2014-04-22 14:20:47 -04:00
---
layout: global
2014-05-18 20:00:57 -04:00
title: Decision Tree - MLlib
displayTitle: < a href = "mllib-guide.html" > MLlib< / a > - Decision Tree
2014-04-22 14:20:47 -04:00
---
* Table of contents
{:toc}
Decision trees 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
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
regression tasks.
## 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 `$D$` .
### Node impurity and information gain
The *node impurity* is a measure of the homogeneity of the labels at the node. The current
implementation provides two impurity measures for classification (Gini impurity and entropy) and one
impurity measure for regression (variance).
< table class = "table" >
< thead >
< tr > < th > Impurity< / th > < th > Task< / th > < th > Formula< / th > < th > Description< / th > < / tr >
< / thead >
< tbody >
< tr >
< td > Gini impurity< / td >
< td > Classification< / td >
< td > $\sum_{i=1}^{M} f_i(1-f_i)$</ td >< td > $f_i$ is the frequency of label $i$ at a node and $M$ is the number of unique labels.</ td >
< / tr >
< tr >
< td > Entropy< / td >
< td > Classification< / td >
< td > $\sum_{i=1}^{M} -f_ilog(f_i)$</ td >< td > $f_i$ is the frequency of label $i$ at a node and $M$ is the number of unique labels.</ td >
< / tr >
< tr >
< td > Variance< / td >
< td > Regression< / td >
< td > $\frac{1}{n} \sum_{i=1}^{N} (x_i - \mu)^2$</ td >< td > $y_i$ is label for an instance,
$N$ is the number of instances and $\mu$ is the mean given by $\frac{1}{N} \sum_{i=1}^n x_i$.</ td >
< / tr >
< / 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:
`$IG(D,s) = Impurity(D) - \frac{N_{left}}{N} Impurity(D_{left}) - \frac{N_{right}}{N} Impurity(D_{right})$`
### Split candidates
**Continuous features**
For small datasets in single machine implementations, the split candidates for each continuous
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.
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**
[MLlib] SPARK-1536: multiclass classification support for decision tree
The ability to perform multiclass classification is a big advantage for using decision trees and was a highly requested feature for mllib. This pull request adds multiclass classification support to the MLlib decision tree. It also adds sample weights support using WeightedLabeledPoint class for handling unbalanced datasets during classification. It will also support algorithms such as AdaBoost which requires instances to be weighted.
It handles the special case where the categorical variables cannot be ordered for multiclass classification and thus the optimizations used for speeding up binary classification cannot be directly used for multiclass classification with categorical variables. More specifically, for m categories in a categorical feature, it analyses all the ```2^(m-1) - 1``` categorical splits provided that #splits are less than the maxBins provided in the input. This condition will not be met for features with large number of categories -- using decision trees is not recommended for such datasets in general since the categorical features are favored over continuous features. Moreover, the user can use a combination of tricks (increasing bin size of the tree algorithms, use binary encoding for categorical features or use one-vs-all classification strategy) to avoid these constraints.
The new code is accompanied by unit tests and has also been tested on the iris and covtype datasets.
cc: mengxr, etrain, hirakendu, atalwalkar, srowen
Author: Manish Amde <manish9ue@gmail.com>
Author: manishamde <manish9ue@gmail.com>
Author: Evan Sparks <sparks@cs.berkeley.edu>
Closes #886 from manishamde/multiclass and squashes the following commits:
26f8acc [Manish Amde] another attempt at fixing mima
c5b2d04 [Manish Amde] more MIMA fixes
1ce7212 [Manish Amde] change problem filter for mima
10fdd82 [Manish Amde] fixing MIMA excludes
e1c970d [Manish Amde] merged master
abf2901 [Manish Amde] adding classes to MimaExcludes.scala
45e767a [Manish Amde] adding developer api annotation for overriden methods
c8428c4 [Manish Amde] fixing weird multiline bug
afced16 [Manish Amde] removed label weights support
2d85a48 [Manish Amde] minor: fixed scalastyle issues reprise
4e85f2c [Manish Amde] minor: fixed scalastyle issues
b2ae41f [Manish Amde] minor: scalastyle
e4c1321 [Manish Amde] using while loop for regression histograms
d75ac32 [Manish Amde] removed WeightedLabeledPoint from this PR
0fecd38 [Manish Amde] minor: add newline to EOF
2061cf5 [Manish Amde] merged from master
06b1690 [Manish Amde] fixed off-by-one error in bin to split conversion
9cc3e31 [Manish Amde] added implicit conversion import
5c1b2ca [Manish Amde] doc for PointConverter class
485eaae [Manish Amde] implicit conversion from LabeledPoint to WeightedLabeledPoint
3d7f911 [Manish Amde] updated doc
8e44ab8 [Manish Amde] updated doc
adc7315 [Manish Amde] support ordered categorical splits for multiclass classification
e3e8843 [Manish Amde] minor code formatting
23d4268 [Manish Amde] minor: another minor code style
34ee7b9 [Manish Amde] minor: code style
237762d [Manish Amde] renaming functions
12e6d0a [Manish Amde] minor: removing line in doc
9a90c93 [Manish Amde] Merge branch 'master' into multiclass
1892a2c [Manish Amde] tests and use multiclass binaggregate length when atleast one categorical feature is present
f5f6b83 [Manish Amde] multiclass for continous variables
8cfd3b6 [Manish Amde] working for categorical multiclass classification
828ff16 [Manish Amde] added categorical variable test
bce835f [Manish Amde] code cleanup
7e5f08c [Manish Amde] minor doc
1dd2735 [Manish Amde] bin search logic for multiclass
f16a9bb [Manish Amde] fixing while loop
d811425 [Manish Amde] multiclass bin aggregate logic
ab5cb21 [Manish Amde] multiclass logic
d8e4a11 [Manish Amde] sample weights
ed5a2df [Manish Amde] fixed classification requirements
d012be7 [Manish Amde] fixed while loop
18d2835 [Manish Amde] changing default values for num classes
6b912dc [Manish Amde] added numclasses to tree runner, predict logic for multiclass, add multiclass option to train
75f2bfc [Manish Amde] minor code style fix
e547151 [Manish Amde] minor modifications
34549d0 [Manish Amde] fixing error during merge
098e8c5 [Manish Amde] merged master
e006f9d [Manish Amde] changing variable names
5c78e1a [Manish Amde] added multiclass support
6c7af22 [Manish Amde] prepared for multiclass without breaking binary classification
46e06ee [Manish Amde] minor mods
3f85a17 [Manish Amde] tests for multiclass classification
4d5f70c [Manish Amde] added multiclass support for find splits bins
46f909c [Manish Amde] todo for multiclass support
455bea9 [Manish Amde] fixed tests
14aea48 [Manish Amde] changing instance format to weighted labeled point
a1a6e09 [Manish Amde] added weighted point class
968ca9d [Manish Amde] merged master
7fc9545 [Manish Amde] added docs
ce004a1 [Manish Amde] minor formatting
b27ad2c [Manish Amde] formatting
426bb28 [Manish Amde] programming guide blurb
8053fed [Manish Amde] more formatting
5eca9e4 [Manish Amde] grammar
4731cda [Manish Amde] formatting
5e82202 [Manish Amde] added documentation, fixed off by 1 error in max level calculation
cbd9f14 [Manish Amde] modified scala.math to math
dad9652 [Manish Amde] removed unused imports
e0426ee [Manish Amde] renamed parameter
718506b [Manish Amde] added unit test
1517155 [Manish Amde] updated documentation
9dbdabe [Manish Amde] merge from master
719d009 [Manish Amde] updating user documentation
fecf89a [manishamde] Merge pull request #6 from etrain/deep_tree
0287772 [Evan Sparks] Fixing scalastyle issue.
2f1e093 [Manish Amde] minor: added doc for maxMemory parameter
2f6072c [manishamde] Merge pull request #5 from etrain/deep_tree
abc5a23 [Evan Sparks] Parameterizing max memory.
50b143a [Manish Amde] adding support for very deep trees
2014-07-18 17:00:13 -04:00
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
2014-04-22 14:20:47 -04:00
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
2014-05-06 23:07:22 -04:00
features are ordered as A followed by C followed B or A, B, C. The two split candidates are A \| C, B
[MLlib] SPARK-1536: multiclass classification support for decision tree
The ability to perform multiclass classification is a big advantage for using decision trees and was a highly requested feature for mllib. This pull request adds multiclass classification support to the MLlib decision tree. It also adds sample weights support using WeightedLabeledPoint class for handling unbalanced datasets during classification. It will also support algorithms such as AdaBoost which requires instances to be weighted.
It handles the special case where the categorical variables cannot be ordered for multiclass classification and thus the optimizations used for speeding up binary classification cannot be directly used for multiclass classification with categorical variables. More specifically, for m categories in a categorical feature, it analyses all the ```2^(m-1) - 1``` categorical splits provided that #splits are less than the maxBins provided in the input. This condition will not be met for features with large number of categories -- using decision trees is not recommended for such datasets in general since the categorical features are favored over continuous features. Moreover, the user can use a combination of tricks (increasing bin size of the tree algorithms, use binary encoding for categorical features or use one-vs-all classification strategy) to avoid these constraints.
The new code is accompanied by unit tests and has also been tested on the iris and covtype datasets.
cc: mengxr, etrain, hirakendu, atalwalkar, srowen
Author: Manish Amde <manish9ue@gmail.com>
Author: manishamde <manish9ue@gmail.com>
Author: Evan Sparks <sparks@cs.berkeley.edu>
Closes #886 from manishamde/multiclass and squashes the following commits:
26f8acc [Manish Amde] another attempt at fixing mima
c5b2d04 [Manish Amde] more MIMA fixes
1ce7212 [Manish Amde] change problem filter for mima
10fdd82 [Manish Amde] fixing MIMA excludes
e1c970d [Manish Amde] merged master
abf2901 [Manish Amde] adding classes to MimaExcludes.scala
45e767a [Manish Amde] adding developer api annotation for overriden methods
c8428c4 [Manish Amde] fixing weird multiline bug
afced16 [Manish Amde] removed label weights support
2d85a48 [Manish Amde] minor: fixed scalastyle issues reprise
4e85f2c [Manish Amde] minor: fixed scalastyle issues
b2ae41f [Manish Amde] minor: scalastyle
e4c1321 [Manish Amde] using while loop for regression histograms
d75ac32 [Manish Amde] removed WeightedLabeledPoint from this PR
0fecd38 [Manish Amde] minor: add newline to EOF
2061cf5 [Manish Amde] merged from master
06b1690 [Manish Amde] fixed off-by-one error in bin to split conversion
9cc3e31 [Manish Amde] added implicit conversion import
5c1b2ca [Manish Amde] doc for PointConverter class
485eaae [Manish Amde] implicit conversion from LabeledPoint to WeightedLabeledPoint
3d7f911 [Manish Amde] updated doc
8e44ab8 [Manish Amde] updated doc
adc7315 [Manish Amde] support ordered categorical splits for multiclass classification
e3e8843 [Manish Amde] minor code formatting
23d4268 [Manish Amde] minor: another minor code style
34ee7b9 [Manish Amde] minor: code style
237762d [Manish Amde] renaming functions
12e6d0a [Manish Amde] minor: removing line in doc
9a90c93 [Manish Amde] Merge branch 'master' into multiclass
1892a2c [Manish Amde] tests and use multiclass binaggregate length when atleast one categorical feature is present
f5f6b83 [Manish Amde] multiclass for continous variables
8cfd3b6 [Manish Amde] working for categorical multiclass classification
828ff16 [Manish Amde] added categorical variable test
bce835f [Manish Amde] code cleanup
7e5f08c [Manish Amde] minor doc
1dd2735 [Manish Amde] bin search logic for multiclass
f16a9bb [Manish Amde] fixing while loop
d811425 [Manish Amde] multiclass bin aggregate logic
ab5cb21 [Manish Amde] multiclass logic
d8e4a11 [Manish Amde] sample weights
ed5a2df [Manish Amde] fixed classification requirements
d012be7 [Manish Amde] fixed while loop
18d2835 [Manish Amde] changing default values for num classes
6b912dc [Manish Amde] added numclasses to tree runner, predict logic for multiclass, add multiclass option to train
75f2bfc [Manish Amde] minor code style fix
e547151 [Manish Amde] minor modifications
34549d0 [Manish Amde] fixing error during merge
098e8c5 [Manish Amde] merged master
e006f9d [Manish Amde] changing variable names
5c78e1a [Manish Amde] added multiclass support
6c7af22 [Manish Amde] prepared for multiclass without breaking binary classification
46e06ee [Manish Amde] minor mods
3f85a17 [Manish Amde] tests for multiclass classification
4d5f70c [Manish Amde] added multiclass support for find splits bins
46f909c [Manish Amde] todo for multiclass support
455bea9 [Manish Amde] fixed tests
14aea48 [Manish Amde] changing instance format to weighted labeled point
a1a6e09 [Manish Amde] added weighted point class
968ca9d [Manish Amde] merged master
7fc9545 [Manish Amde] added docs
ce004a1 [Manish Amde] minor formatting
b27ad2c [Manish Amde] formatting
426bb28 [Manish Amde] programming guide blurb
8053fed [Manish Amde] more formatting
5eca9e4 [Manish Amde] grammar
4731cda [Manish Amde] formatting
5e82202 [Manish Amde] added documentation, fixed off by 1 error in max level calculation
cbd9f14 [Manish Amde] modified scala.math to math
dad9652 [Manish Amde] removed unused imports
e0426ee [Manish Amde] renamed parameter
718506b [Manish Amde] added unit test
1517155 [Manish Amde] updated documentation
9dbdabe [Manish Amde] merge from master
719d009 [Manish Amde] updating user documentation
fecf89a [manishamde] Merge pull request #6 from etrain/deep_tree
0287772 [Evan Sparks] Fixing scalastyle issue.
2f1e093 [Manish Amde] minor: added doc for maxMemory parameter
2f6072c [manishamde] Merge pull request #5 from etrain/deep_tree
abc5a23 [Evan Sparks] Parameterizing max memory.
50b143a [Manish Amde] adding support for very deep trees
2014-07-18 17:00:13 -04:00
and A , B \| C 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.
2014-04-22 14:20:47 -04:00
### Stopping rule
The recursive tree construction is stopped at a node when one of the two conditions is met:
2014-05-06 23:07:22 -04:00
1. The node depth is equal to the `maxDepth` training parameter
2014-04-22 14:20:47 -04:00
2. No split candidate leads to an information gain at the node.
2014-05-07 20:08:38 -04:00
### 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.
2014-04-22 14:20:47 -04:00
### Practical limitations
2014-05-07 20:08:38 -04:00
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.
2014-04-22 14:20:47 -04:00
## Examples
### Classification
The example below demonstrates how to load a CSV file, parse it as an RDD of `LabeledPoint` and then
perform classification using a decision tree using Gini impurity as an impurity measure and a
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
// Load and parse the data file
2014-07-13 22:27:43 -04:00
val data = sc.textFile("data/mllib/sample_tree_data.csv")
2014-04-22 14:20:47 -04:00
val parsedData = data.map { line =>
val parts = line.split(',').map(_.toDouble)
LabeledPoint(parts(0), Vectors.dense(parts.tail))
}
// Run training algorithm to build the model
val maxDepth = 5
val model = DecisionTree.train(parsedData, Classification, Gini, maxDepth)
// Evaluate model on training examples and compute training error
val labelAndPreds = parsedData.map { point =>
val prediction = model.predict(point.features)
(point.label, prediction)
}
val trainErr = labelAndPreds.filter(r => r._1 != r._2).count.toDouble / parsedData.count
println("Training Error = " + trainErr)
{% endhighlight %}
< / div >
< / div >
### Regression
The example below demonstrates how to load a CSV file, parse it as an RDD of `LabeledPoint` and then
perform regression using a decision tree using variance as an impurity measure and a maximum tree
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
// Load and parse the data file
2014-07-13 22:27:43 -04:00
val data = sc.textFile("data/mllib/sample_tree_data.csv")
2014-04-22 14:20:47 -04:00
val parsedData = data.map { line =>
val parts = line.split(',').map(_.toDouble)
LabeledPoint(parts(0), Vectors.dense(parts.tail))
}
// Run training algorithm to build the model
val maxDepth = 5
val model = DecisionTree.train(parsedData, Regression, Variance, maxDepth)
// Evaluate model on training examples and compute training error
val valuesAndPreds = parsedData.map { point =>
val prediction = model.predict(point.features)
(point.label, prediction)
}
2014-05-06 23:07:22 -04:00
val MSE = valuesAndPreds.map{ case(v, p) => math.pow((v - p), 2)}.mean()
2014-04-22 14:20:47 -04:00
println("training Mean Squared Error = " + MSE)
{% endhighlight %}
< / div >
< / div >