lasso程序，从matlab提取_lasso函数matlab,lasso回归matlab资源-CSDN文库

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### Lasso程序在MATLAB中的实现与应用 #### 概述 Lasso（Least Absolute Shrinkage and Selection Operator）是一种回归分析方法，主要用于选择变量、减少模型复杂度以及避免过拟合问题。Lasso通过引入L1正则化来压缩模型参数，可以将一些不重要的特征系数压缩至零，从而实现特征选择。该方法在处理高维数据集时特别有效，尤其当解释变量之间存在多重共线性问题时。 #### MATLAB实现详解 ##### 函数定义在MATLAB中，`lasso`函数被定义为执行Lasso或Elastic Net正则化线性回归的方法。其基本形式为： ```matlab function [B, stats] = lasso(X, Y, varargin) ``` 这里，`X`表示一个数值矩阵，其维度为`N×P`，其中`N`为样本数量，`P`为特征数量；`Y`为一个长度为`N`的数值向量，表示响应变量。 ##### 可选输入参数 - `'Weights'`：观测权重，默认为单位权重或等效地`1/N`的权重。 - `'Alpha'`：Elastic Net混合值，默认为1（即Lasso）。`Alpha`取值范围为[0, 1]，接近0时类似于岭回归。 - `'NumLambda'`：指定的`Lambda`值数量，如果未提供`Lambda`参数，则默认为100个。 - `'LambdaRatio'`：最大值与最小值之间的比例，用于生成`Lambda`序列，合法范围为[0, 1)，默认为0.0001。 - `'Lambda'`：用户自定义的`Lambda`值，若提供，则会覆盖`'NumLambda'`和`'LambdaRatio'`。 - `'DFmax'`：模型中非零系数的最大数量，对于具有大量预测变量的数据集特别有用。 ##### 函数返回值 - `B`：系数矩阵，每一列对应于一个`Lambda`值。 - `stats`：统计信息，包括每个`Lambda`值下的各种统计指标。 #### 代码解读 ##### 基本框架 ```matlab function [B, stats] = lasso(X, Y, varargin) % ... (函数文档注释) ``` 这部分代码定义了函数的基本框架，并提供了对输入参数和输出结果的简要描述。 ##### 输入参数处理 ```matlab '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)). ``` 这里指定了观测权重的默认值及其限制条件。观测权重必须是非负向量，且至少有两个正值。 ```matlab 'Alpha'Elasticnet 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. ``` `Alpha`参数控制L1和L2惩罚项之间的平衡，决定了模型是Lasso还是Elastic Net。 ##### Lambda参数处理 ```matlab 'LambdaRatio'Ratio between the minimum value and maximum value of % lambda to generate, if the parameter "Lambda" is not % 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`参数用于生成`Lambda`序列的比例，其默认值为0.0001。如果设置为0，则Lasso会自动生成一系列的`Lambda`值，并将最小值设为0。 ```matlab '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 % value is just sufficient to produce all zero coefficients B. ``` `Lambda`参数允许用户自定义一组`Lambda`值。这些值将按照升序返回在`stats`结构体中。 #### 总结通过上述分析，我们可以看出MATLAB中的`lasso`函数提供了一个灵活的接口，用于执行Lasso和Elastic Net正则化线性回归。通过对不同参数的调整，用户可以根据具体需求定制回归模型，尤其是在处理高维数据时，这种方法可以有效地进行特征选择和模型简化。此外，通过提供的统计信息，用户还可以评估模型的性能和稳定性。

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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:

% X A numeric matrix (dimension, say, NxP)

% Y A numeric vector of length N

% Optional input 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

% if 'Lambda' is supplied. LASSO may return fewer

% fits than specified by 'NumLambda' if the residual

% error of the fits drops below a threshold percentage

% of the variance of Y.

% 'LambdaRatio' Ratio between the minimum value and maximum value of

% lambda to generate, if the parameter "Lambda" is not

% 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

% value is just sufficient to produce all zero coefficients B.

% You may supply a vector of real, non-negative values of

% lambda for LASSO to use, in place of its default sequence.

% If you supply a value for 'Lambda', 'NumLambda' and

% 'LambdaRatio' are ignored.

% 'DFmax' Maximum number of non-zero coefficients in the model.

% 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.

% Note: X and Y are always centered.

% 'RelTol' Convergence threshold for coordinate descent algorithm.

% The coordinate descent iterations will terminate

% when the relative change in the size of the

% estimated coefficients B drops below this threshold.

% Default: 1e-4. Legal range is (0,1).

% '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'.

% 'MCReps' A positive integer indicating the number of Monte-Carlo

% repetitions for cross-validation. The default value is 1.

% If 'CV' is 'resubstitution' or a cvpartition of type

% 'resubstitution', 'MCReps' must be 1. If 'CV' is a

% cvpartition of type 'holdout', then 'MCReps' must be

% greater than one.

% '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'

% 'UseSubstreams'

% 'Streams'

% For information on these fields see PARALLELSTATS.

% NOTE: If supplied, 'Streams' must be of length one.

% Return values:

% 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.

% Dimension 1xL.

% 'Alpha' The elastic net mixing value that was used.

% 'DF' The number of nonzero coefficients in B for each

% 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

% by cross-validation. Otherwise, 'MSE' is the mean

% sum of squared residuals obtained from the model

% with B and STATS.Intercept.

% If cross-validation was performed, STATS also includes the following

% fields:

% '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:

% % (1) Run the lasso on data obtained from the 1985 Auto Imports Database

% % of the UCI repository.

% % http://archive.ics.uci.edu/ml/machine-learning-databases/autos/imports-85.names

% load imports-85;

% Description

% % 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' ...

% 'horsepower' 'peak-rpm' 'city-mpg' 'highway-mpg'};

% % Compute the default sequence of lasso fits.

% [B,S] = lasso(X,Y,'CV',10,'PredictorNames',predictorNames);

% % Display a trace plot of the lasso fits.

% 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)

% sparseModel = S.PredictorNames(B(:,S.Index1SE)~=0)

% % Fit the sparse model and examine residuals.

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小何在这里~

2021-11-30

没什么用处，都是matlab自带的
jhgfgh96

2020-02-27

挺好的，，，

lutsest
上传者
2020-05-26

非常感谢
Lesleyzf

2019-05-01

几乎没有个人注解

lutsest
上传者
2019-05-06

一定点是一点点。打错了，部分关键步骤有一点注释

lutsest

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