functionalsmoothing.h

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/**
 * @file functionalsmoothing.h
 * @author Ozgur Taylan Turan
 *
 * Smoothing for functional data
 *
 *
 *
 */
#ifndef FUNCTIONALSMOOTHING_H
#define FUNCTIONALSMOOTHING_H
 
namespace algo {
namespace functional {
/*
 * Optimizing the bandwiths for kernel smoothing.
 *
 * @param inputs      Training input matrix 
 * @param labels      Corresponding target/output matrix
 * @param pred_inputs Input points at which predictions will be computed
 * @param bandwidths  Bandwidth parameters for each feature 
 * @param valid       Validation parameter 
 */
template<class KERNEL,class T=DTYPE>
arma::Mat<T> kernelsmoothing ( const arma::Mat<T>& inputs,
                               const arma::Mat<T>& labels,
                               const arma::Mat<T>& pred_inputs,
                               const arma::vec& bandwidths,
                               const double valid)
{
  size_t N = pred_inputs.n_cols;
  size_t M = labels.n_rows;
 
  arma::Mat<T> predictions = arma::zeros<arma::Mat<T>>(M, N);
 
  for(size_t i=0; i<M; i++)
  {
    arma::Row<T> label = labels.row(i);
    arma::Row<T> temp;
 
    mlpack::HyperParameterTuner<algo::regression::Kernel<KERNEL>,
                                     mlpack::MSE,
                                     mlpack::SimpleCV>
                                     hpt(valid, inputs, label);
 
 
    double bandwidth;
    std::tie(bandwidth) = hpt.Optimize(bandwidths);
 
    algo::regression::Kernel<KERNEL> smoother(inputs,label,bandwidth);
 
    smoother.Predict(pred_inputs,temp);
    predictions.row(i) = temp;
  }  
  return predictions;
}
 
/*
 * Kernel smoothing for a fixed bandwidth
 *
 * @param inputs      Training input matrix 
 * @param labels      Corresponding target/output matrix
 * @param pred_inputs Input points at which predictions will be computed
 * @param bandwidth   Bandwidth parameters for each feature 
 */
template<class KERNEL,class T=DTYPE>
arma::Mat<T> kernelsmoothing ( const arma::Mat<T>& inputs,
                               const arma::Mat<T>& labels,
                               const arma::Mat<T>& pred_inputs,
                               const double& bandwidth    )
{
  size_t N = pred_inputs.n_cols;
  size_t M = labels.n_rows;
 
  arma::Mat<T> predictions = arma::zeros<arma::Mat<T>>(M, N);
 
  for(size_t i=0; i<M; i++)
  {
    arma::Row<T> label = labels.row(i);
    arma::Row<T> temp;
 
    algo::regression::Kernel<KERNEL> smoother(inputs,label,bandwidth);
 
    smoother.Predict(pred_inputs,temp);
    predictions.row(i) = temp;
  }  
  return predictions;
}
 
/*
 * Kernel smoothing for a fixed bandwidth and returning the preds at inputs
 *
 * @param inputs      Training input matrix 
 * @param labels      Corresponding target/output matrix
 * @param bandwidth   Bandwidth parameters for each feature 
 */
 
template<class KERNEL,class T=DTYPE>
arma::Mat<T> kernelsmoothing ( const arma::Mat<T>& inputs,
                               const arma::Mat<T>& labels,
                               const double& bandwidth    )
 
{
  return kernelsmoothing<KERNEL>( inputs,labels,inputs,bandwidth );
 
}
 
} // functional
} // utils
#endif