses the Tardy/Lost penalty minimization with common due dates on a single machine. According to this performance measure, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Initially, we present a 2-approximation algorithm and examine its worst case ratio bound. Then, a pseudo-polynomial dynamic programming algorithm is de...
متن کاملOptimal Pareto Parametric Analysis of Two Dimensional Steady-State Heat Conduction Problems by MLPG Method
Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...
متن کاملAn iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint
In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...
متن کاملA Robust Distributed Estimation Algorithm under Alpha-Stable Noise Condition
Robust adaptive estimation of unknown parameter has been an important issue in recent years for reliable operation in the distributed networks. The conventional adaptive estimation algorithms that rely on mean square error (MSE) criterion exhibit good performance in the presence of Gaussian noise, but their performance drastically decreases under impulsive noise. In this paper, we propose a rob...
متن کاملStochastic Optimization Algorithm Applied to Least Median of Squares Regression
The paper presents a stochastic optimization algorithm for computing of least median of squares regression (LMS) introduced by (Rousseeuw and Leroy 1986). As the exact solution is hard to obtain a random approximation is proposed, which is much cheaper in time and easy to program. A MATLAB program is included.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997