void CMT::HistogramNonlinearity::initialize(
const ArrayXXd& inputs,
const ArrayXXd& outputs)
{
if(inputs.rows() != outputs.rows() || inputs.cols() != outputs.cols())
throw Exception("Inputs and outputs have to have same size.");
mHistogram = vector<double>(mBinEdges.size() - 1);
vector<int> counter(mBinEdges.size() - 1);
for(int k = 0; k < mHistogram.size(); ++k) {
mHistogram[k] = 0.;
counter[k] = 0;
}
for(int i = 0; i < inputs.rows(); ++i)
for(int j = 0; j < inputs.cols(); ++j) {
// find bin
int k = bin(inputs(i, j));
// update histogram
counter[k] += 1;
mHistogram[k] += outputs(i, j);
}
for(int k = 0; k < mHistogram.size(); ++k)
if(mHistogram[k] > 0.)
// average output observed in bin k
mHistogram[k] /= counter[k];
}
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::HistogramNonlinearity::operator()(const ArrayXXd& inputs) const {
ArrayXXd outputs(inputs.rows(), inputs.cols());
for(int i = 0; i < inputs.rows(); ++i)
for(int j = 0; j < inputs.cols(); ++j)
outputs(i, j) = mHistogram[bin(inputs(i, j))] + mEpsilon;
return outputs;
}
ArrayXXd CMT::HistogramNonlinearity::gradient(const ArrayXXd& inputs) const {
if(inputs.rows() != 1)
throw Exception("Data has to be stored in one row.");
ArrayXXd gradient = ArrayXXd::Zero(mHistogram.size(), inputs.cols());
for(int i = 0; i < inputs.rows(); ++i)
for(int j = 0; j < inputs.rows(); ++j)
gradient(bin(inputs(i, j)), j) = 1;
return gradient;
}
void NestedSampler::setPosteriorSample(ArrayXXd newPosteriorSample)
{
Ndimensions = newPosteriorSample.rows();
int Nsamples = newPosteriorSample.cols();
posteriorSample.resize(Ndimensions, Nsamples);
posteriorSample = newPosteriorSample;
}
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;
}
ArrayXXd CMT::tanh(const ArrayXXd& arr) {
ArrayXXd result(arr.rows(), arr.cols());
#pragma omp parallel for
for(int i = 0; i < arr.size(); ++i)
result(i) = std::tanh(arr(i));
return result;
}
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;
}
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();
}
void
mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
int N = mxGetScalar(prhs[0]);
double d = mxGetScalar(prhs[1]);
double h = mxGetScalar(prhs[2]);
int Njacv = mxGetScalar(prhs[3]);
double b = mxGetScalar(prhs[4]);
double c = mxGetScalar(prhs[5]);
double dr = mxGetScalar(prhs[6]);
double di = mxGetScalar(prhs[7]);
int threadNum = mxGetScalar(prhs[8]);
double *a0 = mxGetPr(prhs[9]);
double *v = mxGetPr(prhs[10]);
double th = mxGetScalar(prhs[11]);
double phi = mxGetScalar(prhs[12]);
int nstp = mxGetScalar(prhs[13]);
// mwSize isJ = mxGetScalar(prhs[14]);
ArrayXXd av = gintgv(N, d, h, Njacv, b, c, dr, di, threadNum, a0, v, th, phi, nstp);
plhs[0] = mxCreateDoubleMatrix(av.rows(), av.cols(), mxREAL);
memcpy(mxGetPr(plhs[0]), av.data(), av.cols()*av.rows()*sizeof(double));
}
ArrayXXi CMT::sampleBinomial(const ArrayXXi& n, const ArrayXXd& p) {
if(n.rows() != p.rows() || n.cols() != p.cols())
throw Exception("n and p must be of the same size.");
ArrayXXi samples = ArrayXXi::Zero(n.rows(), n.cols());
#pragma omp parallel for
for(int i = 0; i < samples.size(); ++i) {
// very naive algorithm for generating binomial samples
for(int k = 0; k < n(i); ++k)
if(rand() / static_cast<double>(RAND_MAX) < p(i))
samples(i) += 1;
}
return samples;
}
/**
* Algorithm due to Knuth, 1969.
*/
ArrayXXi CMT::samplePoisson(const ArrayXXd& lambda) {
ArrayXXi samples(lambda.rows(), lambda.cols());
ArrayXXd threshold = (-lambda).exp();
#pragma omp parallel for
for(int i = 0; i < samples.size(); ++i) {
double p = rand() / static_cast<double>(RAND_MAX);
int k = 0;
while(p > threshold(i)) {
k += 1;
p *= rand() / static_cast<double>(RAND_MAX);
}
samples(i) = k;
}
return samples;
}
CMT::WhiteningTransform::WhiteningTransform(const ArrayXXd& input, const ArrayXXd& output) {
initialize(input, output.rows());
}
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));
}