private void CalculateModel(IDataset ds, IEnumerable <int> rows, bool scaleInputs = true)
{
this.trainingDataset = (IDataset)ds.Clone();
this.trainingRows = rows.ToArray();
this.inputScaling = scaleInputs ? new Scaling(ds, allowedInputVariables, rows) : null;
x = GetData(ds, this.allowedInputVariables, this.trainingRows, this.inputScaling);
IEnumerable <double> y;
y = ds.GetDoubleValues(targetVariable, rows);
int n = x.GetLength(0);
// calculate cholesky decomposed (lower triangular) covariance matrix
var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, Enumerable.Range(0, x.GetLength(1)));
this.l = CalculateL(x, cov, sqrSigmaNoise);
// calculate mean
var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, Enumerable.Range(0, x.GetLength(1)));
double[] m = Enumerable.Range(0, x.GetLength(0))
.Select(r => mean.Mean(x, r))
.ToArray();
// calculate sum of diagonal elements for likelihood
double diagSum = Enumerable.Range(0, n).Select(i => Math.Log(l[i, i])).Sum();
// solve for alpha
double[] ym = y.Zip(m, (a, b) => a - b).ToArray();
int info;
alglib.densesolverreport denseSolveRep;
alglib.spdmatrixcholeskysolve(l, n, false, ym, out info, out denseSolveRep, out alpha);
for (int i = 0; i < alpha.Length; i++)
{
alpha[i] = alpha[i] / sqrSigmaNoise;
}
negativeLogLikelihood = 0.5 * Util.ScalarProd(ym, alpha) + diagSum + (n / 2.0) * Math.Log(2.0 * Math.PI * sqrSigmaNoise);
// derivatives
int nAllowedVariables = x.GetLength(1);
alglib.matinvreport matInvRep;
double[,] lCopy = new double[l.GetLength(0), l.GetLength(1)];
Array.Copy(l, lCopy, lCopy.Length);
alglib.spdmatrixcholeskyinverse(ref lCopy, n, false, out info, out matInvRep);
if (info != 1)
{
throw new ArgumentException("Can't invert matrix to calculate gradients.");
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j <= i; j++)
{
lCopy[i, j] = lCopy[i, j] / sqrSigmaNoise - alpha[i] * alpha[j];
}
}
double noiseGradient = sqrSigmaNoise * Enumerable.Range(0, n).Select(i => lCopy[i, i]).Sum();
double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
for (int k = 0; k < meanGradients.Length; k++)
{
var meanGrad = Enumerable.Range(0, alpha.Length)
.Select(r => mean.Gradient(x, r, k));
meanGradients[k] = -Util.ScalarProd(meanGrad, alpha);
}
double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
if (covGradients.Length > 0)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < i; j++)
{
var g = cov.CovarianceGradient(x, i, j).ToArray();
for (int k = 0; k < covGradients.Length; k++)
{
covGradients[k] += lCopy[i, j] * g[k];
}
}
var gDiag = cov.CovarianceGradient(x, i, i).ToArray();
for (int k = 0; k < covGradients.Length; k++)
{
// diag
covGradients[k] += 0.5 * lCopy[i, i] * gDiag[k];
}
}
}
hyperparameterGradients =
meanGradients
.Concat(covGradients)
.Concat(new double[] { noiseGradient }).ToArray();
}
private void CalculateModel(IDataset ds, IEnumerable<int> rows, bool scaleInputs = true) {
this.trainingDataset = (IDataset)ds.Clone();
this.trainingRows = rows.ToArray();
this.inputScaling = scaleInputs ? new Scaling(ds, allowedInputVariables, rows) : null;
x = GetData(ds, this.allowedInputVariables, this.trainingRows, this.inputScaling);
IEnumerable<double> y;
y = ds.GetDoubleValues(TargetVariable, rows);
int n = x.GetLength(0);
var columns = Enumerable.Range(0, x.GetLength(1)).ToArray();
// calculate cholesky decomposed (lower triangular) covariance matrix
var cov = covarianceFunction.GetParameterizedCovarianceFunction(covarianceParameter, columns);
this.l = CalculateL(x, cov, sqrSigmaNoise);
// calculate mean
var mean = meanFunction.GetParameterizedMeanFunction(meanParameter, columns);
double[] m = Enumerable.Range(0, x.GetLength(0))
.Select(r => mean.Mean(x, r))
.ToArray();
// calculate sum of diagonal elements for likelihood
double diagSum = Enumerable.Range(0, n).Select(i => Math.Log(l[i, i])).Sum();
// solve for alpha
double[] ym = y.Zip(m, (a, b) => a - b).ToArray();
int info;
alglib.densesolverreport denseSolveRep;
alglib.spdmatrixcholeskysolve(l, n, false, ym, out info, out denseSolveRep, out alpha);
for (int i = 0; i < alpha.Length; i++)
alpha[i] = alpha[i] / sqrSigmaNoise;
negativeLogLikelihood = 0.5 * Util.ScalarProd(ym, alpha) + diagSum + (n / 2.0) * Math.Log(2.0 * Math.PI * sqrSigmaNoise);
// derivatives
int nAllowedVariables = x.GetLength(1);
alglib.matinvreport matInvRep;
double[,] lCopy = new double[l.GetLength(0), l.GetLength(1)];
Array.Copy(l, lCopy, lCopy.Length);
alglib.spdmatrixcholeskyinverse(ref lCopy, n, false, out info, out matInvRep);
if (info != 1) throw new ArgumentException("Can't invert matrix to calculate gradients.");
for (int i = 0; i < n; i++) {
for (int j = 0; j <= i; j++)
lCopy[i, j] = lCopy[i, j] / sqrSigmaNoise - alpha[i] * alpha[j];
}
double noiseGradient = sqrSigmaNoise * Enumerable.Range(0, n).Select(i => lCopy[i, i]).Sum();
double[] meanGradients = new double[meanFunction.GetNumberOfParameters(nAllowedVariables)];
for (int k = 0; k < meanGradients.Length; k++) {
var meanGrad = new double[alpha.Length];
for (int g = 0; g < meanGrad.Length; g++)
meanGrad[g] = mean.Gradient(x, g, k);
meanGradients[k] = -Util.ScalarProd(meanGrad, alpha);
}
double[] covGradients = new double[covarianceFunction.GetNumberOfParameters(nAllowedVariables)];
if (covGradients.Length > 0) {
for (int i = 0; i < n; i++) {
for (int j = 0; j < i; j++) {
var g = cov.CovarianceGradient(x, i, j);
for (int k = 0; k < covGradients.Length; k++) {
covGradients[k] += lCopy[i, j] * g[k];
}
}
var gDiag = cov.CovarianceGradient(x, i, i);
for (int k = 0; k < covGradients.Length; k++) {
// diag
covGradients[k] += 0.5 * lCopy[i, i] * gDiag[k];
}
}
}
hyperparameterGradients =
meanGradients
.Concat(covGradients)
.Concat(new double[] { noiseGradient }).ToArray();
}