/
InformationDecomposition.go
200 lines (167 loc) · 4.72 KB
/
InformationDecomposition.go
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package discrete
import (
"math"
)
func PX(pxyz [][][]float64) []float64 {
r := make([]float64, 2, 2)
r[0] = pxyz[0][0][0] + pxyz[0][0][1] + pxyz[0][1][0] + pxyz[0][1][1]
r[1] = pxyz[1][0][0] + pxyz[1][0][1] + pxyz[1][1][0] + pxyz[1][1][1]
return r
}
func PY(pxyz [][][]float64) []float64 {
r := make([]float64, 2, 2)
r[0] = pxyz[0][0][0] + pxyz[0][0][1] + pxyz[1][0][0] + pxyz[1][0][1]
r[1] = pxyz[0][1][0] + pxyz[0][1][1] + pxyz[1][1][0] + pxyz[1][1][1]
return r
}
func PZ(pxyz [][][]float64) []float64 {
r := make([]float64, 2, 2)
r[0] = pxyz[0][0][0] + pxyz[0][1][0] + pxyz[1][0][0] + pxyz[1][1][0]
r[1] = pxyz[0][0][1] + pxyz[0][1][1] + pxyz[1][0][1] + pxyz[1][1][1]
return r
}
func PYZ(pxyz [][][]float64) [][]float64 {
r := make([][]float64, 2, 2)
r[0] = make([]float64, 2, 2)
r[1] = make([]float64, 2, 2)
r[0][0] = pxyz[0][0][0] + pxyz[1][0][0]
r[0][1] = pxyz[0][0][1] + pxyz[1][0][1]
r[1][0] = pxyz[0][1][0] + pxyz[1][1][0]
r[1][1] = pxyz[0][1][1] + pxyz[1][1][1]
return r
}
func PXZ(pxyz [][][]float64) [][]float64 {
r := make([][]float64, 2, 2)
r[0] = make([]float64, 2, 2)
r[1] = make([]float64, 2, 2)
r[0][0] = pxyz[0][0][0] + pxyz[0][1][0]
r[0][1] = pxyz[0][0][1] + pxyz[0][1][1]
r[1][0] = pxyz[1][0][0] + pxyz[1][1][0]
r[1][1] = pxyz[1][0][1] + pxyz[1][1][1]
return r
}
func PXY(pxyz [][][]float64) [][]float64 {
r := make([][]float64, 2, 2)
r[0] = make([]float64, 2, 2)
r[1] = make([]float64, 2, 2)
r[0][0] = pxyz[0][0][0] + pxyz[0][0][1]
r[0][1] = pxyz[0][1][0] + pxyz[0][1][1]
r[1][0] = pxyz[1][0][0] + pxyz[1][0][1]
r[1][1] = pxyz[1][1][0] + pxyz[1][1][1]
return r
}
func H3(pxyz [][][]float64) float64 {
r := 0.0
for x := 0; x < 2; x++ {
for y := 0; y < 2; y++ {
for z := 0; z < 2; z++ {
r -= pxyz[x][y][z] * math.Log2(pxyz[x][y][z])
}
}
}
return r
}
func H2(pxy [][]float64) float64 {
r := 0.0
for x := 0; x < 2; x++ {
for y := 0; y < 2; y++ {
r -= pxy[x][y] * math.Log2(pxy[x][y])
}
}
return r
}
func H1(px []float64) float64 {
r := 0.0
for x := 0; x < 2; x++ {
r -= px[x] * math.Log2(px[x])
}
return r
}
func Pt(pxyz [][][]float64, a, b float64) [][][]float64 {
A := make([][][]float64, 2, 2)
A[0] = make([][]float64, 2, 2)
A[1] = make([][]float64, 2, 2)
A[0][0] = make([]float64, 2, 2)
A[0][1] = make([]float64, 2, 2)
A[1][0] = make([]float64, 2, 2)
A[1][1] = make([]float64, 2, 2)
B := make([][][]float64, 2, 2)
B[0] = make([][]float64, 2, 2)
B[1] = make([][]float64, 2, 2)
B[0][0] = make([]float64, 2, 2)
B[0][1] = make([]float64, 2, 2)
B[1][0] = make([]float64, 2, 2)
B[1][1] = make([]float64, 2, 2)
A[0][0][0] = 1.0
A[0][0][1] = -1.0
A[0][1][0] = -1.0
A[0][1][1] = 1.0
B[1][0][0] = 1.0
B[1][0][1] = -1.0
B[1][1][0] = -1.0
B[1][1][1] = 1.0
r := make([][][]float64, 2, 2)
for i := 0; i < 2; i++ {
r[i] = make([][]float64, 2, 2)
for j := 0; j < 2; j++ {
r[i][j] = make([]float64, 2, 2)
for k := 0; k < 2; k++ {
r[i][j][k] = pxyz[i][j][k] + a*A[i][j][k] + b*B[i][j][k]
}
}
}
return r
}
func MiXvYgZ(pxyz [][][]float64) float64 {
return H2(PXZ(pxyz)) + H2(PYZ(pxyz)) - H3(pxyz) - H1(PZ(pxyz))
}
func MiXvZgY(pxyz [][][]float64) float64 {
return H2(PXY(pxyz)) + H2(PYZ(pxyz)) - H3(pxyz) - H1(PY(pxyz))
}
func MiXvY(pxyz [][][]float64) float64 {
return H1(PX(pxyz)) + H1(PY(pxyz)) - H2(PXY(pxyz))
}
func MiXvYZ(pxyz [][][]float64) float64 {
return H1(PX(pxyz)) + H2(PYZ(pxyz)) - H3(pxyz)
}
func CoI(pxyz [][][]float64) float64 {
return MiXvY(pxyz) - MiXvYgZ(pxyz)
}
func MinMax(pxyz [][][]float64, resolution int) (float64, float64, float64, float64, float64, float64) {
amin := math.Max(-pxyz[0][0][0], -pxyz[0][1][1])
amax := math.Min(pxyz[0][0][1], pxyz[0][1][0])
adelta := (amax - amin) / float64(resolution)
bmin := math.Max(-pxyz[1][0][0], -pxyz[1][1][1])
bmax := math.Min(pxyz[1][0][1], pxyz[1][1][0])
bdelta := (bmax - bmin) / float64(resolution)
return amin, amax, adelta, bmin, bmax, bdelta
}
// InformationDecomposition return the UI(X;Y\Z), UI(X;Z\Y), CI(X;Y,Z), and SI(X;Y,Z)
// according to
// N. Bertschinger, J. Rauh, E. Olbrich, J. Jost, and N. Ay, Quantifying unique information, CoRR, 2013
func InformationDecomposition(pxyz [][][]float64, resolution int) (float64, float64, float64) {
amin, amax, adelta, bmin, bmax, bdelta := MinMax(pxyz, resolution)
uniqueXY := MiXvYgZ(Pt(pxyz, 0.0, 0.0))
uniqueXZ := MiXvZgY(Pt(pxyz, 0.0, 0.0))
maxCoI := CoI(Pt(pxyz, 0.0, 0.0))
r := 0.0
for a := amin; a <= amax; a += adelta {
for b := bmin; b <= bmax; b += bdelta {
q := Pt(pxyz, a, b)
r = CoI(q)
if r > maxCoI {
maxCoI = r
}
r = MiXvZgY(q)
if r < uniqueXY {
uniqueXY = r
}
r = MiXvYgZ(q)
if r < uniqueXZ {
uniqueXZ = r
}
}
}
coI := maxCoI - CoI(pxyz)
return coI, uniqueXY, uniqueXZ
}