double LogisticRegressionFunction<MatType>::Evaluate(
const arma::mat& parameters,
const size_t begin,
const size_t batchSize) const
{
// Calculating the regularization term.
const double regularization = lambda *
(batchSize / (2.0 * predictors.n_cols)) *
arma::dot(parameters.tail_cols(parameters.n_elem - 1),
parameters.tail_cols(parameters.n_elem - 1));
// Calculating the hypothesis that has to be passed to the sigmoid function.
const arma::rowvec exponents = parameters(0, 0) +
parameters.tail_cols(parameters.n_elem - 1) *
predictors.cols(begin, begin + batchSize - 1);
// Calculating the sigmoid function values.
const arma::rowvec sigmoid = 1.0 / (1.0 + arma::exp(-exponents));
// Iterating for the given batch size from a given point
double result = 0.0;
for (size_t i = 0; i < batchSize; ++i)
{
if (responses[i + begin] == 1)
result += log(sigmoid[i]);
else
result += log(1.0 - sigmoid[i]);
}
// Invert the result, because it's a minimization.
return -result + regularization;
}
void LogisticRegressionFunction<MatType>::Gradient(
const arma::mat& parameters,
arma::mat& gradient) const
{
// Regularization term.
arma::mat regularization;
regularization = lambda * parameters.tail_cols(parameters.n_elem - 1);
const arma::rowvec sigmoids = (1 / (1 + arma::exp(-parameters(0, 0)
- parameters.tail_cols(parameters.n_elem - 1) * predictors)));
gradient.set_size(arma::size(parameters));
gradient[0] = -arma::accu(responses - sigmoids);
gradient.tail_cols(parameters.n_elem - 1) = (sigmoids - responses) *
predictors.t() + regularization;
}
double LogisticRegressionFunction<MatType>::Evaluate(
const arma::mat& parameters) const
{
// 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 and take every term except the last one in the decision variable.
const double regularization = 0.5 * lambda *
arma::dot(parameters.tail_cols(parameters.n_elem - 1),
parameters.tail_cols(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::rowvec exponents = parameters(0, 0) +
parameters.tail_cols(parameters.n_elem - 1) * predictors;
const arma::rowvec 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]);
}
// Invert the result, because it's a minimization.
return -result + regularization;
}
void LogisticRegressionFunction<MatType>::Gradient(
const arma::mat& parameters,
const size_t begin,
GradType& gradient,
const size_t batchSize) const
{
// Regularization term.
arma::mat regularization;
regularization = lambda * parameters.tail_cols(parameters.n_elem - 1)
/ predictors.n_cols * batchSize;
const arma::rowvec exponents = parameters(0, 0) +
parameters.tail_cols(parameters.n_elem - 1) *
predictors.cols(begin, begin + batchSize - 1);
// Calculating the sigmoid function values.
const arma::rowvec sigmoids = 1.0 / (1.0 + arma::exp(-exponents));
gradient.set_size(parameters.n_rows, parameters.n_cols);
gradient[0] = -arma::accu(responses.subvec(begin, begin + batchSize - 1) -
sigmoids);
gradient.tail_cols(parameters.n_elem - 1) =
arma::sum((responses.subvec(begin, begin + batchSize - 1) - sigmoids) *
-predictors.cols(begin, begin + batchSize - 1).t(), 0) + regularization;
}
void LogisticRegressionFunction<MatType>::PartialGradient(
const arma::mat& parameters,
const size_t j,
arma::sp_mat& gradient) const
{
const arma::rowvec diffs = responses - (1 / (1 + arma::exp(-parameters(0, 0)
- parameters.tail_cols(parameters.n_elem - 1) * predictors)));
gradient.set_size(arma::size(parameters));
if (j == 0)
{
gradient[j] = -arma::accu(diffs);
}
else
{
gradient[j] = arma::dot(-predictors.row(j - 1), diffs) + lambda *
parameters(0, j);
}
}