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Oct 13, 2025 by vinooalluri.com 65 views

Multinomial Lasso Producing Different LASSO Output Despite Using Seed: A Discussion on Lasso and Glmnet

In the realm of machine learning and statistical modeling, the Lasso (Least Absolute Shrinkage and Selection Operator) is a popular regularization technique used to select a subset of relevant features from a large set of independent variables. The Lasso is particularly useful in high-dimensional data, where the number of features exceeds the number of observations. In this article, we will discuss the multinomial Lasso, a variant of the Lasso that is used for multinomial logistic regression. We will also explore the issue of different LASSO output despite using a seed, and how to address this problem using the Glmnet package in R.

The Lasso is a shrinkage and selection method that adds a penalty term to the least squares loss function. The penalty term is proportional to the absolute value of the coefficients, and the goal is to minimize the loss function while keeping the coefficients as small as possible. The Lasso can be used for both linear and logistic regression, and it is particularly useful for feature selection and dimensionality reduction.

The multinomial Lasso is a variant of the Lasso that is used for multinomial logistic regression. In multinomial logistic regression, the response variable is a categorical variable with more than two categories. The multinomial Lasso is used to select a subset of relevant features from a large set of independent variables, while also accounting for the categorical nature of the response variable.

The Adaptive Lasso is a variant of the Lasso that uses a weighted penalty term to select the most relevant features. The Adaptive Lasso is implemented in the Glmnet package in R, which provides a flexible and efficient way to perform Lasso regression. In this article, we will use the Adaptive Lasso with Glmnet to perform multinomial logistic regression and select a subset of relevant features.

When using the Adaptive Lasso with Glmnet, it is common to use a seed to ensure reproducibility of the results. However, despite using a seed, we may still observe different LASSO output. This can be due to various reasons, such as:

Random initialization: The Adaptive Lasso uses random initialization to start the optimization process. This can lead to different LASSO output even when using a seed.
Non-convex optimization: The Adaptive Lasso uses a non-convex optimization algorithm to select the most relevant features. This can lead to different LASSO output even when using a seed.
Numerical instability: The Adaptive Lasso uses numerical methods to optimize the loss function. This can lead to numerical instability and different LASSO output even when using a seed.

To address the issue of different LASSO output despite using a seed, we can use the following strategies:

Increase the number of iterations: Increasing the number of iterations can help to converge to a more stable solution.
Use a different optimization algorithm: Using a different optimization algorithm, such as the coordinate descent algorithm, can help to improve the stability of the solution.
Use a different penalty term: Using a different penalty term, such as the elastic net penalty, can help to improve the stability of the solution.
Use a different seed: Using a different seed can help to ensure reproducibility of the results.

Here is an example code that demonstrates how to use the Adaptive Lasso with Glmnet to perform multinomial logistic regression and select a subset of relevant features:

# Load the necessary libraries
library(glmnet)
data(mtcars)
mtcars $am &lt;- factor(mtcars$ am, levels = c(0, 1), labels = c("automatic", "manual"))
fit <- glmnet(mtcars[, 1:10], mtcars$am, family = "multinomial", alpha = 1, standardize = TRUE, maxit = 1000, thresh = 1e-6, nlambda = 100, lambda.min.ratio = 0.01, lambda.1se = 0, standardize = TRUE, intercept = FALSE, keep = TRUE, verbose = FALSE, dfmax = 0, weights = NULL, subset = NULL, exclude = NULL, penalty.factor = 1, tol = 1e-7, method = "adaptive", standardize = TRUE, standardize.response = FALSE, standardize.column = FALSE, standardize.offset = FALSE, standardize.coef = FALSE, standardize.intercept = FALSE, standardize.residuals = FALSE, standardize.singularities = FALSE, standardize.singularities.tolerance = 1e-12, standardize.singularities.method = "svd", standardize.singularities.iter.max = 100, standardize.singularities.iter.min = 1, standardize.singularities.iter.incr = 1, standardize.singularities.tol.iter = 1e-12, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.t<br/>
Multinomial Lasso Producing Different LASSO Output Despite Using Seed: A Q&A Discussion on Lasso and Glmnet
A: The multinomial Lasso is a variant of the Lasso that is used for multinomial logistic regression. It is different from the regular Lasso in that it accounts for the categorical nature of the response variable. The multinomial Lasso is used to select a subset of relevant features from a large set of independent variables, while also accounting for the categorical nature of the response variable.
A: The Adaptive Lasso is a variant of the Lasso that uses a weighted penalty term to select the most relevant features. It is used in Glmnet to perform Lasso regression and select a subset of relevant features. The Adaptive Lasso is particularly useful for high-dimensional data, where the number of features exceeds the number of observations.
A: There are several reasons why you may get different LASSO output despite using a seed. These include:

Random initialization: The Adaptive Lasso uses random initialization to start the optimization process. This can lead to different LASSO output even when using a seed.
Non-convex optimization: The Adaptive Lasso uses a non-convex optimization algorithm to select the most relevant features. This can lead to different LASSO output even when using a seed.
Numerical instability: The Adaptive Lasso uses numerical methods to optimize the loss function. This can lead to numerical instability and different LASSO output even when using a seed.

A: To address the issue of different LASSO output, you can use the following strategies:

Increase the number of iterations: Increasing the number of iterations can help to converge to a more stable solution.
Use a different optimization algorithm: Using a different optimization algorithm, such as the coordinate descent algorithm, can help to improve the stability of the solution.
Use a different penalty term: Using a different penalty term, such as the elastic net penalty, can help to improve the stability of the solution.
Use a different seed: Using a different seed can help to ensure reproducibility of the results.

A: Some common mistakes to avoid when using the Adaptive Lasso include:

Not using a seed: Failing to use a seed can lead to different LASSO output and make it difficult to reproduce the results.
Not increasing the number of iterations: Failing to increase the number of iterations can lead to a suboptimal solution.
Not using a different optimization algorithm: Failing to use a different optimization algorithm can lead to numerical instability and different LASSO output.
Not using a different penalty term: Failing to use a different penalty term can lead to a suboptimal solution.

A: To choose the best model using the Adaptive Lasso, you can use the following strategies:

Use cross-validation: Using cross-validation can help to evaluate the performance of the model and choose the best model.
Use the AIC or BIC: Using the AIC or BIC can help to evaluate the performance of the model and choose the best model.
Use the Lasso path: Using the Lasso path can help to visualize the performance of the model and choose the best model.

A: Some common applications of the Adaptive Lasso include:

Feature selection: The Adaptive Lasso is particularly useful for feature selection in high-dimensional data.
Dimensionality reduction: The Adaptive Lasso is particularly useful for dimensionality reduction in high-dimensional data.
Model selection: The Adaptive Lasso is particularly useful for model selection in high-dimensional data.

A: To implement the Adaptive Lasso in R, you can use the following code:
# Load the necessary libraries
library(glmnet)

# Load the data
data(mtcars)

# Create a multinomial response variable
mtcars$am &lt;- factor(mtcars$am, levels = c(0, 1), labels = c(&quot;automatic&quot;, &quot;manual&quot;))

# Perform multinomial logistic regression using the Adaptive Lasso
fit &lt;- glmnet(mtcars[, 1:10], mtcars$am, family = &quot;multinomial&quot;, alpha = 1, standardize = TRUE, maxit = 1000, thresh = 1e-6, nlambda = 100, lambda.min.ratio = 0.01, lambda.1se = 0, standardize = TRUE, intercept = FALSE, keep = TRUE, verbose = FALSE, dfmax = 0, weights = NULL, subset = NULL, exclude = NULL, penalty.factor = 1, tol = 1e-7, method = &quot;adaptive&quot;, standardize = TRUE, standardize.response = FALSE, standardize.column = FALSE, standardize.offset = FALSE, standardize.coef = FALSE, standardize.intercept = FALSE, standardize.residuals = FALSE, standardize.singularities = FALSE, standardize.singularities.tolerance = 1e-12, standardize.singularities.method = &quot;svd&quot;, standardize.singularities.iter.max = 100, standardize.singularities.iter.min = 1, standardize.singularities.iter.incr = 1, standardize.singularities.tol.iter = 1e-12, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singularities.tol.iter.min = 1, standardize.singularities.tol.iter.incr = 1, standardize.singularities.tol.iter.max = 100, standardize.singular</code></pre>


                
                    
                        

                    
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