void CMT::WhiteningTransform::initialize(const ArrayXXd& input, int dimOut) {
if(input.cols() < input.rows())
throw Exception("Too few inputs to compute whitening transform.");
mMeanIn = input.rowwise().mean();
// compute covariances
MatrixXd covXX = covariance(input);
// input whitening
SelfAdjointEigenSolver<MatrixXd> eigenSolver;
eigenSolver.compute(covXX);
Array<double, 1, Dynamic> eigenvalues = eigenSolver.eigenvalues();
MatrixXd eigenvectors = eigenSolver.eigenvectors();
// don't whiten directions with near-zero variance
for(int i = 0; i < eigenvalues.size(); ++i)
if(eigenvalues[i] < 1e-7)
eigenvalues[i] = 1.;
mPreIn = (eigenvectors.array().rowwise() * eigenvalues.sqrt().cwiseInverse()).matrix()
* eigenvectors.transpose();
mPreInInv = (eigenvectors.array().rowwise() * eigenvalues.sqrt()).matrix()
* eigenvectors.transpose();
mMeanOut = VectorXd::Zero(dimOut);
mPreOut = MatrixXd::Identity(dimOut, dimOut);
mPreOutInv = MatrixXd::Identity(dimOut, dimOut);
mPredictor = MatrixXd::Zero(dimOut, input.rows());
mGradTransform = MatrixXd::Zero(dimOut, input.rows());
mLogJacobian = 1.;
}
ArrayXXd CMT::BlobNonlinearity::gradient(const ArrayXXd& inputs) const {
if(inputs.rows() != 1)
throw Exception("Data has to be stored in one row.");
ArrayXXd diff = ArrayXXd::Zero(mNumComponents, inputs.cols());
diff.rowwise() += inputs.row(0);
diff.colwise() -= mMeans;
ArrayXXd diffSq = diff.square();
ArrayXd precisions = mLogPrecisions.exp();
ArrayXd weights = mLogWeights.exp();
ArrayXXd negEnergy = diffSq.colwise() * (-precisions / 2.);
ArrayXXd negEnergyExp = negEnergy.exp();
ArrayXXd gradient(3 * mNumComponents, inputs.cols());
// gradient of mean
gradient.topRows(mNumComponents) = (diff * negEnergyExp).colwise() * (weights * precisions);
// gradient of log-precisions
gradient.middleRows(mNumComponents, mNumComponents) = (diffSq / 2. * negEnergyExp).colwise() * (-weights * precisions);
// gradient of log-weights
gradient.bottomRows(mNumComponents) = negEnergyExp.colwise() * weights;
return gradient;
}
Array<int, 1, Dynamic> CMT::MCBM::samplePrior(const MatrixXd& input) const {
if(input.rows() != dimIn())
throw Exception("Inputs have wrong dimensionality.");
ArrayXXd featureEnergy = mWeights * (mFeatures.transpose() * input).array().square().matrix();
ArrayXXd biasEnergy = mInputBias.transpose() * input;
ArrayXXd predictorEnergy = mPredictors * input;
ArrayXXd tmp0 = (featureEnergy + biasEnergy).colwise() + mPriors.array();
ArrayXXd tmp1 = (tmp0 + predictorEnergy).colwise() + mOutputBias.array();
ArrayXXd logPrior = tmp0 + tmp1;
logPrior.rowwise() -= logSumExp(logPrior);
ArrayXXd prior = logPrior.exp();
Array<int, 1, Dynamic> labels(input.cols());
#pragma omp parallel for
for(int j = 0; j < input.cols(); ++j) {
int i = 0;
double urand = static_cast<double>(rand()) / (static_cast<long>(RAND_MAX) + 1l);
double cdf;
// compute index
for(cdf = prior(0, j); cdf < urand; cdf += prior(i, j))
++i;
labels[j] = i;
}
return labels;
}
ArrayXXd CMT::BlobNonlinearity::operator()(const ArrayXXd& inputs) const {
if(inputs.rows() != 1)
throw Exception("Data has to be stored in one row.");
ArrayXXd diff = ArrayXXd::Zero(mNumComponents, inputs.cols());
diff.rowwise() += inputs.row(0);
diff.colwise() -= mMeans;
ArrayXXd negEnergy = diff.square().colwise() * (-mLogPrecisions.exp() / 2.);
return (mLogWeights.exp().transpose().matrix() * negEnergy.exp().matrix()).array() + mEpsilon;
}
MatrixXd CMT::MLR::predict(const MatrixXd& input) const {
if(input.rows() != mDimIn)
throw Exception("Inputs have wrong dimensionality.");
MatrixXd output = MatrixXd::Zero(mDimOut, input.cols());
// distribution over outputs
ArrayXXd prob = (mWeights * input).colwise() + mBiases;
prob.rowwise() -= logSumExp(prob);
prob = prob.exp();
return prob;
}
ArrayXXd CMT::BlobNonlinearity::derivative(const ArrayXXd& inputs) const {
if(inputs.rows() != 1)
throw Exception("Data has to be stored in one row.");
ArrayXXd diff = ArrayXXd::Zero(mNumComponents, inputs.cols());
diff.rowwise() -= inputs.row(0);
diff.colwise() += mMeans;
ArrayXd precisions = mLogPrecisions.exp();
ArrayXXd negEnergy = diff.square().colwise() * (-precisions / 2.);
return (mLogWeights.exp() * precisions).transpose().matrix() * (diff * negEnergy.exp()).matrix();
}
Array<double, 1, Dynamic> CMT::MLR::logLikelihood(
const MatrixXd& input,
const MatrixXd& output) const
{
if(input.cols() != output.cols())
throw Exception("Number of inputs and outputs have to be the same.");
if(input.rows() != mDimIn)
throw Exception("Inputs have wrong dimensionality.");
if(output.rows() != mDimOut)
throw Exception("Output has wrong dimensionality.");
// distribution over outputs
ArrayXXd logProb = (mWeights * input).colwise() + mBiases;
logProb.rowwise() -= logSumExp(logProb);
return (logProb * output.array()).colwise().sum();
}
double CMT::MLR::parameterGradient(
const MatrixXd& input,
const MatrixXd& output,
const lbfgsfloatval_t* x,
lbfgsfloatval_t* g,
const Trainable::Parameters& params_) const
{
const Parameters& params = dynamic_cast<const Parameters&>(params_);
MatrixXd weights = mWeights;
VectorXd biases = mBiases;
// copy parameters
int k = 0;
if(params.trainWeights)
for(int i = 1; i < weights.rows(); ++i)
for(int j = 0; j < weights.cols(); ++j, ++k)
weights(i, j) = x[k];
if(params.trainBiases)
for(int i = 1; i < mBiases.rows(); ++i, ++k)
biases[i] = x[k];
// compute distribution over outputs
ArrayXXd logProb = (weights * input).colwise() + biases;
logProb.rowwise() -= logSumExp(logProb);
// difference between prediction and actual output
MatrixXd diff = (logProb.exp().matrix() - output);
// compute gradients
double normConst = output.cols() * log(2.);
if(g) {
int offset = 0;
if(params.trainWeights) {
Map<Matrix<double, Dynamic, Dynamic, RowMajor> > weightsGrad(g, mDimOut - 1, mDimIn);
weightsGrad = (diff * input.transpose() / normConst).bottomRows(mDimOut - 1);
offset += weightsGrad.size();
weightsGrad += params.regularizeWeights.gradient(
weights.bottomRows(mDimOut - 1).transpose()).transpose();
}
if(params.trainBiases) {
VectorLBFGS biasesGrad(g + offset, mDimOut - 1);
biasesGrad = diff.rowwise().sum().bottomRows(mDimOut - 1) / normConst;
biasesGrad += params.regularizeBiases.gradient(biases);
}
}
// return negative average log-likelihood in bits
double value = -(logProb * output.array()).sum() / normConst;
if(params.trainWeights)
value += params.regularizeWeights.evaluate(weights.bottomRows(mDimOut - 1).transpose());
if(params.trainBiases)
value += params.regularizeBiases.evaluate(biases);
return value;
}
bool CMT::Mixture::train(
const MatrixXd& data,
const MatrixXd& dataValid,
const Parameters& parameters,
const Component::Parameters& componentParameters)
{
if(parameters.initialize && !initialized())
initialize(data, parameters, componentParameters);
ArrayXXd logJoint(numComponents(), data.cols());
Array<double, Dynamic, 1> postSum;
Array<double, 1, Dynamic> logLik;
ArrayXXd post;
ArrayXXd weights;
// training and validation log-loss for checking convergence
double avgLogLoss = numeric_limits<double>::infinity();
double avgLogLossNew;
double avgLogLossValid = evaluate(dataValid);
double avgLogLossValidNew = avgLogLossValid;
int counter = 0;
// backup model parameters
VectorXd priors = mPriors;
vector<Component*> components;
for(int k = 0; k < numComponents(); ++k)
components.push_back(mComponents[k]->copy());
for(int i = 0; i < parameters.maxIter; ++i) {
// compute joint probability of data and assignments (E)
#pragma omp parallel for
for(int k = 0; k < numComponents(); ++k)
logJoint.row(k) = mComponents[k]->logLikelihood(data) + log(mPriors[k]);
// compute normalized posterior (E)
logLik = logSumExp(logJoint);
// average negative log-likelihood in bits per component
avgLogLossNew = -logLik.mean() / log(2.) / dim();
if(parameters.verbosity > 0) {
if(i % parameters.valIter == 0) {
// print training and validation error
cout << setw(6) << i;
cout << setw(14) << setprecision(7) << avgLogLossNew;
cout << setw(14) << setprecision(7) << avgLogLossValidNew << endl;
} else {
// print training error
cout << setw(6) << i << setw(14) << setprecision(7) << avgLogLossNew << endl;
}
}
// test for convergence
if(avgLogLoss - avgLogLossNew < parameters.threshold)
return true;
avgLogLoss = avgLogLossNew;
// compute normalized posterior (E)
post = (logJoint.rowwise() - logLik).exp();
postSum = post.rowwise().sum();
weights = post.colwise() / postSum;
// optimize prior weights (M)
if(parameters.trainPriors) {
mPriors = postSum / data.cols() + parameters.regularizePriors;
mPriors /= mPriors.sum();
}
// optimize components (M)
if(parameters.trainComponents) {
#pragma omp parallel for
for(int k = 0; k < numComponents(); ++k)
mComponents[k]->train(data, weights.row(k), componentParameters);
} else {
return true;
}
if((i + 1) % parameters.valIter == 0) {
// check validation error
avgLogLossValidNew = evaluate(dataValid);
if(avgLogLossValidNew < avgLogLossValid) {
// backup new found model parameters
priors = mPriors;
for(int k = 0; k < numComponents(); ++k)
*components[k] = *mComponents[k];
avgLogLossValid = avgLogLossValidNew;
} else {
counter++;
if(parameters.valLookAhead > 0 && counter >= parameters.valLookAhead) {
// set parameters to best parameters found during training
mPriors = priors;
for(int k = 0; k < numComponents(); ++k) {
*mComponents[k] = *components[k];
delete components[k];
}
return true;
}
}
}
}
if(parameters.verbosity > 0)
cout << setw(6) << parameters.maxIter << setw(11) << setprecision(5) << evaluate(data) << endl;
return false;
}
bool CMT::Mixture::train(
const MatrixXd& data,
const Parameters& parameters,
const Component::Parameters& componentParameters)
{
if(data.rows() != dim())
throw Exception("Data has wrong dimensionality.");
if(parameters.initialize && !initialized())
initialize(data, parameters, componentParameters);
ArrayXXd logJoint(numComponents(), data.cols());
Array<double, Dynamic, 1> postSum;
Array<double, 1, Dynamic> logLik;
ArrayXXd post;
ArrayXXd weights;
double avgLogLoss = numeric_limits<double>::infinity();
double avgLogLossNew;
for(int i = 0; i < parameters.maxIter; ++i) {
// compute joint probability of data and assignments (E)
#pragma omp parallel for
for(int k = 0; k < numComponents(); ++k)
logJoint.row(k) = mComponents[k]->logLikelihood(data) + log(mPriors[k]);
// compute normalized posterior (E)
logLik = logSumExp(logJoint);
// average negative log-likelihood in bits per component
avgLogLossNew = -logLik.mean() / log(2.) / dim();
if(parameters.verbosity > 0)
cout << setw(6) << i << setw(14) << setprecision(7) << avgLogLossNew << endl;
// test for convergence
if(avgLogLoss - avgLogLossNew < parameters.threshold)
return true;
avgLogLoss = avgLogLossNew;
// compute normalized posterior (E)
post = (logJoint.rowwise() - logLik).exp();
postSum = post.rowwise().sum();
weights = post.colwise() / postSum;
// optimize prior weights (M)
if(parameters.trainPriors) {
mPriors = postSum / data.cols() + parameters.regularizePriors;
mPriors /= mPriors.sum();
}
// optimize components (M)
if(parameters.trainComponents) {
#pragma omp parallel for
for(int k = 0; k < numComponents(); ++k)
mComponents[k]->train(data, weights.row(k), componentParameters);
} else {
return true;
}
}
if(parameters.verbosity > 0)
cout << setw(6) << parameters.maxIter << setw(14) << setprecision(7) << evaluate(data) << endl;
return false;
}
bool KmeansClusterer::updateClusterCentersUntilConverged(RefArrayXXd sample, RefArrayXXd centers,
RefArrayXd clusterSizes, vector<int> &clusterIndices,
double &sumOfDistancesToClosestCenter, double relTolerance)
{
unsigned int Npoints = sample.cols();
unsigned int Ndimensions = sample.rows();
unsigned int Nclusters = centers.cols();
ArrayXXd updatedCenters = ArrayXXd::Zero(Ndimensions, Nclusters); // coordinates of each of the new cluster centers
// Perform the k-means clustering iteration, each time improving the cluster centers,
// and redetermining which points belongs to which cluster
bool stopIterations = false;
bool convergenceReached;
unsigned int indexOfClosestCenter;
double oldSumOfDistances = 0.0;
double newSumOfDistances = 0.0;
double distanceToClosestCenter;
double distance;
while (!stopIterations)
{
// Find for each point the closest cluster center.
// At the same time recompute/update the new cluster centers, which is simply
// the barycenter of all points belonging to the cluster.
clusterSizes.setZero();
updatedCenters.setZero();
for (int n = 0; n < Npoints; ++n)
{
distanceToClosestCenter = numeric_limits<double>::max();
for (int i = 0; i < Nclusters; ++i)
{
distance = metric.distance(sample.col(n), centers.col(i));
if (distance < distanceToClosestCenter)
{
indexOfClosestCenter = i;
distanceToClosestCenter = distance;
}
}
newSumOfDistances += distanceToClosestCenter;
updatedCenters.col(indexOfClosestCenter) += sample.col(n);
clusterSizes(indexOfClosestCenter) += 1;
clusterIndices[n] = indexOfClosestCenter;
}
// Assert that all clusters contain at least 2 points. If not we probably started
// with an unfortunate set of initial cluster centers. Flag this by immediately
// returning false.
if (!(clusterSizes > 1).all())
{
convergenceReached = false;
return convergenceReached;
}
// Finish computing the new updated centers. Given the check above, we are sure
// that none of the clusters is empty.
updatedCenters.rowwise() /= clusterSizes.transpose();
centers = updatedCenters;
// A new set of clusters has been determined.
// Decide whether the algorithm has converged. Convergence occurs when
// the sum of all distances of all points to their cluster center does
// not change significantly anymore.
// Note: in order for this criterion to work properly, the coordinate
// space should be normalized, so that one particular coordinate
// cannot numerically dominate all other coordinates.
if (oldSumOfDistances == 0.0)
{
// This is the first center-updating iteration, so there is nothing to compare yet.
// Simply set the variables.
oldSumOfDistances = newSumOfDistances;
newSumOfDistances = 0.0;
}
else
{
// If the relative change in sumOfDistances between old and new was smaller than
// the threshold set by the user, stop the iteration loop.
if (fabs(newSumOfDistances - oldSumOfDistances) / oldSumOfDistances < relTolerance)
{
sumOfDistancesToClosestCenter = newSumOfDistances; // will be returned to user
stopIterations = true;
}
else
{
oldSumOfDistances = newSumOfDistances;
newSumOfDistances = 0.0;
}
}
} // end k-means center-updating loop
// Convergence was properly reached, so return
convergenceReached = true;
return convergenceReached;
}
Array<double, 1, Dynamic> CMT::logMeanExp(const ArrayXXd& array) {
Array<double, 1, Dynamic> arrayMax = array.colwise().maxCoeff() - 1.;
return arrayMax + (array.rowwise() - arrayMax).exp().colwise().mean().log();
}
double CMT::MCBM::parameterGradient(
const MatrixXd& inputCompl,
const MatrixXd& outputCompl,
const lbfgsfloatval_t* x,
lbfgsfloatval_t* g,
const Trainable::Parameters& params_) const
{
const Parameters& params = dynamic_cast<const Parameters&>(params_);
// average log-likelihood
double logLik = 0.;
// interpret memory for parameters and gradients
lbfgsfloatval_t* y = const_cast<lbfgsfloatval_t*>(x);
int offset = 0;
VectorLBFGS priors(params.trainPriors ? y : const_cast<double*>(mPriors.data()), mNumComponents);
VectorLBFGS priorsGrad(g, mNumComponents);
if(params.trainPriors)
offset += priors.size();
MatrixLBFGS weights(params.trainWeights ? y + offset : const_cast<double*>(mWeights.data()), mNumComponents, mNumFeatures);
MatrixLBFGS weightsGrad(g + offset, mNumComponents, mNumFeatures);
if(params.trainWeights)
offset += weights.size();
MatrixLBFGS features(params.trainFeatures ? y + offset : const_cast<double*>(mFeatures.data()), mDimIn, mNumFeatures);
MatrixLBFGS featuresGrad(g + offset, mDimIn, mNumFeatures);
if(params.trainFeatures)
offset += features.size();
MatrixLBFGS predictors(params.trainPredictors ? y + offset : const_cast<double*>(mPredictors.data()), mNumComponents, mDimIn);
MatrixLBFGS predictorsGrad(g + offset, mNumComponents, mDimIn);
if(params.trainPredictors)
offset += predictors.size();
MatrixLBFGS inputBias(params.trainInputBias ? y + offset : const_cast<double*>(mInputBias.data()), mDimIn, mNumComponents);
MatrixLBFGS inputBiasGrad(g + offset, mDimIn, mNumComponents);
if(params.trainInputBias)
offset += inputBias.size();
VectorLBFGS outputBias(params.trainOutputBias ? y + offset : const_cast<double*>(mOutputBias.data()), mNumComponents);
VectorLBFGS outputBiasGrad(g + offset, mNumComponents);
if(params.trainOutputBias)
offset += outputBias.size();
if(g) {
// initialize gradients
if(params.trainPriors)
priorsGrad.setZero();
if(params.trainWeights)
weightsGrad.setZero();
if(params.trainFeatures)
featuresGrad.setZero();
if(params.trainPredictors)
predictorsGrad.setZero();
if(params.trainInputBias)
inputBiasGrad.setZero();
if(params.trainOutputBias)
outputBiasGrad.setZero();
}
// split data into batches for better performance
int numData = static_cast<int>(inputCompl.cols());
int batchSize = min(max(params.batchSize, 10), numData);
#pragma omp parallel for
for(int b = 0; b < inputCompl.cols(); b += batchSize) {
const MatrixXd& input = inputCompl.middleCols(b, min(batchSize, numData - b));
const MatrixXd& output = outputCompl.middleCols(b, min(batchSize, numData - b));
ArrayXXd featureOutput = features.transpose() * input;
MatrixXd featureOutputSq = featureOutput.square();
MatrixXd weightsOutput = weights * featureOutputSq;
ArrayXXd predictorOutput = predictors * input;
// unnormalized posteriors over components for both possible outputs
ArrayXXd logPost0 = (weightsOutput + inputBias.transpose() * input).colwise() + priors;
ArrayXXd logPost1 = (logPost0 + predictorOutput).colwise() + outputBias.array();
// sum over components to get unnormalized probabilities of outputs
Array<double, 1, Dynamic> logProb0 = logSumExp(logPost0);
Array<double, 1, Dynamic> logProb1 = logSumExp(logPost1);
// normalize posteriors over components
logPost0.rowwise() -= logProb0;
logPost1.rowwise() -= logProb1;
// stack row vectors
ArrayXXd logProb01(2, input.cols());
logProb01 << logProb0, logProb1;
// normalize log-probabilities
Array<double, 1, Dynamic> logNorm = logSumExp(logProb01);
logProb1 -= logNorm;
logProb0 -= logNorm;
double logLikBatch = (output.array() * logProb1 + (1. - output.array()) * logProb0).sum();
#pragma omp critical
logLik += logLikBatch;
if(!g)
// don't compute gradients
continue;
Array<double, 1, Dynamic> tmp = output.array() * logProb0.exp() - (1. - output.array()) * logProb1.exp();
ArrayXXd post0Tmp = logPost0.exp().rowwise() * tmp;
ArrayXXd post1Tmp = logPost1.exp().rowwise() * tmp;
ArrayXXd postDiffTmp = post1Tmp - post0Tmp;
// update gradients
if(params.trainPriors)
#pragma omp critical
priorsGrad -= postDiffTmp.rowwise().sum().matrix();
if(params.trainWeights)
#pragma omp critical
weightsGrad -= postDiffTmp.matrix() * featureOutputSq.transpose();
if(params.trainFeatures) {
ArrayXXd tmp2 = weights.transpose() * postDiffTmp.matrix() * 2.;
MatrixXd tmp3 = featureOutput * tmp2;
#pragma omp critical
featuresGrad -= input * tmp3.transpose();
}
if(params.trainPredictors)
#pragma omp critical
predictorsGrad -= post1Tmp.matrix() * input.transpose();
if(params.trainInputBias)
#pragma omp critical
inputBiasGrad -= input * postDiffTmp.matrix().transpose();
if(params.trainOutputBias)
#pragma omp critical
outputBiasGrad -= post1Tmp.rowwise().sum().matrix();
}
double normConst = inputCompl.cols() * log(2.) * dimOut();
if(g) {
for(int i = 0; i < offset; ++i)
g[i] /= normConst;
if(params.trainFeatures)
featuresGrad += params.regularizeFeatures.gradient(features);
if(params.trainPredictors)
predictorsGrad += params.regularizePredictors.gradient(predictors.transpose()).transpose();
if(params.trainWeights)
weightsGrad += params.regularizeWeights.gradient(weights);
}
double value = -logLik / normConst;
if(params.trainFeatures)
value += params.regularizeFeatures.evaluate(features);
if(params.trainPredictors)
value += params.regularizePredictors.evaluate(predictors.transpose());
if(params.trainWeights)
value += params.regularizeWeights.evaluate(weights);
return value;
}
pair<pair<ArrayXXd, ArrayXXd>, Array<double, 1, Dynamic> > CMT::STM::computeDataGradient(
const MatrixXd& input,
const MatrixXd& output) const
{
// make sure nonlinearity is differentiable
DifferentiableNonlinearity* nonlinearity =
dynamic_cast<DifferentiableNonlinearity*>(mNonlinearity);
if(!nonlinearity)
throw Exception("Nonlinearity has to be differentiable.");
if(input.rows() != dimIn())
throw Exception("Input has wrong dimensionality.");
if(output.rows() != 1)
throw Exception("Output has wrong dimensionality.");
if(input.cols() != output.cols())
throw Exception("Number of inputs and outputs should be the same.");
if(dimInNonlinear() && !dimInLinear()) {
Array<double, 1, Dynamic> responses;
ArrayXXd jointEnergy;
if(numFeatures() > 0)
jointEnergy = mWeights * (mFeatures.transpose() * input).array().square().matrix()
+ mPredictors * input;
else
jointEnergy = mPredictors * input;
jointEnergy.colwise() += mBiases.array();
jointEnergy *= mSharpness;
responses = logSumExp(jointEnergy);
// posterior over components for each input
MatrixXd posterior = (jointEnergy.rowwise() - responses).array().exp();
responses /= mSharpness;
Array<double, 1, Dynamic> tmp0 = (*mNonlinearity)(responses);
Array<double, 1, Dynamic> tmp1 = -mDistribution->gradient(output, tmp0);
Array<double, 1, Dynamic> tmp2 = nonlinearity->derivative(responses);
ArrayXXd avgPredictor = mPredictors.transpose() * posterior;
ArrayXXd tmp3;
if(numFeatures() > 0) {
ArrayXXd avgWeights = (2. * mWeights).transpose() * posterior;
tmp3 = mFeatures * (avgWeights * (mFeatures.transpose() * input).array()).matrix();
} else {
tmp3 = ArrayXXd::Zero(avgPredictor.rows(), avgPredictor.cols());
}
return make_pair(
make_pair(
(tmp3 + avgPredictor).rowwise() * (tmp1 * tmp2),
ArrayXXd::Zero(output.rows(), output.cols())),
mDistribution->logLikelihood(output, tmp0));
} else if(dimInNonlinear() && dimInLinear()) {
// split inputs into linear and nonlinear components
MatrixXd inputNonlinear = input.topRows(dimInNonlinear());
MatrixXd inputLinear = input.bottomRows(dimInLinear());
Array<double, 1, Dynamic> responses;
ArrayXXd jointEnergy;
if(numFeatures() > 0)
jointEnergy = mWeights * (mFeatures.transpose() * inputNonlinear).array().square().matrix()
+ mPredictors * input;
else
jointEnergy = mPredictors * inputNonlinear;
jointEnergy.colwise() += mBiases.array();
jointEnergy *= mSharpness;
responses = logSumExp(jointEnergy);
// posterior over components for each input
MatrixXd posterior = (jointEnergy.rowwise() - responses).array().exp();
responses /= mSharpness;
responses += (mLinearPredictor.transpose() * inputLinear).array();
Array<double, 1, Dynamic> tmp0 = (*mNonlinearity)(responses);
Array<double, 1, Dynamic> tmp1 = -mDistribution->gradient(output, tmp0);
Array<double, 1, Dynamic> tmp2 = nonlinearity->derivative(responses);
ArrayXXd avgPredictor = mPredictors.transpose() * posterior;
ArrayXXd tmp3;
if(numFeatures() > 0) {
ArrayXXd avgWeights = (2. * mWeights).transpose() * posterior;
tmp3 = mFeatures * (avgWeights * (mFeatures.transpose() * inputNonlinear).array()).matrix();
} else {
tmp3 = ArrayXXd::Zero(avgPredictor.rows(), avgPredictor.cols());
}
// concatenate gradients of nonlinear and linear component
ArrayXXd inputGradient(dimIn(), input.cols());
inputGradient <<
(tmp3 + avgPredictor).rowwise() * (tmp1 * tmp2),
mLinearPredictor * (tmp1 * tmp2).matrix();
return make_pair(
make_pair(
inputGradient,
ArrayXXd::Zero(output.rows(), output.cols())),
mDistribution->logLikelihood(output, tmp0));
} else if(dimInLinear()) {
double avgBias = logSumExp(mSharpness * mBiases)(0, 0) / mSharpness;
Array<double, 1, Dynamic> responses = (mLinearPredictor.transpose() * input).array() + avgBias;
Array<double, 1, Dynamic> tmp0 = (*mNonlinearity)(responses);
Array<double, 1, Dynamic> tmp1 = -mDistribution->gradient(output, tmp0);
Array<double, 1, Dynamic> tmp2 = nonlinearity->derivative(responses);
return make_pair(
make_pair(
mLinearPredictor * (tmp1 * tmp2).matrix(),
ArrayXXd::Zero(output.rows(), output.cols())),
mDistribution->logLikelihood(output, tmp0));
}
return make_pair(
make_pair(
ArrayXXd::Zero(input.rows(), input.cols()),
ArrayXXd::Zero(output.rows(), output.cols())),
logLikelihood(input, output));
}
