Details

Improvement

Status: Resolved

Major

Resolution: Incomplete

None

None
Description
Summary
Currently, data are partitioned by row/instance for DecisionTree and RandomForest. This JIRA argues for partitioning by feature for training deep trees. This is especially relevant for random forests, which are often trained to be deeper than single decision trees.
Details
Dataset dimensions and the depth of the tree to be trained are the main problem parameters determining whether it is better to partition features or instances. For random forests (training many deep trees), partitioning features could be much better.
Notation:
 P = # workers
 N = # instances
 M = # features
 D = depth of tree
Partitioning Features
Algorithm sketch:
 Each worker stores:
 a subset of columns (i.e., a subset of features). If a worker stores feature j, then the worker stores the feature value for all instances (i.e., the whole column).
 all labels
 Train one level at a time.
 Invariants:
 Each worker stores a mapping: instance → node in current level
 On each iteration:
 Each worker: For each node in level, compute (best feature to split, info gain).
 Reduce (P x M) values to M values to find best split for each node.
 Workers who have features used in best splits communicate left/right for relevant instances. Gather total of N bits to master, then broadcast.
 Total communication:
 Depth D iterations
 On each iteration, reduce to M values (~8 bytes each), broadcast N values (1 bit each).
 Estimate: D * (M * 8 + N)
Partitioning Instances
Algorithm sketch:
 Train one group of nodes at a time.
 Invariants:
 Each worker stores a mapping: instance → node
 On each iteration:
 Each worker: For each instance, add to aggregate statistics.
 Aggregate is of size (# nodes in group) x M x (# bins) x (# classes)
 (“# classes” is for classification. 3 for regression)
 Reduce aggregate.
 Master chooses best split for each node in group and broadcasts.
 Local training: Once all instances for a node fit on one machine, it can be best to shuffle data and training subtrees locally. This can mean shuffling the entire dataset for each tree trained.
 Summing over all iterations, reduce to total of:
 (# nodes in tree) x M x (# bins B) x (# classes C) values (~8 bytes each)
 Estimate: 2^D * M * B * C * 8
Comparing Partitioning Methods
Partitioning features cost < partitioning instances cost when:
 D * (M * 8 + N) < 2^D * M * B * C * 8
 D * N < 2^D * M * B * C * 8 (assuming D * M * 8 is small compared to the right hand side)
 N < [ 2^D * M * B * C * 8 ] / D
Example: many instances:
 2 million instances, 3500 features, 100 bins, 5 classes, 6 levels (depth = 5)
 Partitioning features: 6 * ( 3500 * 8 + 2*10^6 ) =~ 1.2 * 10^7
 Partitioning instances: 32 * 3500 * 100 * 5 * 8 =~ 4.5 * 10^8
Attachments
Issue Links
 is blocked by

SPARK4285 Transpose RDD[Vector] to column store for ML
 Resolved
 Is contained by

SPARK14045 DecisionTree improvement umbrella
 Resolved
1.

Transpose RDD[Vector] to column store for ML  Resolved  Unassigned 