Tagged Questions

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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19 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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15 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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16 views

input variables with different order of magnitude

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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12 views

Need a large “interesting” dataset to illustrate LASSO [closed]

Does anyone know some interesting, publicly available, dataset for the sake of illustrating LASSO? It should, preferably, contain a lot of predictors ("large p"). I'd like to use it in my class.
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17 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
37 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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28 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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1answer
34 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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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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31 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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21 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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1answer
37 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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1answer
41 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
48 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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17 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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39 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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13 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 ...
2
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1answer
27 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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1answer
83 views

Ridge & LASSO norms

this post folloms 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
134 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
43 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 ...
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1answer
197 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
32 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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30 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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25 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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51 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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22 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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32 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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136 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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65 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: ...
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1answer
119 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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32 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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45 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
108 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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22 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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1answer
100 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
48 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 ...
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1answer
21 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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28 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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22 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 ...
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1answer
98 views

lasso with missing values and categorical variables

I have a dataset with a lot of missing values and mix of continues and categorical variables. I want to use something like group lasso to do features selection. Probably the output is binary 0,1 and ...
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40 views

How to derive this problem with soft-thresholding method?

The problem is defined as $$ \min_{x} \Bigg\{ a{\|x\|}^2+\frac{b}{2}{\|x-c\|}^2 \Bigg\} $$ where $x\in R^{n \times 1}, c \in R^{n \times 1}$ and $a,b$ are scalars. Equations 2.5 to 2.8 of this paper ...
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2answers
130 views

Why is Lasso regression for high dimensional data better than Stepwise AIC?

I know Lasso eventually set some parameters to zero, acting like variable selection. I also read from paper talking about automated variable selection method like Stepwise AIC can be troublesome. So ...
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1answer
71 views

What is the practical significance of a linear regression, lasso regression, and ridge regression outputting the same coefficients? [closed]

The lasso and ridge regression are tuned to the same alpha parameter. No matter what I tune the parameter to [0,1], the results of all three regressions are always the same (linear, ridge, lasso), ...
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33 views

About the derivation of group Lasso

I've been reading the paper of group lasso, "Model selection and estimation in regression with grouped variables". http://www.stat.washington.edu/courses/stat527/s13/readings/yuanlin07.pdf In page 53 ...
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2answers
30 views

What is the meaning of regularization path in Lasso or related sparsity problems?

If we select different sparsity levels (i.e. that the $\lambda$ controls), we could obtain different solutions with different sparsity levels. Does it mean the regularization path is how to select the ...
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1answer
80 views

What's the typical range of possible values for the shrinkage parameter in penalized regression?

In lasso or ridge regression, one has to specify a shrinkage parameter, often called by $\lambda$ or $\alpha$. This value is often chosen via cross validation by checking a bunch of different values ...
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1answer
78 views

How to Find Adjusted $R^2$ or $R^2$ from Lasso and Ridge regression model

How do I find the adjusted $R^2$ (or $r^2$) from Lasso and Ridge regression? I used the glmnet package. For instance if I have this code so far.... ...
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1answer
75 views

How do you interpret the parameters obtained from lasso logistic regression when the response is binary?

Are we still able to interpret the parameters in the same manner as we would in ordinary logistic regression? I'm asking this because I'm toying with the german credit data ...
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1answer
88 views

LASSO or other regularized regression with censored (missing) data

Here is my problem. I am looking at various time series curves. Let's call them total spend aggregated over all customers on various products versus time. At any given time, I want to predict the ...