// LearnWeightDecay computes the following formula and update WReg.
// (Z'Z+λI)^−1 * Z'
// WReg = (Z'Z + λI)^−1 Z'y
//
func (lr *LinearRegression) LearnWeightDecay() error {
lr.Lambda = math.Pow(10, float64(lr.K))
var err error
// compute X' <=> X transpose
var mX ml.Matrix = lr.Xn
var mXT ml.Matrix
if mXT, err = mX.Transpose(); err != nil {
return err
}
// compute lambda*Identity
var ID ml.Matrix
if ID, err = ml.Identity(len(lr.Xn[0])); err != nil {
return err
}
var mLID ml.Matrix
if mLID, err = ID.Scalar(lr.Lambda); err != nil {
return err
}
// compute Z'Z
var mXP ml.Matrix
if mXP, err = mXT.Product(mX); err != nil {
return err
}
// compute Z'Z + lambda*I
var mS ml.Matrix
if mS, err = mLID.Add(mXP); err != nil {
return err
}
// inverse
var mInv ml.Matrix
if mInv, err = mS.Inverse(); err != nil {
return err
}
// compute product: inverseMatrix Z'
var XDagger ml.Matrix
if XDagger, err = mInv.Product(mXT); err != nil {
return err
}
// set WReg
lr.setWeightReg(XDagger)
return nil
}
// Learn will compute the pseudo inverse X dager and set W vector accordingly
// XDagger = (X'X)^-1 X'
//
func (lr *LinearRegression) Learn() error {
var err error
// compute X' <=> X transpose
var mXn ml.Matrix = lr.Xn
var mXT ml.Matrix
if mXT, err = mXn.Transpose(); err != nil {
return err
}
// compute the product of X' and X
var mXP ml.Matrix
if mXP, err = mXT.Product(mXn); err != nil {
return err
}
// inverse XProduct
var mXInv ml.Matrix
if mXInv, err = mXP.Inverse(); err != nil {
return err
}
// compute product: (X'X)^-1 X'
var XDagger ml.Matrix
if XDagger, err = mXInv.Product(mXT); err != nil {
return err
}
lr.setWeight(XDagger)
return nil
}