week6 lec2

Partial least squares cont.

In Partial Least Squares (PLS), the first component \( T_1 \) is constructed by the equation:

\[ T_k = \Phi_k X \]

Where \( \Phi_k = 1\) and \(|Cov(Z, T_1)|\) is as large as possible.

\[ \hat{\phi}_1 = argmax_{\|\phi_1\|=1} \text{cov}(Z, \phi_1^T X) \]

Tip

The reason why we want to maximize the covariance is because we then combine the variables in a way that explains both the dependent variable and the explanatory variables.