// Estimate computes model parameters using sufficient statistics.
func (g *Model) Estimate() error {
if g.NSamples > minNumSamples {
/* Estimate the mean. */
floatx.Apply(floatx.ScaleFunc(1.0/g.NSamples), g.Sumx, g.Mean)
/*
* Estimate the variance. sigma_sq = 1/n (sumxsq - 1/n sumx^2) or
* 1/n sumxsq - mean^2.
*/
tmp := g.variance // borrow as an intermediate array.
// floatx.Apply(sq, g.Mean, g.tmpArray)
floatx.Sq(g.tmpArray, g.Mean)
floatx.Apply(floatx.ScaleFunc(1.0/g.NSamples), g.Sumxsq, tmp)
floats.SubTo(g.variance, tmp, g.tmpArray)
floatx.Apply(floatx.Floorv(smallVar), g.variance, nil)
} else {
/* Not enough training sample. */
glog.Warningf("not enough training samples, name [%s], num samples [%e]", g.ModelName, g.NSamples)
floatx.Apply(floatx.SetValueFunc(smallVar), g.variance, nil)
floatx.Apply(floatx.SetValueFunc(0), g.Mean, nil)
}
g.setVariance(g.variance) // to update varInv and stddev.
/* Update log Gaussian constant. */
floatx.Log(g.tmpArray, g.variance)
g.const2 = g.const1 - floats.Sum(g.tmpArray)/2.0
glog.V(6).Infof("gaussian reest, name:%s, mean:%v, sd:%v", g.ModelName, g.Mean, g.StdDev)
return nil
}
// Clear resets sufficient statistics.
func (gmm *Model) Clear() {
for _, c := range gmm.Components {
c.Clear()
}
floatx.Apply(floatx.SetValueFunc(0), gmm.PosteriorSum, nil)
gmm.NSamples = 0
gmm.Likelihood = 0
}
// NewModel creates a new Gaussian mixture model.
func NewModel(dim, numComponents int, options ...Option) *Model {
gmm := &Model{
ModelName: "GMM", // default name
ModelDim: dim,
NComponents: numComponents,
Diag: true,
tmpProbs: make([]float64, numComponents),
}
gmm.Type = reflect.TypeOf(*gmm).String()
// Set options.
for _, option := range options {
option(gmm)
}
if len(gmm.PosteriorSum) == 0 {
gmm.PosteriorSum = make([]float64, gmm.NComponents)
}
// Create components if not provided.
if len(gmm.Components) == 0 {
gmm.Components = make([]*gaussian.Model, numComponents, numComponents)
for i := range gmm.Components {
cname := componentName(gmm.ModelName, i, gmm.NComponents)
gmm.Components[i] = gaussian.NewModel(gmm.ModelDim, gaussian.Name(cname))
}
}
// Initialize weights.
// Caller may pass weight, log(weights), or no weights.
switch {
case len(gmm.LogWeights) > 0 && len(gmm.Weights) > 0:
glog.Fatal("options not allowed: provide only one of LogWeights or Weights")
case len(gmm.LogWeights) == 0 && len(gmm.Weights) == 0:
gmm.LogWeights = make([]float64, numComponents)
logw := -math.Log(float64(gmm.NComponents))
floatx.Apply(floatx.SetValueFunc(logw), gmm.LogWeights, nil)
gmm.Weights = make([]float64, gmm.NComponents)
floatx.Exp(gmm.Weights, gmm.LogWeights)
glog.Infof("init weights with equal values: %.6f", gmm.Weights[0])
case len(gmm.LogWeights) > 0:
gmm.Weights = make([]float64, gmm.NComponents)
floatx.Exp(gmm.Weights, gmm.LogWeights)
case len(gmm.Weights) > 0:
gmm.LogWeights = make([]float64, numComponents)
floatx.Log(gmm.LogWeights, gmm.Weights)
}
return gmm
}
// UpdateOne updates sufficient statistics using one observation.
func (g *Model) UpdateOne(o model.Obs, w float64) {
glog.V(6).Infof("gaussian update, name:%s, obs:%v, weight:%e", g.ModelName, o, w)
/* Update sufficient statistics. */
obs, _, _ := model.ObsToF64(o)
floatx.Apply(floatx.ScaleFunc(w), obs, g.tmpArray)
floats.Add(g.Sumx, g.tmpArray)
floatx.Sq(g.tmpArray, obs)
floats.Scale(w, g.tmpArray)
floats.Add(g.Sumxsq, g.tmpArray)
g.NSamples += w
}
// Estimate computes model parameters using sufficient statistics.
func (gmm *Model) Estimate() error {
// Estimate mixture weights.
floatx.Apply(floatx.ScaleFunc(1.0/gmm.NSamples), gmm.PosteriorSum, gmm.Weights)
floatx.Log(gmm.LogWeights, gmm.Weights)
// Estimate component density.
for _, c := range gmm.Components {
err := c.Estimate()
if err != nil {
return err
}
}
gmm.Iteration++
return nil
}
// Estimate computes model parameters using sufficient statistics.
func (gmm *Model) UpdateOne(o model.Obs, w float64) {
obs, _, _ := model.ObsToF64(o)
maxProb := gmm.logProbInternal(obs, gmm.tmpProbs)
gmm.Likelihood += maxProb
floatx.Apply(floatx.AddScalarFunc(-maxProb+math.Log(w)), gmm.tmpProbs, nil)
// Compute posterior probabilities.
floatx.Exp(gmm.tmpProbs, gmm.tmpProbs)
// Update posterior sum, needed to compute mixture weights.
floats.Add(gmm.PosteriorSum, gmm.tmpProbs)
// Update Gaussian components.
for i, c := range gmm.Components {
c.UpdateOne(o, gmm.tmpProbs[i])
}
// Count number of observations.
gmm.NSamples += w
}
// NewModel creates a new Gaussian model.
func NewModel(dim int, options ...Option) *Model {
g := &Model{
ModelName: "Gaussian",
ModelDim: dim,
Diag: true,
variance: make([]float64, dim),
varianceInv: make([]float64, dim),
tmpArray: make([]float64, dim),
}
g.Type = reflect.TypeOf(*g).String()
// Set options.
for _, option := range options {
option(g)
}
if len(g.Sumx) == 0 {
g.Sumx = make([]float64, dim)
}
if len(g.Sumxsq) == 0 {
g.Sumxsq = make([]float64, dim)
}
if g.Mean == nil {
g.Mean = make([]float64, dim)
}
if g.StdDev == nil {
g.StdDev = make([]float64, dim)
floatx.Apply(floatx.SetValueFunc(smallSD), g.StdDev, nil)
}
floatx.Sq(g.variance, g.StdDev)
// Initializes variance, varianceInv, and StdDev.
g.setVariance(g.variance)
floatx.Log(g.tmpArray, g.variance)
g.const1 = -float64(g.ModelDim) * math.Log(2.0*math.Pi) / 2.0
g.const2 = g.const1 - floats.Sum(g.tmpArray)/2.0
return g
}
func (g *Model) setVariance(variance []float64) {
copy(g.variance, variance)
floatx.Apply(floatx.Inv, g.variance, g.varianceInv)
g.StdDev = g.standardDeviation()
}
// Clear resets sufficient statistics.
func (g *Model) Clear() {
floatx.Apply(floatx.SetValueFunc(0), g.Sumx, nil)
floatx.Apply(floatx.SetValueFunc(0), g.Sumxsq, nil)
g.NSamples = 0
}