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/*
* File: logitFunction.cpp
*
* Likelihood, gradient and initialisation of logit function
* Functor, based on mlpack: www.mlpack.org
*/
#include "linkFunction.hpp"
/**
* Evaluate the logistic regression objective function given the estimated
* parameters.
*/
double LogitLikelihood::operator()(const column_vector& parameters_in)
const
{
// Convert from dlib column matrix to armadillo column matrix
arma::vec parameters = dlib_to_arma(parameters_in);
// The objective function is the log-likelihood function (w is the parameters
// vector for the model; y is the responses; x is the predictors; sig() is the
// sigmoid function):
// f(w) = sum(y log(sig(w'x)) + (1 - y) log(sig(1 - w'x))).
// We want to minimize this function. L2-regularization is just lambda
// multiplied by the squared l2-norm of the parameters then divided by two.
// For the regularization, we ignore the first term, which is the intercept
// term.
const double regularization = 0.5 * lambda *
arma::dot(parameters.col(0).subvec(1, parameters.n_elem - 1),
parameters.col(0).subvec(1, parameters.n_elem - 1));
// Calculate vectors of sigmoids. The intercept term is parameters(0, 0) and
// does not need to be multiplied by any of the predictors.
const arma::vec exponents = parameters(0) + predictors *
parameters.col(0).subvec(1, parameters.n_elem - 1);
const arma::vec sigmoid = 1.0 / (1.0 + arma::exp(-exponents));
// Assemble full objective function. Often the objective function and the
// regularization as given are divided by the number of features, but this
// doesn't actually affect the optimization result, so we'll just ignore those
// terms for computational efficiency.
double result = 0.0;
for (size_t i = 0; i < responses.n_elem; ++i)
{
if (responses[i] == 1)
result += log(sigmoid[i]);
else
result += log(1.0 - sigmoid[i]);
}
return result - regularization;
}
// Evaluate the gradient of the logistic regression objective function.
column_vector LogitLikelihoodGradient::operator()(const column_vector& parameters_in)
const
{
// Convert from dlib column matrix to armadillo column matrix
arma::vec parameters = dlib_to_arma(parameters_in);
arma::vec gradient(parameters.n_elem);
// Regularization term.
arma::mat regularization;
regularization = lambda * parameters.col(0).subvec(1, parameters.n_elem - 1);
const arma::vec sigmoids = 1 / (1 + arma::exp(-parameters(0, 0)
- predictors * parameters.col(0).subvec(1, parameters.n_elem - 1)));
gradient[0] = arma::accu(responses - sigmoids);
gradient.col(0).subvec(1, parameters.n_elem - 1) = predictors.t() * (responses -
sigmoids) - regularization;
return arma_to_dlib(gradient);
}
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