func HypothesisHistory(thetas Parameters, trainingEx TrainingExample) []*matrix.Matrix {
// Describes the current working values (a_1, a_2, ...)
curValues := trainingEx.Input
// Is simply a 1 in a 1x1 matrix to b
// inserted into a vector as the bias unit
biasValueMatrix := matrix.Ones(1, 1)
history := make([]*matrix.Matrix, 0, len(thetas)+1)
history = append(history, curValues.InsertRows(biasValueMatrix, 0))
for i, theta := range thetas {
// Insert the bias unit, multiply with theta and apply the sigmoid function
curValues = theta.Mul(history[len(history)-1]).Apply(sigmoidMatrix)
if i != len(thetas)-1 {
history = append(history, curValues.InsertRows(biasValueMatrix, 0))
} else {
history = append(history, curValues)
}
}
return history
}
func DeltaTerms(thetas Parameters, trainingEx TrainingExample) Deltas {
deltas := make(Deltas, len(thetas))
biasValueMatrix := matrix.Ones(1, 1)
deltas[len(deltas)-1], _ = Hypothesis(thetas, trainingEx).Sub(trainingEx.ExpectedOutput)
for i := len(deltas) - 2; i >= 0; i-- {
workingTheta := thetas[i+1]
levelPrediction := Hypothesis(thetas[:i+1], trainingEx).InsertRows(biasValueMatrix, 0)
tmp, _ := matrix.Ones(levelPrediction.R(), 1).Sub(levelPrediction)
levelGradient := levelPrediction.EWProd(tmp)
deltas[i] = workingTheta.Transpose().Mul(deltas[i+1]).EWProd(levelGradient).RemoveRow(1)
}
return deltas
}
func Hypothesis(thetas Parameters, trainingEx TrainingExample) *matrix.Matrix {
// Describes the current working values (a_1, a_2, ...)
curValues := trainingEx.Input
// Is simply a 1 in a 1x1 matrix to b
// inserted into a vector as the bias unit
biasValueMatrix := matrix.Ones(1, 1)
for _, theta := range thetas {
// Insert the bias unit, multiply with theta and apply the sigmoid function
curValues = theta.Mul(curValues.InsertRows(biasValueMatrix, 0)).Apply(sigmoidMatrix)
}
return curValues
}