RACH-Space: Reconstructing Adaptive Convex Hull Space with Applications in Weak Supervision

TL;DR

RACH-Space is a geometrically inspired algorithm for labeling unlabelled data in weak supervision, offering simplicity and robustness without strict assumptions, and showing strong empirical performance.

Contribution

It introduces a novel convex hull-based method for weak supervision that is simple, assumption-free, and bridges geometry with label accuracy analysis.

Findings

Performs well in practice on weakly supervised tasks

Outperforms existing label models in empirical tests

Provides theoretical insights into convex hull relationships

Abstract

We introduce RACH-Space, an algorithm for labelling unlabelled data in weakly supervised learning, given incomplete, noisy information about the labels. RACH-Space offers simplicity in implementation without requiring hard assumptions on data or the sources of weak supervision, and is well suited for practical applications where fully labelled data is not available. Our method is built upon a geometrical interpretation of the space spanned by the set of weak signals. We also analyze the theoretical properties underlying the relationship between the convex hulls in this space and the accuracy of our output labels, bridging geometry with machine learning. Empirical results demonstrate that RACH-Space works well in practice and compares favorably to the best existing label models for weakly supervised learning.