Model Evaluation, Feature Selection, and Regularized Linear Regression

Summary

This tutorial explains bias, variance, irreducible error, and how model complexity relates to underfitting and overfitting. It then surveys feature-selection approaches: evaluating feature subsets, using forward, backward, or bidirectional greedy search, inspecting pairwise correlations, and applying regularization. Exhaustive subset search grows exponentially with the number of features, while greedy methods save computation but may miss the globally best subset. Correlation matrices can help identify redundant predictors.

The final section compares ridge regression, LASSO, and elastic net as ways to constrain linear-model coefficients. Ridge uses an L2 penalty to shrink coefficients, LASSO uses an L1 penalty that can set coefficients to zero, and elastic net combines both penalties. It recommends choosing penalty strength with validation data rather than the final test set. The article is an introductory explanation with illustrative examples and code references, not a trading study; it gives no market-specific results and simplifies some statistical details, so implementation choices and out-of-sample evaluation still matter.

Key ideas

• Bias, variance, and irreducible error are distinct sources of prediction error.
• Simple models can underfit, while overly complex models can overfit.
• Greedy feature selection reduces search cost but can miss the best overall subset.
• Correlation analysis can reveal redundant features that may be removed or represented by fewer variables.
• Ridge shrinks coefficients, LASSO can zero them, and elastic net combines the two penalties.
• Use validation data to tune regularization strength and reserve test data for final evaluation.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.