Model Selection

Mathematical Modeling · Axiom Academy

LESSON Model Selection - Mathematical Modeling Unit 7: Data-Driven Modeling - Mathematical Modeling Model selection is the process of choosing the best model from a set of candidate models to describe the underlying relationship in data. It answers the fundamental question: "Which model best balances accuracy and simplicity?" Model selection is critical because: Multiple models may fit the same data reasonably well More complex models are not always better The goal is prediction, not just fitting the training data Good selection prevents overfitting and underfitting At the heart of model selection lies the fundamental bias-variance tradeoff. The total prediction error decomposes into three components that must be balanced. Information criteria provide a principled way to compare models by penalizing complexity. Akaike Information Criterion (AIC) where L is the maximum likelihood and k is the number of parameters. Interpretation: Lower AIC is better. AIC balances goodness of fit (-2 ln(L)) with a penalty for complexity (2k). Bayesian Information Criterion (BIC) Interpretation: BIC penalizes complexity more heavily than AIC, especially for large samples. Preferred when seeking the "true" model. Interpretation: Corrects for finite sample bias. Use when n/k < 40 . Example: Comparing Polynomial Models Fitting data with 50 observations to polynomials of degree 1, 2, and 3:

This is the written version of the interactive lesson above. See the full Mathematical Modeling course.