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==================
Objective function
==================

.. _alg_objective_function:


.. include::  ../../../includes/objective-function/objective-function-introduction.rst


-----------------------------
Supported objective functions
-----------------------------

.. toctree::
   :titlesonly:

   logloss.rst

------------------------
Mathematical formulation
------------------------

.. _objective_function_c_math:

Computing
---------

Algorithm takes dataset :math:`X = \{ x_1, \ldots, x_n \}` with :math:`n` feature vectors of dimension :math:`p`, vector with correct class labels
:math:`y = \{ y_1, \ldots, y_n \}` and coefficients vector `w = \{ w_0, \ldots, w_p \}`of size :math:`p + 1` as input. Then it calculates 
logistic loss, its gradient or hessian.

#####
Value 
#####

:math:`L(X, w, y)` - value of objective function. 

########
Gradient
########

:math:`\overline{grad} = \frac{\partial L}{\partial w}` - gradient of objective function.

#######
Hessian
#######

:math:`H = (h_{ij}) = \frac{\partial L}{\partial w \partial w}` - hessian of objective function.

.. _objective_function_c_dense_batch:

Computation method: *dense_batch*
---------------------------------
The method computes value of objective function, its gradient or hessian for the dense data.
This is the default and the only method supported.

---------------------
Programming Interface
---------------------

Refer to :ref:`API Reference: Objective Function <api_objective_function>`.

----------------
Distributed mode
----------------

Currently algorithm does not support distributed execution in SMPD mode.

.. rubric:: Examples: Logistic Loss

.. include::  ../../../includes/objective-function/logloss-examples.rst