Competitive Adaptive Reweighted Sampling (CARS) for Variable Selection

This post discusses another variable selection method, Competitive Adaptive Reweighted Sampling (CARS).

What is CARS?

CARS performs iterative variable selection by adaptive sampling and elimination of less relevant variables. This method ensures that only the most influential variables are retained to build simpler and more robust models. The essence of CARS lies in how it leverages adaptive reweighting and competition among variables over multiple iterations. At each step, variables with lesser importance are progressively removed, allowing the algorithm to zero in on the optimal subset.

How Does CARS Work?

The CARS algorithm proceeds in four major steps:

1. Monte Carlo Sampling

CARS uses Monte Carlo sampling to generate random subsets of the data across iterations. This ensures variability in the selected variables and prevents the algorithm from getting stuck in local optima.

2. PLS Regression Modeling

In each iteration, the algorithm fits Partial Least Squares (PLS) regression models on the sampled data. The PLS model provides regression coefficients, which measure the importance of each variable.

3. Adaptive Reweighting

After evaluating the variable importance, adaptive reweighting is applied. This step assigns higher probabilities to important variables and lower probabilities to unimportant ones. This weighted sampling mechanism ensures that relevant variables have a higher chance of being selected in subsequent iterations.

4. Elimination by Competition

As the iterations proceed, less relevant variables are eliminated through competition. The algorithm ensures that only the most predictive variables survive. The final model uses the optimal subset of variables, which maximizes model performance with minimum complexity.