DenseMatrix[] sigmas; //covariance of the 3D gaussians.
#endregion Fields
#region Constructors
public CD_HMM(MarkovChain A, DenseVector pi, DenseVector[] mus, DenseMatrix[] sigmas)
{
this.A = A;
this.pi = pi;
this.mus = mus;
this.sigmas = sigmas;
}
public void reestimateParameters(DenseVector[][] observationsCollection)
{
int K = observationsCollection.Length;
int[] times = new int[K];
int N = A.numberOfStates;
for (int k = 0; k < K; k++)
{
times[k] = observationsCollection[k].Length; //possible error?
}
double[][,] alphabars = new double[K][,];
double[][,] alphahats = new double[K][,];
double[][] scales = new double[K][];
double[][,] betahats = new double[K][,];
double[][,,] digammas = new double[K][,,];
double[][,] gammas = new double[K][,];
//Initialize arrays to proper sizes.
for (int k = 0; k < K; k++)
{
alphahats[k] = new double[times[k], N];
alphabars[k] = new double[times[k], N];
scales[k] = new double[times[k]];
betahats[k] = new double[times[k], N];
digammas[k] = new double[times[k],N,N];
gammas[k] = new double[times[k],N];
}
for (int k = 0; k < K; k++)
{
//The alpha pass
scales[k][0] = 0;
#region The alpha Pass
for (int i = 0; i < N; i++)
{
alphabars[k][0, i] = pi[i] * queryGuassian(observationsCollection[k][0], mus[i], sigmas[i]);
scales[k][0] += alphabars[k][0, i];
}
scales[k][0] = 1 / (scales[k][0]);
for (int i = 0; i < N; i++)
{
alphahats[k][0, i] = scales[k][0]*alphabars[k][0,i];
}
for (int t = 1; t < times[k]; t++)
{
scales[k][t] = 0;
for (int i = 0; i < N; i++)
{
alphabars[k][t, i] = 0;
for (int j = 0; j < N; j++)
{
alphabars[k][t, i] += alphahats[k][t - 1, j] * A.getTransitionProb(j, i);
}
alphabars[k][t, i] *= queryGuassian(observationsCollection[k][t], mus[i], sigmas[i]);
scales[k][t] += alphabars[k][t, i];
}
scales[k][t] = 1 / (scales[k][t]);
for (int i = 0; i < N; i++)
{
alphahats[k][t, i] = scales[k][t]*alphabars[k][t,i];
}
}
#endregion
#region The beta pass
for (int i = 1; i < N; i++)
{
betahats[k][times[k] - 1, i] = scales[k][times[k] - 1];
}
for (int t = times[k] - 2; t >= 0; t--)
{
for (int i = 0; i < N; i++)
{
betahats[k][t, i] = 0;
for (int j = 0; j < N; j++)
{
betahats[k][t, i] += A.getTransitionProb(i, j) * queryGuassian(observationsCollection[k][t + 1], mus[j], sigmas[j]) * betahats[k][t + 1, j];
}
betahats[k][t, i] *= scales[k][t];
}
}
#endregion
#region The gamma pass
for (int t = 0; t < times[k] - 1; t++)
{
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
digammas[k][t, i, j] = alphahats[k][t, i] * A.getTransitionProb(i, j) *
queryGuassian(observationsCollection[k][t + 1], mus[j], sigmas[j]) * betahats[k][t + 1, j];
}
gammas[k][t, i] = alphahats[k][t, i] * betahats[k][t, i] * (1 / scales[k][t]);
}
}
#endregion
}
#region re-estimate pi
DenseVector newPi = new DenseVector(N);
double numer, denom, piComp;
for (int i = 0; i < N; i++)
{
numer = 0; denom = 0; piComp = 0;
for (int k = 0; k < K; k++)
{
numer += gammas[k][0, i];
}
for (int j = 0; j < numer; j++)
{
for (int k = 0; k < K; k++)
{
denom += gammas[k][0, j];
}
}
piComp = numer / denom;
newPi[i] = piComp;
}
#endregion
#region re-estimate A
DenseMatrix newA;
double[,] newAarray = new double[N, N];
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
numer = 0; denom = 0;
//Can these be simplified with the gammas?
for (int k = 0; k < K; k++)
{
for (int t = 0; t < times[k] - 1; t++)
{
numer += alphahats[k][t, i] * A.getTransitionProb(i, j) *
queryGuassian(observationsCollection[k][t + 1], mus[j], sigmas[j]) * betahats[k][t + 1, j];
}
}
for (int k = 0; k < K; k++)
{
for (int t = 0; t < times[k] - 1; t++)
{
denom += alphahats[k][t, i] * betahats[k][t, i] * (1 / scales[k][t]);
}
}
newAarray[i, j] = (numer / denom);
}
}
newA = new DenseMatrix(newAarray);
#endregion
#region re-estimate mus
DenseVector[] newMus = new DenseVector[N];
//Initialize and zero the new mus
for (int j = 0; j < N; j++)
{
newMus[j] = new DenseVector(observationsCollection[0][0].Count);
for (int l = 0; l < observationsCollection[0][0].Count; l++)
{
newMus[j][l] = 0;
}
}
for (int j = 0; j < N; j++)
{
denom = 0;
for (int k = 0; k < K; k++)
{
for (int t = 0; t < times[k]; t++)
{
newMus[j] += gammas[k][t, j] * observationsCollection[k][t];
denom += gammas[k][t, j];
}
}
newMus[j] = (newMus[j] / denom);
}
#endregion
#region re-estimate Sigmas
DenseMatrix[] newSigmas = new DenseMatrix[N];
DenseMatrix temp = new DenseMatrix(observationsCollection[0][0].Count);
DenseVector tempvec = new DenseVector(observationsCollection[0][0].Count);
for (int j = 0; j < N; j++)
{
newSigmas[j] = new DenseMatrix(observationsCollection[0][0].Count);
for (int l = 0; l < observationsCollection[0][0].Count; l++)
{
for (int m = 0; m < observationsCollection[0][0].Count; m++)
{
newSigmas[j][l, m] = 0;
}
}
}
for (int j = 0; j < N; j++)
{
denom = 0;
for (int k = 0; k < K; k++)
{
for (int t = 0; t < times[k]; t++)
{
tempvec = observationsCollection[k][t] - newMus[j];
temp = DenseVector.OuterProduct(tempvec, tempvec);
newSigmas[j] += temp;
denom += gammas[k][t, j];
}
}
newSigmas[j] = newSigmas[j] * (1 / denom);
}
#endregion
pi = newPi;
A = new MarkovChain(newA);
mus = newMus;
sigmas = newSigmas;
}