On the Interpretability of Conditional Probability Estimates in the Agnostic Setting
This work addresses the problem of ensuring reliable probability estimates for decision-making in machine learning, particularly in agnostic scenarios, though it appears incremental as it builds on existing calibration concepts.
The paper tackles the interpretability of conditional probability estimates in binary classification under the agnostic setting, where estimates may not reflect true probabilities but have a calibration property. It defines a novel measure for this property, proves uniform convergence, and provides formal justification and new insights for using Bayes Decision Theory in cost-sensitive decisions.
We study the interpretability of conditional probability estimates for binary classification under the agnostic setting or scenario. Under the agnostic setting, conditional probability estimates do not necessarily reflect the true conditional probabilities. Instead, they have a certain calibration property: among all data points that the classifier has predicted P(Y = 1|X) = p, p portion of them actually have label Y = 1. For cost-sensitive decision problems, this calibration property provides adequate support for us to use Bayes Decision Theory. In this paper, we define a novel measure for the calibration property together with its empirical counterpart, and prove an uniform convergence result between them. This new measure enables us to formally justify the calibration property of conditional probability estimations, and provides new insights on the problem of estimating and calibrating conditional probabilities.