How to Regularize Your Regression

A series of regression instances in a pharmaceutical application. Can we learn how to set the regularization parameter \(\lambda\) from similar domain-specific data? Overview. Perhaps the simplest relation between a real dependent variable \(y\) and a vector of features \(X\) is a linear model \(y = \beta X\). Given some training examples or datapoints consisting of pairs of features and dependent variables \((X_1, y_1),(X_2, y_2),\dots,(X_m,y_m)\), we would like to learn \(\beta\) which would give the best prediction \(y’\) given features …

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