Search results
Results From The WOW.Com Content Network
In statistics, least-angle regression (LARS) is an algorithm for fitting linear regression models to high-dimensional data, developed by Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani. [1] Suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates.
The result of fitting a set of data points with a quadratic function Conic fitting a set of points using least-squares approximation. In regression analysis, least squares is a parameter estimation method based on minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each ...
Unlike Tikhonov regularization, this scheme does not have a convenient closed-form solution: instead, the solution is typically found using quadratic programming or more general convex optimization methods, as well as by specific algorithms such as the least-angle regression algorithm.
The partial least squares regression is the extension of the PCR method which does not suffer from the mentioned deficiency. Least-angle regression [6] is an estimation procedure for linear regression models that was developed to handle high-dimensional covariate vectors, potentially with more covariates than observations.
The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters of the model curve (,) so that the sum of the squares of the deviations () is minimized:
Lasso-regularized models can be fit using techniques including subgradient methods, least-angle regression (LARS), and proximal gradient methods. Determining the optimal value for the regularization parameter is an important part of ensuring that the model performs well; it is typically chosen using cross-validation.
IRLS can be used for ℓ 1 minimization and smoothed ℓ p minimization, p < 1, in compressed sensing problems. It has been proved that the algorithm has a linear rate of convergence for ℓ 1 norm and superlinear for ℓ t with t < 1, under the restricted isometry property, which is generally a sufficient condition for sparse solutions.
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals.