Evaluating High-Order Predictive Distributions in Deep Learning
This addresses a bottleneck in uncertainty estimation for decision-making in supervised learning, particularly for high-dimensional inputs, but is incremental as it builds on prior work on predictive distributions.
The paper tackles the problem of evaluating joint predictive distributions in high-dimensional settings, showing that existing methods become impractical as input dimension increases, and introduces dyadic sampling to efficiently distinguish agents on both simple and complex data.
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive distributions with inputs sampled i.i.d. from the testing distribution. With low-dimensional inputs, these methods distinguish agents that effectively estimate uncertainty from those that do not. We establish that the predictive distribution order required for such differentiation increases greatly with input dimension, rendering these methods impractical. To accommodate high-dimensional inputs, we introduce \textit{dyadic sampling}, which focuses on predictive distributions associated with random \textit{pairs} of inputs. We demonstrate that this approach efficiently distinguishes agents in high-dimensional examples involving simple logistic regression as well as complex synthetic and empirical data.