More Supervision, Less Computation: Statistical-Computational Tradeoffs in Weakly Supervised Learning
This work addresses the trade-offs between supervision and computation in weakly supervised learning, providing theoretical insights for researchers in machine learning and statistics, though it is incremental in nature.
The paper tackles the weakly supervised binary classification problem with randomly flipped labels, establishing how statistical accuracy and computational efficiency depend on the degree of supervision quantified by α. It shows that increased supervision (higher α) not only improves optimal statistical accuracy but also narrows the computational gap for achieving it.
We consider the weakly supervised binary classification problem where the labels are randomly flipped with probability $1- α$. Although there exist numerous algorithms for this problem, it remains theoretically unexplored how the statistical accuracies and computational efficiency of these algorithms depend on the degree of supervision, which is quantified by $α$. In this paper, we characterize the effect of $α$ by establishing the information-theoretic and computational boundaries, namely, the minimax-optimal statistical accuracy that can be achieved by all algorithms, and polynomial-time algorithms under an oracle computational model. For small $α$, our result shows a gap between these two boundaries, which represents the computational price of achieving the information-theoretic boundary due to the lack of supervision. Interestingly, we also show that this gap narrows as $α$ increases. In other words, having more supervision, i.e., more correct labels, not only improves the optimal statistical accuracy as expected, but also enhances the computational efficiency for achieving such accuracy.