Github user jkbradley commented on a diff in the pull request:
https://github.com/apache/spark/pull/10207#discussion_r47039765
--- Diff: docs/ml-classification-regression.md ---
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+---
+layout: global
+title: Classification and regression - spark.ml
+displayTitle: Classification and regression in spark.ml
+---
+
+
+`\[
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\E}{\mathbb{E}}
+\newcommand{\x}{\mathbf{x}}
+\newcommand{\y}{\mathbf{y}}
+\newcommand{\wv}{\mathbf{w}}
+\newcommand{\av}{\mathbf{\alpha}}
+\newcommand{\bv}{\mathbf{b}}
+\newcommand{\N}{\mathbb{N}}
+\newcommand{\id}{\mathbf{I}}
+\newcommand{\ind}{\mathbf{1}}
+\newcommand{\0}{\mathbf{0}}
+\newcommand{\unit}{\mathbf{e}}
+\newcommand{\one}{\mathbf{1}}
+\newcommand{\zero}{\mathbf{0}}
+\]`
+
+**Table of Contents**
+
+* This will become a table of contents (this text will be scraped).
+{:toc}
+
+In MLlib, we implement popular linear methods such as logistic
+regression and linear least squares with $L_1$ or $L_2$ regularization.
+Refer to [the linear methods in mllib](mllib-linear-methods.html) for
+details. In `spark.ml`, we also include Pipelines API for [Elastic
+net](http://en.wikipedia.org/wiki/Elastic_net_regularization), a hybrid
+of $L_1$ and $L_2$ regularization proposed in [Zou et al, Regularization
+and variable selection via the elastic
+net](http://users.stat.umn.edu/~zouxx019/Papers/elasticnet.pdf).
+Mathematically, it is defined as a convex combination of the $L_1$ and
+the $L_2$ regularization terms:
+`\[
+\alpha \left( \lambda \|\wv\|_1 \right) + (1-\alpha) \left(
\frac{\lambda}{2}\|\wv\|_2^2 \right) , \alpha \in [0, 1], \lambda \geq 0
+\]`
+By setting $\alpha$ properly, elastic net contains both $L_1$ and $L_2$
+regularization as special cases. For example, if a [linear
+regression](https://en.wikipedia.org/wiki/Linear_regression) model is
+trained with the elastic net parameter $\alpha$ set to $1$, it is
+equivalent to a
+[Lasso](http://en.wikipedia.org/wiki/Least_squares#Lasso_method) model.
+On the other hand, if $\alpha$ is set to $0$, the trained model reduces
+to a [ridge
+regression](http://en.wikipedia.org/wiki/Tikhonov_regularization) model.
+We implement Pipelines API for both linear regression and logistic
+regression with elastic net regularization.
+
+
+# Classification
+
+## Logistic regression
+
+Logistic regression is a popular method to predict a binary response. It
is a special case of [Generalized Linear
models](https://en.wikipedia.org/wiki/Generalized_linear_model) that predicts
the probability of the outcome.
+For more background and more details about the implementation, refer to
the documentation of the [logistic regression in
`spark.mllib`](mllib-linear-methods.html#logistic-regression).
+
+ > The current implementation of logistic regression in `spark.ml` only
supports binary classes. Support for multiclass regression will be added in the
future.
+
+The following example shows how to train a logistic regression model
+with elastic net regularization. `elasticNetParam` corresponds to
+$\alpha$ and `regParam` corresponds to $\lambda$.
+
+<div class="codetabs">
+
+<div data-lang="scala" markdown="1">
+{% include_example
scala/org/apache/spark/examples/ml/LogisticRegressionWithElasticNetExample.scala
%}
+</div>
+
+<div data-lang="java" markdown="1">
+{% include_example
java/org/apache/spark/examples/ml/JavaLogisticRegressionWithElasticNetExample.java
%}
+</div>
+
+<div data-lang="python" markdown="1">
+{% include_example python/ml/logistic_regression_with_elastic_net.py %}
+</div>
+
+</div>
+
+The `spark.ml` implementation of logistic regression also supports
+extracting a summary of the model over the training set. Note that the
+predictions and metrics which are stored as `Dataframe` in
+`BinaryLogisticRegressionSummary` are annotated `@transient` and hence
+only available on the driver.
+
+<div class="codetabs">
+
+<div data-lang="scala" markdown="1">
+
+[`LogisticRegressionTrainingSummary`](api/scala/index.html#org.apache.spark.ml.classification.LogisticRegressionTrainingSummary)
+provides a summary for a
+[`LogisticRegressionModel`](api/scala/index.html#org.apache.spark.ml.classification.LogisticRegressionModel).
+Currently, only binary classification is supported and the
+summary must be explicitly cast to
+[`BinaryLogisticRegressionTrainingSummary`](api/scala/index.html#org.apache.spark.ml.classification.BinaryLogisticRegressionTrainingSummary).
+This will likely change when multiclass classification is supported.
+
+Continuing the earlier example:
+
+{% include_example
scala/org/apache/spark/examples/ml/LogisticRegressionSummaryExample.scala %}
+</div>
+
+<div data-lang="java" markdown="1">
+[`LogisticRegressionTrainingSummary`](api/java/org/apache/spark/ml/classification/LogisticRegressionTrainingSummary.html)
+provides a summary for a
+[`LogisticRegressionModel`](api/java/org/apache/spark/ml/classification/LogisticRegressionModel.html).
+Currently, only binary classification is supported and the
+summary must be explicitly cast to
+[`BinaryLogisticRegressionTrainingSummary`](api/java/org/apache/spark/ml/classification/BinaryLogisticRegressionTrainingSummary.html).
+This will likely change when multiclass classification is supported.
+
+Continuing the earlier example:
+
+{% include_example
java/org/apache/spark/examples/ml/JavaLogisticRegressionSummaryExample.java %}
+</div>
+
+<!--- TODO: Add python model summaries once implemented -->
+<div data-lang="python" markdown="1">
+Logistic regression model summary is not yet supported in Python.
+</div>
+
+</div>
+
+
+## Classification with decision trees
+
+Decision trees are a popular family of classification and regression
methods.
+More information about the `spark.ml` implementation can be found further
in the [section on decision trees](#decision-trees).
+
+The following examples load a dataset in LibSVM format, split it into
training and test sets, train on the first dataset, and then evaluate on the
held-out test set.
+We use two feature transformers to prepare the data; these help index
categories for the label and categorical features, adding metadata to the
`DataFrame` which the Decision Tree algorithm can recognize.
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+
+More details on parameters can be found in the [Scala API
documentation](api/scala/index.html#org.apache.spark.ml.classification.DecisionTreeClassifier).
+
+{% include_example
scala/org/apache/spark/examples/ml/DecisionTreeClassificationExample.scala %}
+
+</div>
+
+<div data-lang="java" markdown="1">
+
+More details on parameters can be found in the [Java API
documentation](api/java/org/apache/spark/ml/classification/DecisionTreeClassifier.html).
+
+{% include_example
java/org/apache/spark/examples/ml/JavaDecisionTreeClassificationExample.java %}
+
+</div>
+
+<div data-lang="python" markdown="1">
+
+More details on parameters can be found in the [Python API
documentation](api/python/pyspark.ml.html#pyspark.ml.classification.DecisionTreeClassifier).
+
+{% include_example python/ml/decision_tree_classification_example.py %}
+
+</div>
+
+</div>
+
+## Classification with random forests
+
+Random forests are a popular family of classification and regression
methods.
+More information about the `spark.ml` implementation can be found further
in the [section on random forests](#random-forests).
+
+The following examples load a dataset in LibSVM format, split it into
training and test sets, train on the first dataset, and then evaluate on the
held-out test set.
+We use two feature transformers to prepare the data; these help index
categories for the label and categorical features, adding metadata to the
`DataFrame` which the tree-based algorithms can recognize.
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+
+Refer to the [Scala API
docs](api/scala/index.html#org.apache.spark.ml.classification.RandomForestClassifier)
for more details.
+
+{% include_example
scala/org/apache/spark/examples/ml/RandomForestClassifierExample.scala %}
+</div>
+
+<div data-lang="java" markdown="1">
+
+Refer to the [Java API
docs](api/java/org/apache/spark/ml/classification/RandomForestClassifier.html)
for more details.
+
+{% include_example
java/org/apache/spark/examples/ml/JavaRandomForestClassifierExample.java %}
+</div>
+
+<div data-lang="python" markdown="1">
+
+Refer to the [Python API
docs](api/python/pyspark.ml.html#pyspark.ml.classification.RandomForestClassifier)
for more details.
+
+{% include_example python/ml/random_forest_classifier_example.py %}
+</div>
+</div>
+
+## Classification with gradient-boosted trees
+
+Gradient-boosted trees (GBTs) are a popular classification and regression
method using ensembles of decision trees.
+More information about the `spark.ml` implementation can be found further
in the [section on GBTs](#gradient-boosted-trees-gbts).
+
+The following examples load a dataset in LibSVM format, split it into
training and test sets, train on the first dataset, and then evaluate on the
held-out test set.
+We use two feature transformers to prepare the data; these help index
categories for the label and categorical features, adding metadata to the
`DataFrame` which the tree-based algorithms can recognize.
+
+<div class="codetabs">
+<div data-lang="scala" markdown="1">
+
+Refer to the [Scala API
docs](api/scala/index.html#org.apache.spark.ml.classification.GBTClassifier)
for more details.
+
+{% include_example
scala/org/apache/spark/examples/ml/GradientBoostedTreeClassifierExample.scala %}
+</div>
+
+<div data-lang="java" markdown="1">
+
+Refer to the [Java API
docs](api/java/org/apache/spark/ml/classification/GBTClassifier.html) for more
details.
+
+{% include_example
java/org/apache/spark/examples/ml/JavaGradientBoostedTreeClassifierExample.java
%}
+</div>
+
+<div data-lang="python" markdown="1">
+
+Refer to the [Python API
docs](api/python/pyspark.ml.html#pyspark.ml.classification.GBTClassifier) for
more details.
+
+{% include_example python/ml/gradient_boosted_tree_classifier_example.py %}
+</div>
+</div>
+
+## Multilayer perceptron classifier
+
+Multilayer perceptron classifier (MLPC) is a classifier based on the
[feedforward artificial neural
network](https://en.wikipedia.org/wiki/Feedforward_neural_network).
+MLPC consists of multiple layers of nodes.
+Each layer is fully connected to the next layer in the network. Nodes in
the input layer represent the input data. All other nodes maps inputs to the
outputs
+by performing linear combination of the inputs with the node's weights
`$\wv$` and bias `$\bv$` and applying an activation function.
+It can be written in matrix form for MLPC with `$K+1$` layers as follows:
+`\[
+\mathrm{y}(\x) = \mathrm{f_K}(...\mathrm{f_2}(\wv_2^T\mathrm{f_1}(\wv_1^T
\x+b_1)+b_2)...+b_K)
+\]`
+Nodes in intermediate layers use sigmoid (logistic) function:
+`\[
+\mathrm{f}(z_i) = \frac{1}{1 + e^{-z_i}}
+\]`
+Nodes in the output layer use softmax function:
+`\[
+\mathrm{f}(z_i) = \frac{e^{z_i}}{\sum_{k=1}^N e^{z_k}}
+\]`
+The number of nodes `$N$` in the output layer corresponds to the number of
classes.
+
+MLPC employes backpropagation for learning the model. We use logistic loss
function for optimization and L-BFGS as optimization routine.
+
+**Examples**
--- End diff --
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