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 --- @@ -0,0 +1,762 @@ +--- +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 -- use header
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