/// <summary>
/// Get the predictive distribution for the N+1 time, used for the multivariate volatility experiments
/// </summary>
/// <param name="model"></param>
/// <returns></returns>
public static VectorGaussian CorrelatedPredictions(INetworkModel model)
{
var noisePrecisionPost = model.Marginal <Gamma[]>("noisePrecisionArray");
var f = model.Marginal <Gaussian[][]>("nodeFunctionValuesPredictive");
var W = model.Marginal <Gaussian[, ][]>("weightFunctionValuesPredictive");
int ni = model.N - 1;
var mean = Vector.Zero(model.D);
var cov = new PositiveDefiniteMatrix(model.D, model.D);
for (int i = 0; i < model.D; i++)
{
cov[i, i] = noisePrecisionPost[i].GetMeanInverse();
for (int k = 0; k < model.Q; k++)
{
mean[i] += W[i, k][ni].GetMean() * f[k][ni].GetMean();
cov[i, i] += W[i, k][ni].GetVariance() * (f[k][ni].GetMean() * f[k][ni].GetMean() + f[k][ni].GetVariance());
}
for (int j = 0; j < model.D; j++)
{
for (int k = 0; k < model.Q; k++)
{
cov[i, j] += W[i, k][ni].GetMean() * W[j, k][ni].GetMean() * f[k][ni].GetVariance();
}
}
}
return(VectorGaussian.FromMeanAndVariance(mean, cov));
}
/// <summary>
/// Get the fitted NOISE covariance only over the time series
/// </summary>
/// <param name="model"></param>
/// <returns></returns>
public static PositiveDefiniteMatrix[] HistoricalNoiseCovariances(INetworkModel model)
{
var noisePrecisionPost = model.Marginal <Gamma[]>("noisePrecisionArray");
var nodeSignalPrecisionsPost = model.Marginal <Gamma[]>("nodeSignalPrecisions");
var W = model.Marginal <Gaussian[, ][]>("weightFunctionValuesPredictive");
var result = new PositiveDefiniteMatrix[model.N];
for (int ni = 0; ni < model.N; ni++)
{
var cov = new PositiveDefiniteMatrix(model.D, model.D);
for (int i = 0; i < model.D; i++)
{
cov[i, i] = noisePrecisionPost[i].GetMeanInverse();
for (int j = 0; j < model.D; j++)
{
for (int k = 0; k < model.Q; k++)
{
cov[i, j] += W[i, k][ni].GetMean() * W[j, k][ni].GetMean() * nodeSignalPrecisionsPost[k].GetMeanInverse();
}
}
}
result[ni] = cov;
}
return(result);
}
/// <summary>
/// Assess the fitted model on held out data.
/// </summary>
/// <param name="model">Fitted model</param>
/// <param name="data">All data</param>
/// <param name="isMissing">Which elements are missing (heldout)</param>
/// <param name="logTransform">Whether the data was log transformed</param>
/// <param name="means">The means used to normalise the data, if normalised</param>
/// <param name="vars">The variances used to normalise the data, if normalised</param>
/// <returns>Array of error measures</returns>
public static double[] AssessOnMissing(INetworkModel model, double[,] data, bool[,] isMissing, bool logTransform, double[] means = null, double[] vars = null)
{
double logProb = 0, error = 0, counter = 0;
for (int d = 0; d < data.GetLength(0); d++)
{
for (int n = 0; n < data.GetLength(1); n++)
{
if (isMissing[d, n])
{
counter += 1;
var prediction = GaussianOp.SampleAverageLogarithm(model.Marginal <Gaussian[, ]>("noiseLessY")[d, n], model.Marginal <Gamma[]>("noisePrecisionArray")[d]);
logProb += prediction.GetLogProb(data[d, n]);
double predMean = prediction.GetMean();
double dataPoint = data[d, n];
if (means != null)
{
predMean = predMean * Math.Sqrt(vars[d]) + means[d];
dataPoint = dataPoint * Math.Sqrt(vars[d]) + means[d];
}
if (logTransform)
{
predMean = Math.Exp(predMean);
dataPoint = Math.Exp(dataPoint);
}
error += Math.Abs(predMean - dataPoint);
}
}
}
logProb /= counter;
error /= counter;
return(new double[] { logProb, error });
}