A form of regularization used in the estimation of regression coefficients that shrinks coefficient estimates by penalizing their absolute value (i.e. the $L_1$ norm of the estimates). Some coefficients may be shrunk to zero; thus the LASSO performs variable selection. The LASSO is equivalent to the ...

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59 views

How to use LASSO to select glm model gaussian

I have a small sample size n<20. I want to find which combination of 8 variables better predict y. I was using a stepAICc but it is suggested to away stepwise model selection. I have tried lars ...
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38 views

Why is there no intercept in the lars output for LASSO in Stata?

This is my first time using lars, so this question is probably obvious. When I run lars on my data I get an output with a model and coefficients assigned to predictors, but there is no intercept. I ...
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63 views

Using LASSO for variable selection, then using Logit

I know this would muddy the statistical inference, but I am really only concerned with getting as close to an accurate model as I can. I have a dichotomous outcome variable, with a large set of ...
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14 views

Generation of synthetic data for lasso

I am seeking a principled method to generate synthetic data which is an appropriate application for the lasso. More specifically, I want a linear model with sparse coefficients, where the coefficients ...
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21 views

LASSO plot label lines with names using glmnet

First, thanks to all of you, this message board is truly helpful, at least up until now;) I used the search option and checked all related questions about LASSO but I could not find an appropriate ...
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23 views

Searching for the non-zero coefficients in lasso regression using glmnet.

I have to analyze genomic data set: ~ 22 000 of gene expressions for the two groups each of 40 subjects. I have tried different methods to find genes, which are significantly different among two ...
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1answer
30 views

How to convert the objective function to canonic form of sparse coding?

As we know the conventional sparse coding problem (LASSO) is: $\min_{\alpha} \| X-D\alpha\|_F^2 + \lambda \|\alpha\|_{1} \tag{1}$ where $X$ , $D$, and $\alpha$ are data, dictionary and coefficients ...
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37 views

Why does this multi-response Guassian LASSO not give a sparse solution?

I tried the glmnet package to learn multi-response Gaussian family. I have looked at the coefficients of the final model. The result is odd. All the features have ...
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34 views

Tuning alpha parameter in LASSO linear model in scikitlearn

I'm using the LASSO method, in the problem of text classification (sentiment classification). The features I'm using are mainly Ngrams (every N consecutive words) and I'm using the LASSO specifically ...
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134 views

Pointwise convergence in probablity of lasso

In the Knight and Fu's paper, in Equation 6 authors consider the pointwise convergence in probability as $$\underset{\phi \in K}{\operatorname{sup}} | Z_n(\phi)-Z(\phi)-\sigma^2| \longrightarrow_p ...
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171 views

Dealing with hierarchical (panel, multi-level) data and fixed effects in LASSO?

The question pretty much explains itself. When running a Lasso regression on a lot of indexed (say by time and location) explanatory variables, is it best practice to transform all data using a ...
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39 views

regarding using Lasso and Random forest based on the variable selection result coming from other processes

After the process of data exploration process and discussion with client, we set up a set of variables as follows: T1, T2, T3, T6, T8, T2*T3, T1*t6 During ...
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25 views

Why all coeficents of features of model are zero while I have high deviance using glmnet?

I'm using gmlnet to learn lasso regression model. model<-cv.glmnet(x, y, alpha=1, nfolds=10,parallel= TRUE) when I learn model and look at the model it's like this : ...
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19 views

input variables with different order of magnitude [duplicate]

I need to build a prediction model based on a data set with 5 different independent variables. The data set looks like as follows. The variables in col4 and ...
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1answer
45 views

Coordinate descent soft-thresholding update operator for LASSO

I was reading this paper (Friedman et al, 2010, Regularization Paths for Generalized Linear Models via Coordinate Descent) describing the coordinate descent algorithm for LASSO, and I can't quite ...
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1answer
67 views

R-squared for elastic net

How is the R-squared calculated for an elastic net? How about LASSO? Should be different from OLS, or not? Edit: The main problem is as follows: We have all kinds of fruits like $f_1, f_2, ..., fn$ ...
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38 views

Are LASSO regression predicted values also biased?

Since LASSO regression biases coefficients to reduce variance, aren't the predicted values also biased? In my case I am looking at fitted values from a predictive logistic regression model with LASSO ...
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67 views

Relation between the tuning parameter $\lambda$, parameter estimates $\beta_i$ and constraint $s$ in LASSO logistic regression

In the context of LASSO logistic regression, I understand that $\lambda$ is the tuning parameter obtained by cross validation. There is also the constraint parameter $s$ ($\sum_{i=1}^p|\hat\beta_i|\le ...
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64 views

Why is 'relaxed LASSO' different from LASSO?

If we start with a set of data $(X,Y)$, apply LASSO to it and obtain a solution $\beta^L$, we can apply LASSO again to the data set $(X_S, Y_S)$, where $S$ is the set of non-zero indexes of $\beta^L$, ...
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42 views

Cross validation of result from glmnet [closed]

I am trying to experiment with glmnet for building the regression model. The cross validation result is shown in the following figure. Looks like to me that mean-square error is totally out of ...
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31 views

questions on glmnet result

I am trying to experiment with glmnet for a data set, which has 41 independent variables is 41. There are 80 data points in total. ...
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72 views

Elastic net regularization: mean square error monotonically increases with lambda

This is quite coincidental as my question is nearly identical to this one asked shortly before, but I am also using elastic net regularization with R's glmnet library as a method of variable selection ...
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45 views

Is there a way to add inequality constraints on the LASSO in R?

I am trying to use LASSO for model selection, but I need my fitted values to remain non-negative. Is there a way to implement this simply in R? I've found that the penalized package allows for non ...
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1answer
67 views

How can I implement lasso in R using optim function

As you know lasso is a popular variable selection method of the form of $ (y-x\beta)'(y-X\beta)+\lambda \sum_i|\beta_i| $ the first is that it is possible to use optim() function in R to minimize ...
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28 views

Slow Lasso Performance Using sklearn

I am trying to use scikit-learn's LassoCV and/or ElasticNetCV functions to model a dataset with a large (>800) number of ...
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51 views

LASSO prediction model question

I am trying to create a prediction model with 33 predictors (brain metabolite levels in various regions) and 8 observations (cognitive test scores) with p>>n problem using LASSO in MATLAB (...
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21 views

Meta-parameter search for elastic net regularization of general objective function

In their 2004 paper on elastic net regularization, Zou and Hastie present an efficient method for finding the meta-parameters by folding the $L_2$-regularization component into the OLS problem and ...
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1answer
28 views

Least Angle regression coefficient reaches zero after included

In LARS how is it possible that after including a variable it could reach zero again? http://www.cc.gatech.edu/~isbell/reading/papers/lasso_simple.html.pdf I understood that it works like: 1) choose ...
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128 views

Ridge & LASSO norms

This post follows this one: Why does ridge estimate become better than OLS by adding a constant to the diagonal? Here is my question: As far as I know, ridge regularization uses a l2-norm (euclidean ...
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2answers
176 views

Quadratic Programming and Lasso

I'm trying to perform a lasso regression, which has following form: Minimize $w$ in $(Y - Xw)'(Y - Xw) + \lambda \;\text{norm}(w,1)$ Given a $\lambda$, I was advised to find the optimal $w$ with ...
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2answers
50 views

Coordinate descent on objective function with discontinuous derivative

I'm trying to perform a customized nonlinear regression. I'm using the Linex loss function instead of least-squares. I'm doing LASSO-style regularization, so that my objective function has ...
4
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1answer
212 views

How to interpret variables that are excluded from or included in the lasso model?

I got from other posts that one cannot attribute 'importance' or 'significance' to predictor variables that enter a lasso model because calculating those variables' p-values or standard deviations is ...
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1answer
58 views

Is standardizing data necessary for glasso?

I am wondering, if it is necessary to standardize data (mean zero and stddev eq. 1) for glasso. In many papers on glasso this is mentioned to have data with mean=0 and stddev 1, while using covarience ...
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70 views

model selection through sparse group lasso

I am trying to get familiar with the package SGL. The reference is http://cran.r-project.org/web/packages/SGL/SGL.pdf. I typed the example in, and tried to get the coefficients of the fitted penalized ...
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30 views

Lasso equivalent estimator with differenziable penalty function

The lasso estimator is define as $argmin_{\beta}~ MSE +\lambda \parallel \beta\parallel_1$ I am wondering if there is an alternative penalty function that is $C^\infty$ and that preserves the sparsity ...
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91 views

Deviance measure in glmnet package

for my current reseach I'm using the Lasso method via the glmnet package in R on a binomial dependent variable. In glmnet the optimal lambda is found via cross-validation and the resulting models ...
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24 views

Least-squares fitting with only optimum features, after Lasso - valid?

Using Lasso reduces the coefficients of features of a model, reducing some to zero, and thereby performing feature selection. The number of features depends on the value of $\alpha$ aka $\lambda$. In ...
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38 views

Which R packages offer the foldid (or simliar) parameter for cross-validation of group lasso?

My situation: small sample size: 116 binary outcome variable long list of explanatory variables: 50 (both continuous and categorical) explanatory variables did not come from the top of my head; ...
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162 views

Writing a coordinate descent algorithm for elastic net in SAS

In order to run Lasso and elastic net multiple regressions on my company's SAS server (which doesn't support R), I've been working on a coordinate descent macro for performing least squares ...
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119 views

covariate selection for a cox model by Lasso using glmnet

I would like to use model selection through shrinkage (Lasso) using glmnet. So far I did the following: ...
0
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1answer
200 views

model selection through shrinkage (Lasso) using glmnet

I would like to use model selection through shrinkage (Lasso) using glmnet. After trying the example of the glmnet manual and tried the procedure with my data. ...
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39 views

Connection between Lasso formulations

This question might be dumb, but I noticed that there are two different formulations of the Lasso regression. We know that the Lasso problem is to minimize the objective consisting of the square loss ...
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53 views

How to compare variables' coefficients obtained from lasso?

My situation: small sample size: 116 binary outcome variable long list of explanatory variables: 50 explanatory variables did not come from the top of my head; their choice was based on the ...
2
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1answer
127 views

How to ensure that the most appropriate value for lambda is chosen in lasso?

My situation: small sample size: 116 binary outcome variable long list of explanatory variables: 50 explanatory variables did not come from the top of my head; their choice was based on the ...
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0answers
23 views

Applications of High-dimensional data analysis techniques in Industry

The high-dimensional data analysis in statistics/biostatistics is booming over recent two decades, and is becoming the frontier of modern statistics research. The penalized regularization techniques, ...
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149 views

How to evaluate collinearity or correlation of predictors in logistic regression?

In linear regression it is possible to render predictors insignificant due to multicollinearity, as discussed in this question: How can a regression be significant yet all predictors be ...
2
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1answer
52 views

How is lasso an M-Estimator?

The definition of an M-estimator is an estimator (from Casella and Berger) of the form $$\hat{\theta}=\min \sum_{i=1}^n \rho(X_i-\theta),$$ where $X_1,X_2, \cdots, X_n$ is the data for some function ...
2
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1answer
24 views

Variable selection: Why certain categories are chosen but not others?

I'm doing variable selection using the Lasso. To explain my response variable I have several predictors, both categorical and numerical, but I have problems to explain the process that underlies ...
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35 views

Code for $\ell_1$/ $\ell_2$ sparse multivariate regression algorithm

Where can I find the code (Matlab or R) for the block-regularized Lasso problem defined as follows: $\min_{B} \| Y-XB\|_F^2 + \lambda \|B\|_{1,2}$ where $Y$, $X$, and $B$ are matrices. This is a ...
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32 views

Apply LASSO Model with nominal target in SAS?

I'm building a classification model with a pool of independent variables (hundreds of them). I'm in the step of variable selection/feature selection. Now I'm trying to figure out if there are any ...