// Loss returns the weighted exponential loss.
// It determines which samples are positive vs. negative
// by checking the sign of the element in the expected
// vector.
func (w *WeightedExpLoss) Loss(actual autofunc.Result, expected linalg.Vector) autofunc.Result {
expVar := &autofunc.Variable{Vector: expected.Copy().Scale(-1)}
dots := autofunc.Mul(actual, expVar)
exps := autofunc.Exp{}.Apply(dots)
weightVec := &autofunc.Variable{Vector: make(linalg.Vector, len(expected))}
for i, x := range expected {
if x > 0 {
weightVec.Vector[i] = w.PosWeight
} else {
weightVec.Vector[i] = 1
}
}
return autofunc.SumAll(autofunc.Mul(exps, weightVec))
}
func (s *SumClassifier) Classify(list SampleList) linalg.Vector {
if len(s.Classifiers) == 0 {
return make(linalg.Vector, list.Len())
} else if len(s.Classifiers) != len(s.Weights) {
panic("classifier count must match weight count")
}
var res linalg.Vector
for i, c := range s.Classifiers {
w := s.Weights[i]
if res == nil {
res = c.Classify(list).Scale(w)
} else {
res.Add(c.Classify(list).Scale(w))
}
}
return res
}
func (s *stateOutBlockRResult) PropagateRGradient(u, uR []linalg.Vector, su []RStateGrad,
rg autofunc.RGradient, g autofunc.Gradient) []RStateGrad {
downstream := make([]RStateGrad, len(s.WrappedOut.Outputs()))
for i := range s.WrappedOut.Outputs() {
var vec, vecR linalg.Vector
if u != nil {
vec = u[i].Copy()
vecR = uR[i].Copy()
}
if su != nil && su[i] != nil {
sVec := su[i].(VecRStateGrad)
if vec == nil {
vec = sVec.State.Copy()
vecR = sVec.RState.Copy()
} else {
vec.Add(sVec.State)
vecR.Add(sVec.RState)
}
}
if vec != nil {
downstream[i] = VecRStateGrad{State: vec, RState: vecR}
}
}
return s.WrappedOut.PropagateRGradient(nil, nil, downstream, rg, g)
}
func (g *gradientIterator) optimalStep(d linalg.Vector) float64 {
// The optimal step size is (d'*b - c'*A*d)/(d'*A*d)
// where d is the direction, A is the matrix, x is
// the current approximate solution, and b is all 1's.
dMat := &linalg.Matrix{
Rows: len(d),
Cols: 1,
Data: d,
}
ad := linalg.Vector(g.matrix.Mul(dMat).Data)
summer := kahan.NewSummer64()
for _, x := range d {
summer.Add(x)
}
numerator := summer.Sum() - g.solution.Dot(ad)
denominator := d.Dot(ad)
return numerator / denominator
}
func (s *stateOutBlockResult) PropagateGradient(u []linalg.Vector, su []StateGrad,
g autofunc.Gradient) []StateGrad {
downstream := make([]StateGrad, len(s.WrappedOut.Outputs()))
for i := range s.WrappedOut.Outputs() {
var vec linalg.Vector
if u != nil {
vec = u[i].Copy()
}
if su != nil && su[i] != nil {
sVec := su[i].(VecStateGrad)
if vec == nil {
vec = linalg.Vector(sVec).Copy()
} else {
vec.Add(linalg.Vector(sVec))
}
}
if vec != nil {
downstream[i] = VecStateGrad(vec)
}
}
return s.WrappedOut.PropagateGradient(nil, downstream, g)
}
// Step adds d.Scale(amount) to coeffs.
// If any of the entries in coeffs hits a
// constraint, then the step is stopped
// short and true is returned to indicate
// that a new constraint has been added.
//
// This may modify d in any way it pleases.
func (a *activeSet) Step(coeffs, d linalg.Vector, amount float64) bool {
var maxStep, minStep float64
var maxIdx, minIdx int
isFirst := true
for i, x := range d {
if x == 0 {
continue
}
coeff := coeffs[i]
maxValue := (a.MaxCoeff - coeff) / x
minValue := -coeff / x
if x < 0 {
maxValue, minValue = minValue, maxValue
}
if isFirst {
isFirst = false
minStep, maxStep = minValue, maxValue
maxIdx, minIdx = i, i
} else {
if minValue > minStep {
minStep = minValue
minIdx = i
}
if maxValue < maxStep {
maxStep = maxValue
maxIdx = i
}
}
}
if isFirst {
return false
}
if amount < minStep {
coeffs.Add(d.Scale(minStep))
a.addConstraint(coeffs, minIdx)
} else if amount > maxStep {
coeffs.Add(d.Scale(maxStep))
a.addConstraint(coeffs, maxIdx)
} else {
coeffs.Add(d.Scale(amount))
return false
}
return true
}
// Loss returns the exponential loss, as given by
// exp(-actual*expected).
func (_ ExpLoss) Loss(actual autofunc.Result, expected linalg.Vector) autofunc.Result {
expVar := &autofunc.Variable{Vector: expected.Copy().Scale(-1)}
dots := autofunc.Mul(actual, expVar)
exps := autofunc.Exp{}.Apply(dots)
return autofunc.SumAll(exps)
}
// OptimalStep returns the value a which minimizes
// the squared distance between y and x0+a*x.
func (_ SquareLoss) OptimalStep(x0, x, y linalg.Vector) float64 {
return (x.Dot(y) - x.Dot(x0)) / x.Dot(x)
}
// Loss returns the squared magnitude of the difference
// between actual and expected.
func (_ SquareLoss) Loss(actual autofunc.Result, expected linalg.Vector) autofunc.Result {
expVar := &autofunc.Variable{Vector: expected.Copy().Scale(-1)}
return autofunc.SumAll(autofunc.Square(autofunc.Add(actual, expVar)))
}
func (_ MeanSquaredCost) CostR(v autofunc.RVector, a linalg.Vector,
x autofunc.RResult) autofunc.RResult {
aVar := &autofunc.Variable{a.Copy().Scale(-1)}
aVarR := autofunc.NewRVariable(aVar, v)
return autofunc.SquaredNorm{}.ApplyR(v, autofunc.AddR(aVarR, x))
}
