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Empirical risk minimization

For data $(X_i,Y_i)$ and predictions $h_\beta(X)=\beta^TX$, it is convenient to write
$$
R_n(\beta)=\frac1{2n}\sum_{i=1}^n(\beta^TX_i-Y_i)^2.
$$
Its <gradient> is
$$
\nabla R_n(\beta)=\frac1n\sum_{i=1}^n(\beta^TX_i-Y_i)X_i.
$$

Squared-loss empirical risk for linear prediction

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 31J / f / Solution

Squared-loss empirical risk for linear prediction

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Squared-loss empirical risk for linear prediction

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