HuberLoss.h

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/*!
 * 
 * \brief       Implements the Huber loss function for robust regression
 * 
 *
 * \author    Oswin Krause
 * \date        2014
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <http://shark-ml.org/>
 * 
 * Shark is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published 
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */

#ifndef SHARK_OBJECTIVEFUNCTIONS_LOSS_HUBERLOSS_H
#define SHARK_OBJECTIVEFUNCTIONS_LOSS_HUBERLOSS_H

#include <shark/ObjectiveFunctions/Loss/AbstractLoss.h>

namespace shark {

/// \brief Huber-loss for for robust regression
///
/// The Huber loss is a function that is quadratic if\f$ ||f(x)-y||_2 \leq \delta \f$. 
/// Outside this region, whn the error is larger, it is defined as a linear continuation. The function is once
/// but not twice differentiable. This loss is important for regression as it weights outliers lower than
/// ordinary least squares regression while still preserving a convex shape of the loss function.
///
/// Please not that, due to its nature, the error function is not scale invariant. thus rescaling the dataset
/// changes the behaviour. This function has the hyper parameter delta which marks thee region where
/// the function changes from quadratic to linear.
class HuberLoss : public AbstractLoss<RealVector, RealVector>
{
public:
    /// constructor
    HuberLoss(double delta = 1.0):m_delta(delta){ 
        m_features |= base_type::HAS_FIRST_DERIVATIVE;
    }
    
    /// \brief Returns class name "HuberLoss"
    std::string name() const
    { return "HuberLoss"; }


    ///\brief calculates the sum of all 
    double eval(BatchLabelType const& labels, BatchOutputType const& predictions) const{
        SIZE_CHECK(labels.size1() == predictions.size1());
        SIZE_CHECK(labels.size2() == predictions.size2());
        std::size_t numInputs = labels.size1();
        
        double error = 0;
        for(std::size_t i = 0; i != numInputs;++i){
            double norm2 = norm_sqr(row(predictions,i)-row(labels,i));
            
            //check whether we are in the quadratic area
            if(norm2 <= sqr(m_delta)){
                error += 0.5*norm2;
            }
            else{
                error += m_delta*std::sqrt(norm2)-0.5*sqr(m_delta);
            }
        }
        return error;
    }

    double evalDerivative(BatchLabelType const& labels, BatchOutputType const& predictions, BatchOutputType& gradient)const{
        SIZE_CHECK(labels.size1() == predictions.size1());
        SIZE_CHECK(labels.size2() == predictions.size2());
        std::size_t numInputs = predictions.size1();
        std::size_t outputDim = predictions.size2();

        gradient.resize(numInputs,outputDim);
        double error = 0;
        for(std::size_t i = 0; i != numInputs;++i){
            double norm2 = norm_sqr(row(predictions,i)-row(labels,i));
            
            //check whether we are in the quadratic area
            if(norm2 <= sqr(m_delta)){
                error += 0.5*norm2;
                noalias(row(gradient,i)) = row(predictions,i)-row(labels,i);
            }
            else{
                double norm = std::sqrt(norm2);
                error += m_delta*norm-0.5*sqr(m_delta);
                noalias(row(gradient,i)) = m_delta/norm*(row(predictions,i)-row(labels,i));
            }
        }
        return error;
    }
    
private: 
    double m_delta;
};

}
#endif