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https://github.com/gonum/gonum.git
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Add ConditionNormal
This commit is contained in:
btracey
@@ -1,6 +1,7 @@
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package distmv
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import (
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"math"
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"testing"
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"github.com/gonum/floats"
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@@ -96,3 +97,216 @@ func TestNormRand(t *testing.T) {
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}
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}
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}
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func TestConditionNormal(t *testing.T) {
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// Uncorrelated values shouldn't influence the updated values.
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for _, test := range []struct {
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mu []float64
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sigma *mat64.SymDense
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observed []int
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values []float64
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newMu []float64
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newSigma *mat64.SymDense
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}{
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{
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mu: []float64{2, 3},
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sigma: mat64.NewSymDense(2, []float64{2, 0, 0, 5}),
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observed: []int{0},
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values: []float64{10},
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newMu: []float64{3},
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newSigma: mat64.NewSymDense(1, []float64{5}),
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},
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{
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mu: []float64{2, 3},
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sigma: mat64.NewSymDense(2, []float64{2, 0, 0, 5}),
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observed: []int{1},
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values: []float64{10},
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newMu: []float64{2},
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newSigma: mat64.NewSymDense(1, []float64{2}),
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},
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{
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mu: []float64{2, 3, 4},
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sigma: mat64.NewSymDense(3, []float64{2, 0, 0, 0, 5, 0, 0, 0, 10}),
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observed: []int{1},
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values: []float64{10},
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newMu: []float64{2, 4},
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newSigma: mat64.NewSymDense(2, []float64{2, 0, 0, 10}),
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},
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{
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mu: []float64{2, 3, 4},
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sigma: mat64.NewSymDense(3, []float64{2, 0, 0, 0, 5, 0, 0, 0, 10}),
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observed: []int{0, 1},
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values: []float64{10, 15},
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newMu: []float64{4},
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newSigma: mat64.NewSymDense(1, []float64{10}),
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},
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{
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mu: []float64{2, 3, 4, 5},
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sigma: mat64.NewSymDense(4, []float64{2, 0.5, 0, 0, 0.5, 5, 0, 0, 0, 0, 10, 2, 0, 0, 2, 3}),
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observed: []int{0, 1},
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values: []float64{10, 15},
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newMu: []float64{4, 5},
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newSigma: mat64.NewSymDense(2, []float64{10, 2, 2, 3}),
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},
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} {
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normal, ok := NewNormal(test.mu, test.sigma, nil)
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if !ok {
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t.Fatalf("Bad test, original sigma not positive definite")
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}
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newNormal, ok := normal.ConditionNormal(test.observed, test.values, nil)
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if !ok {
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t.Fatalf("Bad test, update failure")
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}
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if !floats.EqualApprox(test.newMu, newNormal.mu, 1e-12) {
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t.Errorf("Updated mean mismatch. Want %v, got %v.", test.newMu, newNormal.mu)
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}
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var sigma mat64.SymDense
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sigma.FromCholesky(&newNormal.chol)
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if !mat64.EqualApprox(test.newSigma, &sigma, 1e-12) {
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t.Errorf("Updated sigma mismatch\n.Want:\n% v\nGot:\n% v\n", test.newSigma, sigma)
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}
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}
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// Test bivariate case where the update rule is analytic
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for _, test := range []struct {
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mu []float64
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std []float64
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rho float64
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value float64
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}{
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{
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mu: []float64{2, 3},
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std: []float64{3, 5},
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rho: 0.9,
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value: 1000,
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},
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{
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mu: []float64{2, 3},
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std: []float64{3, 5},
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rho: -0.9,
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value: 1000,
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},
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} {
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std := test.std
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rho := test.rho
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sigma := mat64.NewSymDense(2, []float64{std[0] * std[0], std[0] * std[1] * rho, std[0] * std[1] * rho, std[1] * std[1]})
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normal, ok := NewNormal(test.mu, sigma, nil)
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if !ok {
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t.Fatalf("Bad test, original sigma not positive definite")
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}
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newNormal, ok := normal.ConditionNormal([]int{1}, []float64{test.value}, nil)
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if !ok {
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t.Fatalf("Bad test, update failed")
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}
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var newSigma mat64.SymDense
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newSigma.FromCholesky(&newNormal.chol)
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trueMean := test.mu[0] + rho*(std[0]/std[1])*(test.value-test.mu[1])
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if math.Abs(trueMean-newNormal.mu[0]) > 1e-14 {
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t.Errorf("Mean mismatch. Want %v, got %v", trueMean, newNormal.mu[0])
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}
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trueVar := (1 - rho*rho) * std[0] * std[0]
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if math.Abs(trueVar-newSigma.At(0, 0)) > 1e-14 {
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t.Errorf("Std mismatch. Want %v, got %v", trueMean, newNormal.mu[0])
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}
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}
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// Test via sampling.
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for _, test := range []struct {
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mu []float64
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sigma *mat64.SymDense
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observed []int
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unobserved []int
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value []float64
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}{
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// The indices in unobserved must be in ascending order for this test.
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{
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mu: []float64{2, 3, 4},
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sigma: mat64.NewSymDense(3, []float64{2, 0.5, 3, 0.5, 1, 0.6, 3, 0.6, 10}),
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observed: []int{0},
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unobserved: []int{1, 2},
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value: []float64{1.9},
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},
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{
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mu: []float64{2, 3, 4, 5},
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sigma: mat64.NewSymDense(4, []float64{2, 0.5, 3, 0.1, 0.5, 1, 0.6, 0.2, 3, 0.6, 10, 0.3, 0.1, 0.2, 0.3, 3}),
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observed: []int{0, 3},
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unobserved: []int{1, 2},
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value: []float64{1.9, 2.9},
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},
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} {
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totalSamp := 4000000
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var nSamp int
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samples := mat64.NewDense(totalSamp, len(test.mu), nil)
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normal, ok := NewNormal(test.mu, test.sigma, nil)
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if !ok {
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t.Errorf("bad test")
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}
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sample := make([]float64, len(test.mu))
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for i := 0; i < totalSamp; i++ {
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normal.Rand(sample)
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isClose := true
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for i, v := range test.observed {
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if math.Abs(sample[v]-test.value[i]) > 1e-1 {
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isClose = false
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break
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}
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}
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if isClose {
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samples.SetRow(nSamp, sample)
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nSamp++
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}
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}
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if nSamp < 100 {
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t.Errorf("bad test, not enough samples")
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continue
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}
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samples = samples.View(0, 0, nSamp, len(test.mu)).(*mat64.Dense)
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// Compute mean and covariance matrix.
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estMean := make([]float64, len(test.mu))
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for i := range estMean {
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estMean[i] = stat.Mean(mat64.Col(nil, i, samples), nil)
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}
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estCov := stat.CovarianceMatrix(nil, samples, nil)
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// Compute update rule.
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newNormal, ok := normal.ConditionNormal(test.observed, test.value, nil)
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if !ok {
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t.Fatalf("Bad test, update failure")
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}
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var subEstMean []float64
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for _, v := range test.unobserved {
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subEstMean = append(subEstMean, estMean[v])
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}
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subEstCov := mat64.NewSymDense(len(test.unobserved), nil)
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for i := 0; i < len(test.unobserved); i++ {
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for j := i; j < len(test.unobserved); j++ {
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subEstCov.SetSym(i, j, estCov.At(test.unobserved[i], test.unobserved[j]))
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}
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}
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for i, v := range subEstMean {
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if math.Abs(newNormal.mu[i]-v) > 5e-2 {
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t.Errorf("Mean mismatch. Want %v, got %v.", newNormal.mu[i], v)
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}
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}
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var sigma mat64.SymDense
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sigma.FromCholesky(&newNormal.chol)
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if !mat64.EqualApprox(&sigma, subEstCov, 1e-1) {
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t.Errorf("Covariance mismatch. Want:\n%0.8v\nGot:\n%0.8v\n", subEstCov, sigma)
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}
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}
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}
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