

``mx.symbol.LogisticRegressionOutput``
============================================================================

Description
----------------------

Applies a logistic function to the input.

The logistic function, also known as the sigmoid function, is computed as
:math:`\frac{1}{1+exp(-\textbf{x})}`.

Commonly, the sigmoid is used to squash the real-valued output of a linear model
:math:`wTx+b` into the [0,1] range so that it can be interpreted as a probability.
It is suitable for binary classification or probability prediction tasks.


.. note::    Use the LogisticRegressionOutput as the final output layer of a net.

The storage type of ``label`` can be ``default`` or ``csr``

- LogisticRegressionOutput(default, default) = default
- LogisticRegressionOutput(default, csr) = default

The loss function used is the Binary Cross Entropy Loss:

:math:`-{(y\log(p) + (1 - y)\log(1 - p))}`

Where `y` is the ground truth probability of positive outcome for a given example, and `p` the probability predicted by the model. By default, gradients of this loss function are scaled by factor `1/m`, where m is the number of regression outputs of a training example.
The parameter `grad_scale` can be used to change this scale to `grad_scale/m`.


Usage
----------

.. code:: r

	mx.symbol.LogisticRegressionOutput(...)

Arguments
------------------

+----------------------------------------+------------------------------------------------------------+
| Argument                               | Description                                                |
+========================================+============================================================+
| ``data``                               | NDArray-or-Symbol.                                         |
|                                        |                                                            |
|                                        | Input data to the function.                                |
+----------------------------------------+------------------------------------------------------------+
| ``label``                              | NDArray-or-Symbol.                                         |
|                                        |                                                            |
|                                        | Input label to the function.                               |
+----------------------------------------+------------------------------------------------------------+
| ``grad.scale``                         | float, optional, default=1.                                |
|                                        |                                                            |
|                                        | Scale the gradient by a float factor                       |
+----------------------------------------+------------------------------------------------------------+
| ``name``                               | string, optional.                                          |
|                                        |                                                            |
|                                        | Name of the resulting symbol.                              |
+----------------------------------------+------------------------------------------------------------+

Value
----------

``out`` The result mx.symbol


Link to Source Code: http://github.com/apache/incubator-mxnet/blob/1.6.0/src/operator/regression_output.cc#L152