lasso程序，从matlab提取

function [B,stats] = lasso(X,Y,varargin)

%LASSO Perform lasso or elastic net regularization for linear regression.

% [B,STATS] = lasso(X,Y,...) Performs L1-constrained linear least

% squares fits (lasso) or L1- and L2-constrained fits (elastic net)

% relating the predictors in X to the responses in Y. The default is a

% lasso fit, or constraint on the L1-norm of the coefficients B.

%

% Positional parameters:

% 'Weights' Observation weights 观察值. Must be a vector of non-negative

% values, of the same length as columns of X. At least

% two values must be positive. (default ones(N,1) or

% equivalently (1/N)*ones(N,1)).

% 'Alpha' Elastic net mixing value, or the relative balance

% between L2 and L1 penalty (default 1, range (0,1]).

% Alpha=1 ==> lasso, otherwise elastic net.

% Alpha near zero ==> nearly ridge regression.

% 'NumLambda' The number of lambda values to use, if the parameter

% 'Lambda' is not supplied (default 100). Ignored

% supplied. Legal range is [0,1). Default is 0.0001.

% If 'LambdaRatio' is zero, LASSO will generate its

% default sequence of lambda values but replace the

% smallest value in this sequence with the value zero.

% 'LambdaRatio' is ignored if 'Lambda' is supplied.

% 'Lambda' Lambda values. Will be returned in return argument

% STATS in ascending order. The default is to have LASSO

% generate a sequence of lambda values, based on 'NumLambda'

% and 'LambdaRatio'. LASSO will generate a sequence, based

% on the values in X and Y, such that the largest LAMBDA

% Can be useful with large numbers of predictors.

% Results only for lambda values that satisfy this

% degree of sparseness will be returned. Default is

% to not limit the number of non-zero coefficients.

% 'Standardize' Whether to scale X prior to fitting the model 是否缩放

% sequence. This affects whether the regularization is

% applied to the coefficients on the standardized

% scale or the original scale. The results are always

% presented on the original data scale. Default is

% TRUE, do scale X.

% 'CV' If present, indicates the method used to compute MSE.

% When 'CV' is a positive integer K, LASSO uses K-fold

% cross-validation. Set 'CV' to a cross-validation

% partition, created using CVPARTITION, to use other

% forms of cross-validation. You cannot use a

% 'Leaveout' partition with LASSO.

% When 'CV' is 'resubstitution', LASSO uses X and Y

% both to fit the model and to estimate the mean

% squared errors, without cross-validation.

% The default is 'resubstitution'.

% 'MaxIter' Maximum number of iterations allowed. Default is 1e5.

% 'PredictorNames' A cell array of names for the predictor variables,

% in the order in which they appear in X.

% Default: {}

% 'Options' A structure that contains options specifying whether to

% conduct cross-validation evaluations in parallel, and

% options specifying how to use random numbers when computing

% cross validation partitions. This argument can be created

% by a call to STATSET. CROSSVAL uses the following fields:

% 'UseParallel'

% B The fitted coefficients for each model.

% B will have dimension PxL, where

% P = size(X,2) is the number of predictors, and

% L = length(lambda).

% STATS STATS is a struct that contains information about the

% sequence of model fits corresponding to the columns

% of B. STATS contains the following fields:

%

% 'Intercept' The intercept term for each model. Dimension 1xL.

% 'Lambda' The sequence of lambda penalties used, in ascending order.

% value of lambda. Dimension 1xL.

% 'MSE' The mean squared error of the fitted model for each

% value of lambda. If cross-validation was performed,

% the values for 'MSE' represent Mean Prediction

% Squared Error for each value of lambda, as calculated

%

% 'SE' The standard error of MSE for each lambda, as

% calculated during cross-validation. Dimension 1xL.

% 'LambdaMinMSE' The lambda value with minimum MSE. Scalar.

% 'Lambda1SE' The largest lambda such that MSE is within

% one standard error of the minimum. Scalar.

% 'IndexMinMSE' The index of Lambda with value LambdaMinMSE.

% 'Index1SE' The index of Lambda with value Lambda1SE.

%

% Examples:

%

% % Extract Price as the response variable and extract non-categorical

% % variables related to auto construction and performance

% %

% X = X(~any(isnan(X(:,1:16)),2),:);

% Y = X(:,16);

% Y = log(Y);

% X = X(:,3:15);

% predictorNames = {'wheel-base' 'length' 'width' 'height' ...

% 'curb-weight' 'engine-size' 'bore' 'stroke' 'compression-ratio' ...

% axTrace = lassoPlot(B,S);

% % Display the sequence of cross-validated predictive MSEs.

% axCV = lassoPlot(B,S,'PlotType','CV');

% % Look at the kind of fit information returned by lasso.

% S

%

% % What variables are in the model corresponding to minimum

% % cross-validated MSE, and in the sparsest model within one

% % standard error of that minimum.

% minMSEModel = S.PredictorNames(B(:,S.IndexMinMSE)~=0)

% Xplus = [ones(size(X,1),1) X];

% fitSparse = Xplus * [S.Intercept(S.Index1SE); B(:,S.Index1SE)];

% corr(fitSparse,Y-fitSparse)

% figure

% plot(fitSparse,Y-fitSparse,'o')

% plot(fitDF6,Y-fitDF6,'o')

%

% % (2) Run lasso on some random data with 250 predictors

% %

% n = 1000; p = 250;

% X = randn(n,p);

% beta = randn(p,1); beta0 = randn;

% Y = beta0 + X*beta + randn(n,1);

% lambda = 0:.01:.5;

% [B,S] = lasso(X,Y,'Lambda',lambda);

% plot(bls,[S.Intercept; B],'.');

%

% % Run the same lasso fit but restricting the number of

% % non-zero coefficients in the fitted model.

% %

% [B2,S2] = lasso(X,Y,'Lambda',lambda,'DFmax',12);

%

% See also lassoPlot, ridge, parallelstats.

% via the lasso. Journal of the Royal Statistical Society,

% Series B, Vol 58, No. 1, pp. 267-288.

% [2] Zou, H. and T. Hastie. (2005) Regularization and variable

% selection via the elastic net. Journal of the Royal Statistical

% Society, Series B, Vol. 67, No. 2, pp. 301-320.

% [3] Friedman, J., R. Tibshirani, and T. Hastie. (2010) Regularization

% paths for generalized linear models via coordinate descent.

% Journal of Statistical Software, Vol 33, No. 1,

% http://www.jstatsoft.org/v33/i01.

% [4] Hastie, T., R. Tibshirani, and J. Friedman. (2008) The Elements

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