ML: Subset Selection & Shrinkage Methods (2024)

FAQs

What is the difference between shrinkage and subset selection? ›

In the linear regression context, subsetting means choosing a subset from available variables to include in the model, thus reducing its dimensionality. Shrinkage, on the other hand, means reducing the size of the coefficient estimates (shrinking them towards zero).

Shrinkage estimators are commonly used when the objective function of the regression model has a U-statistic structure . Shrinkage can be achieved through various methods, such as ridge regression or LMMSE estimation, which aim to find a balance between bias and variance in the estimation process .

The feature subset selection process involves identifying and selecting a subset of relevant features from a given dataset. It aims to improve model performance, reduce overfitting, and enhance interpretability.

An alternative to stepwise selection of variables is best subset selection. This method uses the branch-and-bound algorithm of Furnival and Wilson (1974) to find a specified number of best models containing one, two, or three variables, and so on, up to the single model containing all of the explanatory variables.

For the subset selection problem, a binary encoding can be used where one indicates a number is picked. In our problem formulation, the list of numbers is represented by L and the binary encoded variable by x. The customization requires writing custom operators in order to solve this problem efficiently.

They cannot handle datasets with missing values. They are computationally expensive for large datasets. They assume a linear relationship between the independent and dependent variables. They are not suitable for datasets with categorical predictors.

Shrinkage and selection aim at improving upon the simple linear regression. It may not be immediately obvious why such a constraint should improve the fit, but it turns out that shrinking the coefficient estimates can significantly reduce their variance.

Ridge regression shrinks all regression coefficients towards zero; the lasso tends to give a set of zero regression coefficients and leads to a sparse solution. Note that for both ridge regression and the lasso the regression coefficients can move from positive to negative values as they are shrunk toward zero.

Methods of Attribute Subset Selection

1. Stepwise Forward Selection. 2. Stepwise Backward Elimination.

What are the 3 subsets of machine learning? ›

Machine learning involves showing a large volume of data to a machine so that it can learn and make predictions, find patterns, or classify data. The three machine learning types are supervised, unsupervised, and reinforcement learning.

Exhaustive feature selection, also known as best subset selection, is a method used to select the best combination of features from a given set of features in a machine learning problem. The goal is to find the subset of features that maximizes the performance of the model.

When selecting subsets of data, square brackets [] are used. Inside these brackets, you can use a single column/row label, a list of column/row labels, a slice of labels, a conditional expression or a colon. Select specific rows and/or columns using loc when using the row and column names.

The number of models that this procedure fits multiplies quickly. If you have 10 independent variables, it fits 1024 models. However, if you have 20 variables, it fits 1,048,576 models! Best subsets regression fits 2^P models, where P is the number of predictors in the dataset.

While stepwise regression select variables sequentially, the best subsets approach aims to find out the best fit model from all possible subset models (2). If there are p covariates, the number of all subsets is 2^p. There are also varieties of statistical methods to compare the fit of subset models.

Generally speaking, the lasso and best subset selection differ in terms of their “aggressiveness” in selecting and estimating the coefficients in a linear model, with the lasso being less aggressive than best subset selection; meanwhile, forward stepwise lands somewhere in the middle, in terms of its aggressiveness.

In statistics, shrinkage is the reduction in the effects of sampling variation. In regression analysis, a fitted relationship appears to perform less well on a new data set than on the data set used for fitting. In particular the value of the coefficient of determination 'shrinks'.

Feature Selection: Selects a subset of relevant features while keeping the original feature space intact. The focus is on identifying the most informative features for modelling. Dimensionality Reduction: Projects the data onto a lower-dimensional space by transforming the feature space.