 
Summary: Supplemental Material
Ridge Shrinkage and the Effective Degrees of Freedom
Here we give a more thorough description of how ridge regression shrinks the model
coefficients and recount a rough derivation of the effective degrees of freedom, Ndf, based
largely on a discussion originally presented in (Hastie et al., 2001).
The singular value decomposition (SVD) of the centered neural input matrix is
given by
T
USVR = , (S1)
where U and V are orthogonal matrices containing the singular vectors and S is a diagonal
matrix containing the nonzero singular values of R, where s1 s 2 ... s n 0. Using
Equation S1, the least squares fitted estimate, LS
X^ , can also be expressed as a projection
of X onto the orthonormal basis U, that is
XUU
XRRRRBRX
T
TTLSLS
=
== 
