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Updated DecisionTree documentation. Added Java, Python examples.
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jkbradley committed Aug 20, 2014
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Expand Up @@ -7,20 +7,26 @@ displayTitle: <a href="mllib-guide.html">MLlib</a> - Decision Tree
* Table of contents
{:toc}

Decision trees and their ensembles are popular methods for the machine learning tasks of
[Decision trees](http://en.wikipedia.org/wiki/Decision_tree_learning)
and their ensembles are popular methods for the machine learning tasks of
classification and regression. Decision trees are widely used since they are easy to interpret,
handle categorical variables, extend to the multiclass classification setting, do not require
handle categorical features, extend to the multiclass classification setting, do not require
feature scaling and are able to capture nonlinearities and feature interactions. Tree ensemble
algorithms such as decision forest and boosting are among the top performers for classification and
algorithms such as decision forests and boosting are among the top performers for classification and
regression tasks.

MLlib supports decision trees for binary and multiclass classification and for regression,
using both continuous and categorical features. The implementation partitions data by rows,
allowing distributed training with millions of instances.

## Basic algorithm

The decision tree is a greedy algorithm that performs a recursive binary partitioning of the feature
space by choosing a single element from the *best split set* where each element of the set maximizes
the information gain at a tree node. In other words, the split chosen at each tree node is chosen
from the set `$\underset{s}{\operatorname{argmax}} IG(D,s)$` where `$IG(D,s)$` is the information
gain when a split `$s$` is applied to a dataset `$D$`.
space. The tree predicts the same label for each bottommost (leaf) partition.
Each partition is chosen greedily by selecting the *best split* from a set of possible splits,
in order to maximize the information gain at a tree node. In other words, the split chosen at each
tree node is chosen from the set `$\underset{s}{\operatorname{argmax}} IG(D,s)$` where `$IG(D,s)$`
is the information gain when a split `$s$` is applied to a dataset `$D$`.

### Node impurity and information gain

Expand Down Expand Up @@ -52,58 +58,73 @@ impurity measure for regression (variance).
</tbody>
</table>

The *information gain* is the difference in the parent node impurity and the weighted sum of the two
child node impurities. Assuming that a split $s$ partitions the dataset `$D$` of size `$N$` into two
datasets `$D_{left}$` and `$D_{right}$` of sizes `$N_{left}$` and `$N_{right}$`, respectively:
The *information gain* is the difference between the parent node impurity and the weighted sum of
the two child node impurities. Assuming that a split $s$ partitions the dataset `$D$` of size `$N$`
into two datasets `$D_{left}$` and `$D_{right}$` of sizes `$N_{left}$` and `$N_{right}$`,
respectively, the information gain is:

`$IG(D,s) = Impurity(D) - \frac{N_{left}}{N} Impurity(D_{left}) - \frac{N_{right}}{N} Impurity(D_{right})$`

### Split candidates

**Continuous features**

For small datasets in single machine implementations, the split candidates for each continuous
For small datasets in single-machine implementations, the split candidates for each continuous
feature are typically the unique values for the feature. Some implementations sort the feature
values and then use the ordered unique values as split candidates for faster tree calculations.

Finding ordered unique feature values is computationally intensive for large distributed
datasets. One can get an approximate set of split candidates by performing a quantile calculation
over a sampled fraction of the data. The ordered splits create "bins" and the maximum number of such
bins can be specified using the `maxBins` parameters.
Sorting feature values is expensive for large distributed datasets.
This implementation computes an approximate set of split candidates by performing a quantile
calculation over a sampled fraction of the data.
The ordered splits create "bins" and the maximum number of such
bins can be specified using the `maxBins` parameter.

Note that the number of bins cannot be greater than the number of instances `$N$` (a rare scenario
since the default `maxBins` value is 100). The tree algorithm automatically reduces the number of
bins if the condition is not satisfied.

**Categorical features**

For `$M$` categorical feature values, one could come up with `$2^(M-1)-1$` split candidates. For
binary classification, we can reduce the number of split candidates to `$M-1$` by ordering the
For a categorical feature with `$M$` possible values (categories), one could come up with
`$2^{M-1}-1$` split candidates. For binary classification and regression,
we can reduce the number of split candidates to `$M-1$` by ordering the
categorical feature values by the proportion of labels falling in one of the two classes (see
Section 9.2.4 in
[Elements of Statistical Machine Learning](http://statweb.stanford.edu/~tibs/ElemStatLearn/) for
details). For example, for a binary classification problem with one categorical feature with three
categories A, B and C with corresponding proportion of label 1 as 0.2, 0.6 and 0.4, the categorical
features are ordered as A followed by C followed B or A, C, B. The two split candidates are A \| C, B
categories A, B and C whose corresponding proportions of label 1 are 0.2, 0.6 and 0.4, the categorical
features are ordered as A, C, B. The two split candidates are A \| C, B
and A , C \| B where \| denotes the split. A similar heuristic is used for multiclass classification
when `$2^(M-1)-1$` is greater than the number of bins -- the impurity for each categorical feature value
is used for ordering.
when `$2^{M-1}-1$` is greater than the `maxBins` parameter: the impurity for each categorical feature value
is used for ordering. In multiclass classification, all `$2^{M-1}-1$` possible splits are used
whenever possible.

Note that the `maxBins` parameter must be at least `$M_{max}$`, the maximum number of categories for
any categorical feature.

### Stopping rule

The recursive tree construction is stopped at a node when one of the two conditions is met:

1. The node depth is equal to the `maxDepth` training parameter
1. The node depth is equal to the `maxDepth` training parameter.
2. No split candidate leads to an information gain at the node.

### Max memory requirements

For faster processing, the decision tree algorithm performs simultaneous histogram computations for all nodes at each level of the tree. This could lead to high memory requirements at deeper levels of the tree leading to memory overflow errors. To alleviate this problem, a 'maxMemoryInMB' training parameter is provided which specifies the maximum amount of memory at the workers (twice as much at the master) to be allocated to the histogram computation. The default value is conservatively chosen to be 128 MB to allow the decision algorithm to work in most scenarios. Once the memory requirements for a level-wise computation crosses the `maxMemoryInMB` threshold, the node training tasks at each subsequent level is split into smaller tasks.
For faster processing, the decision tree algorithm performs simultaneous histogram computations for
all nodes at each level of the tree. This could lead to high memory requirements at deeper levels
of the tree, leading to memory overflow errors. To alleviate this problem, a `maxMemoryInMB`
training parameter specifies the maximum amount of memory at the workers (twice as much at the
master) to be allocated to the histogram computation. The default value is conservatively chosen to
be 128 MB to allow the decision algorithm to work in most scenarios. Once the memory requirements
for a level-wise computation cross the `maxMemoryInMB` threshold, the node training tasks at each
subsequent level are split into smaller tasks.

### Practical limitations

1. The implemented algorithm reads both sparse and dense data. However, it is not optimized for sparse input.
2. Python is not supported in this release.
2. Computation scales approximately linearly in the number of training instances,
in the number of features, and in the `maxBins` parameter.

## Examples

Expand All @@ -114,35 +135,101 @@ perform classification using a decision tree using Gini impurity as an impurity
maximum tree depth of 5. The training error is calculated to measure the algorithm accuracy.

<div class="codetabs">

<div data-lang="scala">
{% highlight scala %}
import org.apache.spark.SparkContext
import org.apache.spark.mllib.tree.DecisionTree
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.tree.configuration.Algo._
import org.apache.spark.mllib.tree.impurity.Gini
import org.apache.spark.mllib.util.MLUtils

// Load and parse the data file
val data = sc.textFile("data/mllib/sample_tree_data.csv")
val parsedData = data.map { line =>
val parts = line.split(',').map(_.toDouble)
LabeledPoint(parts(0), Vectors.dense(parts.tail))
}
val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")

// Run training algorithm to build the model
// Train a DecisionTree model.
// Empty categoricalFeaturesInfo indicates all features are continuous.
val numClasses = 2
val categoricalFeaturesInfo = Map[Int, Int]()
val impurity = "gini"
val maxDepth = 5
val model = DecisionTree.train(parsedData, Classification, Gini, maxDepth)
val maxBins = 100

val model = DecisionTree.trainClassifier(data, numClasses, categoricalFeaturesInfo, impurity,
maxDepth, maxBins)

// Evaluate model on training examples and compute training error
val labelAndPreds = parsedData.map { point =>
// Evaluate model on training instances and compute training error
val labelAndPreds = data.map { point =>
val prediction = model.predict(point.features)
(point.label, prediction)
}
val trainErr = labelAndPreds.filter(r => r._1 != r._2).count.toDouble / parsedData.count
val trainErr = labelAndPreds.filter(r => r._1 != r._2).count.toDouble / data.count
println("Training Error = " + trainErr)
{% endhighlight %}
</div>

<div data-lang="java">
{% highlight java %}
import org.apache.spark.api.java.JavaPairRDD;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.api.java.function.Function;
import org.apache.spark.api.java.function.PairFunction;
import org.apache.spark.mllib.regression.LabeledPoint;
import org.apache.spark.mllib.tree.DecisionTree;
import org.apache.spark.mllib.tree.model.DecisionTreeModel;
import scala.Tuple2;

JavaRDD<LabeledPoint> data = ... // data set

// Train a DecisionTree model.
// Empty categoricalFeaturesInfo indicates all features are continuous.
Integer numClasses = ... // number of classes
HashMap<Integer, Integer> categoricalFeaturesInfo = new HashMap<Integer, Integer>();
String impurity = "gini";
Integer maxDepth = 5;
Integer maxBins = 100;

final DecisionTreeModel model = DecisionTree.trainClassifier(data.rdd(), numClasses,
categoricalFeaturesInfo, impurity, maxDepth, maxBins);

// Evaluate model on training instances and compute training error
JavaPairRDD<Double, Double> predictionAndLabel =
data.mapToPair(new PairFunction<LabeledPoint, Double, Double>() {
@Override public Tuple2<Double, Double> call(LabeledPoint p) {
return new Tuple2<Double, Double>(model.predict(p.features()), p.label());
}
});
Double trainErr = 1.0 * predictionAndLabel.filter(new Function<Tuple2<Double, Double>, Boolean>() {
@Override public Boolean call(Tuple2<Double, Double> pl) {
return pl._1() != pl._2();
}
}).count() / data.count();
{% endhighlight %}
</div>

<div data-lang="python">
{% highlight python %}
from pyspark.mllib.regression import LabeledPoint
from pyspark.mllib.tree import DecisionTree
from pyspark.mllib.util import MLUtils

# an RDD of LabeledPoint
data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt')

# Train a DecisionTree model.
# Empty categoricalFeaturesInfo indicates all features are continuous.
model = DecisionTree.trainClassifier(data, numClasses=2, categoricalFeaturesInfo={},
impurity='gini', maxDepth=5, maxBins=100)

# Evaluate model on training instances and compute training error
predictions = model.predict(data.map(lambda x: x.features))
labelsAndPredictions = data.map(lambda lp: lp.label).zip(predictions)
trainErr = labelsAndPredictions.filter(lambda (v, p): v != p).count() / float(data.count())
print('Training Error = ' + str(trainErr))
{% endhighlight %}

Note: When making predictions for a dataset, it is more efficient to do batch prediction rather
than separately calling `predict` on each data point. This is because the Python code makes calls
to an underlying `DecisionTree` model in Scala.
</div>

</div>

### Regression
Expand All @@ -153,33 +240,98 @@ depth of 5. The Mean Squared Error (MSE) is computed at the end to evaluate
[goodness of fit](http://en.wikipedia.org/wiki/Goodness_of_fit).

<div class="codetabs">

<div data-lang="scala">
{% highlight scala %}
import org.apache.spark.SparkContext
import org.apache.spark.mllib.tree.DecisionTree
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.tree.configuration.Algo._
import org.apache.spark.mllib.tree.impurity.Variance
import org.apache.spark.mllib.util.MLUtils

// Load and parse the data file
val data = sc.textFile("data/mllib/sample_tree_data.csv")
val parsedData = data.map { line =>
val parts = line.split(',').map(_.toDouble)
LabeledPoint(parts(0), Vectors.dense(parts.tail))
}
val data = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt")

// Run training algorithm to build the model
// Train a DecisionTree model.
// Empty categoricalFeaturesInfo indicates all features are continuous.
val categoricalFeaturesInfo = Map[Int, Int]()
val impurity = "variance"
val maxDepth = 5
val model = DecisionTree.train(parsedData, Regression, Variance, maxDepth)
val maxBins = 100

// Evaluate model on training examples and compute training error
val valuesAndPreds = parsedData.map { point =>
val model = DecisionTree.trainRegressor(data, categoricalFeaturesInfo, impurity,
maxDepth, maxBins)

// Evaluate model on training instances and compute training error
val labelsAndPredictions = data.map { point =>
val prediction = model.predict(point.features)
(point.label, prediction)
}
val MSE = valuesAndPreds.map{ case(v, p) => math.pow((v - p), 2)}.mean()
println("training Mean Squared Error = " + MSE)
val trainMSE = labelsAndPredictions.map{ case(v, p) => math.pow((v - p), 2)}.mean()
println("Training Mean Squared Error = " + trainMSE)
{% endhighlight %}
</div>

<div data-lang="java">
{% highlight java %}
import org.apache.spark.api.java.JavaPairRDD;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.api.java.function.Function;
import org.apache.spark.api.java.function.PairFunction;
import org.apache.spark.mllib.regression.LabeledPoint;
import org.apache.spark.mllib.tree.DecisionTree;
import org.apache.spark.mllib.tree.model.DecisionTreeModel;
import scala.Tuple2;

JavaRDD<LabeledPoint> data = ... // data set

// Train a DecisionTree model.
// Empty categoricalFeaturesInfo indicates all features are continuous.
HashMap<Integer, Integer> categoricalFeaturesInfo = new HashMap<Integer, Integer>();
String impurity = "variance";
Integer maxDepth = 5;
Integer maxBins = 100;

final DecisionTreeModel model = DecisionTree.trainRegressor(data.rdd(),
categoricalFeaturesInfo, impurity, maxDepth, maxBins);

// Evaluate model on training instances and compute training error
JavaPairRDD<Double, Double> predictionAndLabel =
data.mapToPair(new PairFunction<LabeledPoint, Double, Double>() {
@Override public Tuple2<Double, Double> call(LabeledPoint p) {
return new Tuple2<Double, Double>(model.predict(p.features()), p.label());
}
});
Double trainMSE = predictionAndLabel.map(new Function<Tuple2<Double, Double>, Double>() {
@Override public Double call(Tuple2<Double, Double> pl) {
Double diff = pl._1() - pl._2();
return diff * diff;
}
}).sum() / data.count();
{% endhighlight %}
</div>

<div data-lang="python">
{% highlight python %}
from pyspark.mllib.regression import LabeledPoint
from pyspark.mllib.tree import DecisionTree
from pyspark.mllib.util import MLUtils

# an RDD of LabeledPoint
data = MLUtils.loadLibSVMFile(sc, 'data/mllib/sample_libsvm_data.txt')

# Train a DecisionTree model.
# Empty categoricalFeaturesInfo indicates all features are continuous.
model = DecisionTree.trainRegressor(data, categoricalFeaturesInfo={},
impurity='variance', maxDepth=5, maxBins=100)

# Evaluate model on training instances and compute training error
predictions = model.predict(data.map(lambda x: x.features))
labelsAndPredictions = data.map(lambda lp: lp.label).zip(predictions)
trainMSE = labelsAndPredictions.map(lambda (v, p): (v - p) * (v - p)).sum() / float(data.count())
print('Training Mean Squared Error = ' + str(trainMSE))
{% endhighlight %}

Note: When making predictions for a dataset, it is more efficient to do batch prediction rather
than separately calling `predict` on each data point. This is because the Python code makes calls
to an underlying `DecisionTree` model in Scala.
</div>

</div>

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