Title: Sketching Linear Classifiers over Data Streams,
Abstract: We introduce a new sub-linear space sketch---the Weight-Median Sketch---for
learning compressed linear classifiers over data streams while supporting the
efficient recovery of large-magnitude weights in the model. This enables
memory-limited execution of several statistical analyses over streams,
including online feature selection, streaming data explanation, relative
deltoid detection, and streaming estimation of pointwise mutual information.
Unlike related sketches that capture the most frequently-occurring features (or
items) in a data stream, the Weight-Median Sketch captures the features that
are most discriminative of one stream (or class) compared to another. The
Weight-Median Sketch adopts the core data structure used in the Count-Sketch,
but, instead of sketching counts, it captures sketched gradient updates to the
model parameters. We provide a theoretical analysis that establishes recovery
guarantees for batch and online learning, and demonstrate empirical
improvements in memory-accuracy trade-offs over alternative memory-budgeted
methods, including count-based sketches and feature hashing.