/**
* Modifies this map through a single backpropagation iteration using the given error values on
* the output nodes.
*
* @param error
*/
public void train(List<Double> error, double learningRate) {
RealVector eOut = new ArrayRealVector(error.size());
for (int i : series(error.size())) eOut.setEntry(i, error.get(i));
// * gHidden: delta for the non-bias nodes of the hidden layer
gHidden.setSubVector(0, stateHidden.getSubVector(0, n)); // optimize
for (int i : Series.series(gHidden.getDimension()))
gHidden.setEntry(i, activation.derivative(gHidden.getEntry(i)));
eHiddenL = weights1.transpose().operate(eOut);
eHidden.setSubVector(0, eHiddenL.getSubVector(0, h));
for (int i : series(h)) eHidden.setEntry(i, eHidden.getEntry(i) * gHidden.getEntry(i));
weights1Delta = MatrixTools.outer(eOut, stateHidden);
weights1Delta = weights1Delta.scalarMultiply(-1.0 * learningRate); // optimize
weights0Delta = MatrixTools.outer(eHidden, stateIn);
weights0Delta = weights0Delta.scalarMultiply(-1.0 * learningRate);
weights0 = weights0.add(weights0Delta);
weights1 = weights1.add(weights1Delta);
}
/**
* Solve an estimation problem using a least squares criterion.
*
* <p>This method set the unbound parameters of the given problem starting from their current
* values through several iterations. At each step, the unbound parameters are changed in order to
* minimize a weighted least square criterion based on the measurements of the problem.
*
* <p>The iterations are stopped either when the criterion goes below a physical threshold under
* which improvement are considered useless or when the algorithm is unable to improve it (even if
* it is still high). The first condition that is met stops the iterations. If the convergence it
* not reached before the maximum number of iterations, an {@link EstimationException} is thrown.
*
* @param problem estimation problem to solve
* @exception EstimationException if the problem cannot be solved
* @see EstimationProblem
*/
@Override
public void estimate(EstimationProblem problem) throws EstimationException {
initializeEstimate(problem);
// work matrices
double[] grad = new double[parameters.length];
ArrayRealVector bDecrement = new ArrayRealVector(parameters.length);
double[] bDecrementData = bDecrement.getDataRef();
RealMatrix wGradGradT = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
// iterate until convergence is reached
double previous = Double.POSITIVE_INFINITY;
do {
// build the linear problem
incrementJacobianEvaluationsCounter();
RealVector b = new ArrayRealVector(parameters.length);
RealMatrix a = MatrixUtils.createRealMatrix(parameters.length, parameters.length);
for (int i = 0; i < measurements.length; ++i) {
if (!measurements[i].isIgnored()) {
double weight = measurements[i].getWeight();
double residual = measurements[i].getResidual();
// compute the normal equation
for (int j = 0; j < parameters.length; ++j) {
grad[j] = measurements[i].getPartial(parameters[j]);
bDecrementData[j] = weight * residual * grad[j];
}
// build the contribution matrix for measurement i
for (int k = 0; k < parameters.length; ++k) {
double gk = grad[k];
for (int l = 0; l < parameters.length; ++l) {
wGradGradT.setEntry(k, l, weight * gk * grad[l]);
}
}
// update the matrices
a = a.add(wGradGradT);
b = b.add(bDecrement);
}
}
try {
// solve the linearized least squares problem
RealVector dX = new LUDecompositionImpl(a).getSolver().solve(b);
// update the estimated parameters
for (int i = 0; i < parameters.length; ++i) {
parameters[i].setEstimate(parameters[i].getEstimate() + dX.getEntry(i));
}
} catch (InvalidMatrixException e) {
throw new EstimationException("unable to solve: singular problem");
}
previous = cost;
updateResidualsAndCost();
} while ((getCostEvaluations() < 2)
|| (Math.abs(previous - cost) > (cost * steadyStateThreshold)
&& (Math.abs(cost) > convergence)));
}
