/// <summary>
/// Finds the unidimensional criterion that maximizes accuracy for detecting the target category in a sample.
/// </summary>
/// <param name="targetCat">The target category.</param>
/// <param name="cat">The category labels for each datum in the sample.</param>
/// <param name="x">The univariate value for each datum in the sample.</param>
/// <param name="idx">The index into x[.] and cat[.] which rank-orders the sample in terms of increasing x.</param>
/// <param name="catWeight">The weight of each category on the accuracy.</param>
/// <returns>The unidimensional criterion.</returns>
public static UniCrit MaximumAccuracy(int targetCat, byte[] cat, float[] x, int[] idx, double[] catWeight)
{
UniCrit output = new UniCrit();
output.MaximizeAccuracy(targetCat, cat, x, idx, catWeight);
return(output);
}
public UniCrit Copy()
{
UniCrit output = new UniCrit();
output.Accuracy = this.Accuracy;
output.CritIndex = this.CritIndex;
output.CritValue = this.CritValue;
output.TargetUpper = this.TargetUpper;
return(output);
}
/// <summary>
/// Trains the classifier by optimizing parameters based on the training data using specified solver options.
/// This can only be called once.
/// </summary>
/// <param name="data">The training data.
/// WARNING: In order to save memory, this data is altered in palce (instead of copying a new object).</param>
/// <param name="ops">Sets the member variable <see cref="Classifier.Options"/>. If a value is not provided, default options are used.</param>
/// <param name="ops">The pre-optimization analysis <see cref="Classifier.Analysis"/>. If a value is not provided, default options are used.</param>
public async Task <Trainer> Train(CategorizedData data, SolverOptions ops = null, PreOptimizationAnalysis analysis = null)
{
lock (this)
{
if (this.trainerIsRunning)
{
throw new ApplicationException("The Train method can only be called once at a time. You might consider creating multiple Trainer objects.");
}
this.trainerIsRunning = true;
}
try
{
if (data.Ncats != this.Classifier.Instance.Ncats)
{
throw new ArgumentException("The number of categories in the classifier must be equal to the number of categories in the training set.");
}
//-----------------------
// Set the solver otions.
//-----------------------
if (ops == null)
{
ops = new SolverOptions();
}
this.options = ops;
//-----------------------
// Compute CatWeights.
//-----------------------
double cwTotal = 0.0;
this.totalWeight = 0.0; // Total weight across all training data.
if (this.options.WeightingRule == WeightingRule.EqualPriors)
{
for (int iCat = 0; iCat < data.Ncats; iCat++)
{
double w = (double)data.Ntotal / (double)data.Neach[iCat] / (double)data.Ncats;
this.CatWeights[iCat] = w;
cwTotal += w;
this.totalWeight += w * (double)data.Neach[iCat];
}
}
else if (this.options.WeightingRule == WeightingRule.ObservedPriors)
{
for (int iCat = 0; iCat < data.Ncats; iCat++)
{
this.totalWeight += (float)data.Neach[iCat];
this.CatWeights[iCat] = 1.0f;
cwTotal += 1.0f;
}
}
else
{
throw new ApplicationException("Unhandled weighting rule.");
}
// [iDatum] Used for identifying the category label for each datum.
byte[] catVec = new byte[data.Ntotal];
// [iDatum] Used for storing the polynomial calculation for each datum.
float[][] yVec = Static.NewArrays <float>(this.Classifier.Instance.Npoly, data.Ntotal);
// [iPoly][iDatum] Used for sorting data rows. Sort order is preserved for each polynomial.
int[][] idxVec = Static.NewArrays <int>(this.Classifier.Instance.Npoly, data.Ntotal);
//-----------------------
// Prepare category labels for each datum.
//-----------------------
int iDatum = 0;
for (int iCat = 0; iCat < data.Ncats; iCat++)
{
int nRows = data.X[iCat].Length;
for (int iRow = 0; iRow < nRows; iRow++)
{
catVec[iDatum++] = (byte)iCat;
}
}
if (analysis != null)
{
this.Analysis = analysis;
}
else
{
//-----------------------
// Condition the data and perform a polynomial expansion.
//-----------------------
this.Analysis = new PreOptimizationAnalysis();
this.Analysis.ConditionMeasurer = SpatialConditionMeasurer.Measure(data);
this.Analysis.Conditioner = this.Analysis.ConditionMeasurer.Conditioner();
this.Analysis.Conditioner.Condition(data);
data.Expand(this.Classifier.Instance.Coeffs);
this.Analysis.ParamScale = new float[this.Classifier.Instance.Coeffs.Ncoeffs];
this.Analysis.ParamInit = Static.NewArrays <float>(this.Classifier.Instance.Ncats, this.Classifier.Instance.Coeffs.Ncoeffs);
//if (ops.InitializeParams)
this.Analysis.Crits = Static.NewArrays <UniCrit>(this.Classifier.Instance.Ncats, this.Classifier.Instance.Coeffs.Ncoeffs);
//-----------------------
// Get the parameter scale.
//-----------------------
float scale;
int i15 = (int)(0.5 + 0.15 * (double)(data.Ntotal - 1));
int i50 = (int)(0.5 + 0.50 * (double)(data.Ntotal - 1));
int i85 = (int)(0.5 + 0.85 * (double)(data.Ntotal - 1));
float[] xVec = yVec[0];
for (int iCoeff = 0; iCoeff < this.Classifier.Instance.Coeffs.Ncoeffs; iCoeff++)
{
// Quantiles determine the parameter scale.
Static.FillSeries(idxVec[0]);
iDatum = 0;
for (int iCat = 0; iCat < data.Ncats; iCat++)
{
int nSamp = data.Neach[iCat];
for (int iSamp = 0; iSamp < nSamp; iSamp++)
{
xVec[iDatum++] = data.X[iCat][iSamp][iCoeff];
}
}
Static.QuickSortIndex(idxVec[0], xVec, 0, xVec.Length - 1);
scale = xVec[idxVec[0][i85]] - xVec[idxVec[0][i15]];
this.Analysis.ParamScale[iCoeff] = (float)(1.0 / scale);
//if (ops.InitializeParams)
//{
// Get univariate classification criteria to get a first-order clue about the saliency of each feature.
for (int iCat = 0; iCat < data.Ncats; iCat++)
{
this.Analysis.Crits[iCat][iCoeff] = UniCrit.MaximumAccuracy(iCat, catVec, xVec, idxVec[0], this.CatWeights);
}
//}
}
//-----------------------
// Compute initial params.
//-----------------------
// Compute the expected minimum value for the univariate 2-category classification accuracy.
double[] accMin = new double[data.Ncats];
for (int iCat = 0; iCat < data.Ncats; iCat++)
{
accMin[iCat] = (this.totalWeight - this.CatWeights[iCat] * (double)data.Neach[iCat]) / this.totalWeight;
if (accMin[iCat] < 0.5)
{
accMin[iCat] = 1.0 - accMin[iCat];
}
}
// The magnitude of each parameter is a function of univariate classification accuracy for the corresponding spatial dimension.
double invNtotal = 1.0 / data.Ntotal;
for (int iCoeff = 0; iCoeff < this.Classifier.Instance.Coeffs.Ncoeffs; iCoeff++)
{
if (this.Classifier.Instance.Npoly == 1)
{
double tAcc = 0.5 *
(
Math.Max(0.0, this.Analysis.Crits[0][iCoeff].Accuracy - accMin[0])
+
Math.Max(0.0, this.Analysis.Crits[1][iCoeff].Accuracy - accMin[1])
);
tAcc /= (1.0 - 0.5 * (accMin[0] + accMin[1]) + invNtotal);
if (this.Analysis.Crits[0][iCoeff].TargetUpper)
{
this.Analysis.ParamInit[0][iCoeff] = (float)tAcc * this.Analysis.ParamScale[iCoeff];
}
else
{
this.Analysis.ParamInit[0][iCoeff] = -(float)tAcc * this.Analysis.ParamScale[iCoeff];
}
}
else
{
for (int iPoly = 0; iPoly < this.Classifier.Instance.Npoly; iPoly++)
{
double tAcc = Math.Max(0.0, this.Analysis.Crits[iPoly][iCoeff].Accuracy - accMin[iPoly]);
tAcc /= (1.0 - accMin[iPoly] + invNtotal);
if (this.Analysis.Crits[iPoly][iCoeff].TargetUpper)
{
this.Analysis.ParamInit[iPoly][iCoeff] = (float)tAcc * this.Analysis.ParamScale[iCoeff];
}
else
{
this.Analysis.ParamInit[iPoly][iCoeff] = -(float)tAcc * this.Analysis.ParamScale[iCoeff];
}
}
}
}
}
//-----------------------
// Set classifier parameters.
//-----------------------
if (ops.InitializeParams)
{
Static.Copy <float>(this.Analysis.ParamInit, this.Classifier.Instance.Params);
}
else
{
// Inherit parameters passed in by the classifier. We assume the classifier was already initialized with parameters.
Static.Copy <float>(this.Classifier.Instance.Params, this.Analysis.ParamInit);
}
//-----------------------
// Perform dual optimizations.
//-----------------------
if (this.Classifier.Instance.Npoly > 2 && this.options.InitializeParams)
{
SolverOptions dualOps = this.options.Copy();
dualOps.WeightingRule = WeightingRule.EqualPriors;
Task <Trainer>[] dualTasks = new Task <Trainer> [this.Classifier.Instance.Npoly];
for (int iPoly = 0; iPoly < this.Classifier.Instance.Npoly; iPoly++)
{
Trainer t = new Trainer(this.Classifier.Instance.GetDual(iPoly));
dualTasks[iPoly] = t.Train(data.GetDual(iPoly), dualOps);
}
for (int iPoly = 0; iPoly < this.Classifier.Instance.Npoly; iPoly++)
{
Trainer t = await dualTasks[iPoly];
Array.Copy(t.Classifier.Instance.Params, this.Analysis.ParamInit[iPoly], this.Classifier.Instance.Coeffs.Ncoeffs);
}
Static.Copy <float>(this.Analysis.ParamInit, this.Classifier.Instance.Params);
}
//-----------------------
// Finish constructing the classifier for the first time.
//-----------------------
MonotonicRegressor regressor = new MonotonicRegressor();
for (int iPoly = 0; iPoly < this.Classifier.Instance.Npoly; iPoly++)
{
Static.FillSeries(idxVec[iPoly]);
}
for (int iPoly = 0; iPoly < this.Classifier.Instance.Npoly; iPoly++)
{
// Set the quantized probability limits.
double nPerQuantile = (double)Math.Min(data.Neach[iPoly], data.Ntotal - data.Neach[iPoly]) / (double)this.Classifier.Instance.Quant[iPoly].Nquantiles;
this.Classifier.Instance.Quant[iPoly].Pmin = 1.0 / nPerQuantile;
this.Classifier.Instance.Quant[iPoly].Pmax = 1.0 - this.Classifier.Instance.Quant[iPoly].Pmin;
// Evaluate the polynomial expression for each datum.
iDatum = 0;
for (int iCat = 0; iCat < data.Ncats; iCat++)
{
int nSamp = data.Neach[iCat];
for (int iSamp = 0; iSamp < nSamp; iSamp++)
{
// Evaluate the polynomial expression.
yVec[iPoly][iDatum++] = (float)this.Classifier.Instance.EvalPolyFromExpanded(iPoly, data.X[iCat][iSamp]);
}
}
// Sort the output. Indexes are preserved to speed up subsequent sorts.
Static.QuickSortIndex(idxVec[iPoly], yVec[iPoly], 0, data.Ntotal - 1);
// Quantize the output.
this.Classifier.Instance.Quant[iPoly].Measure(idxVec[iPoly], yVec[iPoly], catVec, (byte)iPoly, this.CatWeights, totalWeight, regressor);
}
//-----------------------
// Measure the conditional entropy.
//-----------------------
float[] y = new float[this.Classifier.Instance.Npoly];
double[] p;
double fit = 0.0;
byte c;
for (iDatum = 0; iDatum < data.Ntotal; iDatum++)
{
for (int iPoly = 0; iPoly < this.Classifier.Instance.Npoly; iPoly++)
{
y[iPoly] = yVec[iPoly][iDatum];
}
p = this.Classifier.Instance.ClassifyPolynomialOutputs(y);
c = catVec[iDatum];
fit += Math.Log(p[c]) * this.CatWeights[c];
}
// Change logarithm base and normalize by total weight.
this.Classifier.Fit = -fit / totalWeight / Math.Log((double)data.Ncats); // <-- The conditional entropy... we want to minimize it.
//-----------------------
// Prepare optimization memory.
//-----------------------
// Initialize an orthonormal if the parameter space is small enough.
float[][][] ortho = null;
int nParams = this.Classifier.Instance.Npoly * this.Classifier.Instance.Coeffs.Ncoeffs;
if (nParams <= 100)
{
ortho = this.randomDeviates();
}
int iOrtho = 0;
int ctOrtho = 0;
int ctSteps = 0;
// Every `modOrtho` steps through the orthonormal basis, we try a gradient search.
int modOrtho = Math.Min(10, nParams);
// For a trip through `modOrtho` bases, changes in entropy are partialled across the parameter space.
float[][] dhOrtho = Static.NewArrays <float>(this.Classifier.Instance.Npoly, this.Classifier.Instance.Coeffs.Ncoeffs);
//-----------------------
// Optimize.
//-----------------------
// The attempted classifier.
Classifier cTry = this.Classifier.Instance.Copy();
// The initial step size.
float stepSize = this.Options.ParamDiffMax;
// The optimization mode. We start by iterating through the orthogonal bases.
OptimizationMode mode = OptimizationMode.Ortho;
throw new NotImplementedException("TO DO");
bool keepOptimizing = true;
while (keepOptimizing)
{
if (mode == OptimizationMode.Ortho)
{
if (iOrtho >= modOrtho)
{
iOrtho = 0;
}
}
else if (mode == OptimizationMode.Gradient)
{
}
else
{
throw new ApplicationException("Unhandled optimization mode.");
}
}
}
finally
{
this.trainerIsRunning = false;
}
}