Downdate ridge regression

function downdate_ridge_regression(x:Real[_], N':Real[_,_], Λ':LLT, α':Real, γ':Real[_], u:Real[_]) -> (Real[_,_], LLT, Real, Real[_])

Downdate parameters for a linear-Gaussian ridge regression.

  • x: The variate.
  • N': Posterior precision times mean for weights, where each column represents the mean of the weight for a separate output.
  • Λ': Common posterior precision.
  • α': Common posterior weight and likelihood covariance shape.
  • β': Posterior covariance scale accumulators.
  • u: Input.

Returns: the prior hyperparameters N, Λ, γ, and β.