The method of iteratively reweighted least squares (IRLS) is used to solve certain optimization problems. It solves objective functions of the form:
by an iterative method in which each step involves solving a weighted least squares problem of the form:
IRLS is used to find the maximum likelihood estimates of a generalized linear model, and in robust regression to find an M-estimator, as a way of mitigating the influence of outliers in an otherwise normally-distributed data set. For example, by minimizing the least absolute error rather than the least square error.
Although not a linear regression problem, Weiszfeld's algorithm for approximating the geometric median can also be viewed as a special case of iteratively reweighted least squares, in which the objective function is the sum of distances of the estimator from the samples.
One of the advantages of IRLS over linear and convex programming is that it can be used with Gauss–Newton and Levenberg–Marquardt numerical algorithms.
Famous quotes containing the word squares:
“And New York is the most beautiful city in the world? It is not far from it. No urban night is like the night there.... Squares after squares of flame, set up and cut into the aether. Here is our poetry, for we have pulled down the stars to our will.”
—Ezra Pound (1885–1972)