Decision Tree Induction in Hierarchic Distributed Systems With: Amir Bar-Or, Ran Wolff, Daniel Keren

Motivation Large distributed computation is costly Especially data intensive and synchronization intensive ones; e.g., data mining Decision tree induction: –Collect global statistics (thousands) for every attribute (thousands) in every tree node (hundreds) –Global statistics – global synchronization

Motivation Hierarchy Helps Simplifies synchronization –Synchronize on each level Simplifies communication An “industrial strength” architecture –The way real systems (including grids) are often organized

Motivation Mining highly dimensional data Thousands of sources Central control Examples: –Genomically enriched healthcare data –Text repositories

Objectives of the Algorithm Exact results –Common approaches would either Collect a sample of the data Build independent models at each site and then use centralized meta-learning atop of them Communication efficiency –Naive approach: collect exact statistics for each tree node would result in GBytes of communication

Decision tree in a Teaspoon A tree were at each level the learning samples are splitted according to one attribute’s value Hill-climbing heuristic is used to induce the tree –The attribute that maximized a gain function is taken –Gain functions: Gini or Information Gain No real need to compute the gain

Main Idea Infer deterministic bounds on the gain of each attribute Improve bounds until best attribute is provenly better than the rest Communication efficiency is achieved because bounds require just limited data –Partial statistics for promising attributes –Rough bound on irrelevant attributes

Hierarchical Algorithm At each level of the hierarchy –Wait for reports from all descendants Contain upper and lower bounds on the gain of each attribute, number of samples from each class –Use descendant's report to compute cumulative bounds –If no clear separation, request descendants to tighten bounds by sending more data –At worst, all data is gathered

Deterministic Bounds Upper bound Lower bound

Performance Figures 99% reduction in communication bandwidth Out of 1000 SNP, only ~12 were reported to higher levels of the hierarchy Percent declines with hierarchy level

Performance Figures 99% reduction in communication bandwidth Out of 1000 SNP, only ~12 were reported to higher levels of the hierarchy Percent declines with hierarchy level

More Performance Figures Larger datasets require lower bandwidth Outlier noise is not a big issue –White noise even better

More Performance Figures Larger datasets require lower bandwidth Outlier noise is not a big issue –White noise even better

Future Work Text mining Incremental algorithm Accommodation of failure Testing on a real grid system Is this a general framework?