Regularization (lasso and ridge)
A technique that penalizes the size of a model's coefficients to prevent overfitting, lasso also able to zero out useless variables, bringing statistical learning closer to actuarial credibility.
Regularization adds to the function the model seeks to minimize a penalty term proportional to the size of its coefficients. The model must then trade off fitting the data well against staying simple. The ridge penalty applies to the sum of squared coefficients: it shrinks them all toward zero without eliminating any, which stabilizes estimates when variables are correlated. The lasso penalty, proposed by Robert Tibshirani in 1996, applies to the sum of their absolute values: it can bring the coefficients of unhelpful variables exactly to zero, thus performing variable selection. The combination of the two, called elastic net, combines their advantages. Penalty strength is chosen by cross-validation. In pricing, regularization applied to generalized linear models is particularly valuable for variables with many levels, geographic zones, vehicle models, occupations, where many levels have few observations. It then joins the intuition of actuarial credibility: a coefficient estimated on little data is pulled toward the mean, to an extent that depends on the amount of information available.
Textbook case: a motor tariff has 2,000 vehicle models, half of which have fewer than 50 policies. Without regularization, some rare models get a coefficient three times the average because of two claims; with a lasso penalty, these coefficients are pulled close to the mean, and 600 levels are merged with their group.
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