Tree gradient, numerical "proof"

main.go

// Numerically verify that you should average gradients at
// the leaves in a gradient boosted tree.

package main

import (
	"fmt"

	"github.com/unixpickle/anydiff"
	"github.com/unixpickle/anyvec/anyvec64"
)

func main() {
	x := anydiff.NewConst(anyvec64.MakeVectorData([]float64{3, 1.5, 2}))
	a := anydiff.NewVar(anyvec64.MakeVectorData([]float64{2.25}))
	b := anydiff.NewVar(anyvec64.MakeVectorData([]float64{2}))

	grad := anydiff.NewGrad(a, b)
	computeLoss(x, a, b).Propagate(anyvec64.MakeVectorData([]float64{1}), grad)
	fmt.Println(grad[a].Data(), grad[b].Data())
}

func computeLoss(x, a, b anydiff.Res) anydiff.Res {
	vec := anydiff.Concat(a, a, b)
	return anydiff.Mul(
		anydiff.Dot(vec, x),
		anydiff.Pow(anydiff.Dot(vec, vec), -0.5),
	)
}