Approximation to Object Conditional Validity with Inductive Conformal Predictors
This work addresses the need for more reliable prediction intervals in machine learning, particularly for applications requiring conditional guarantees, though it is incremental as it focuses on approximation rather than full conditional validity.
The paper tackles the problem of achieving conditional validity in conformal predictors, which is impossible for finite samples, by introducing a new algorithm that iteratively adjusts a conformity measure to approximate object conditional validity. Experimental results on three datasets show the algorithm effectively alleviates the lack of conditional validity in real-world tasks.
Conformal predictors are machine learning algorithms that output prediction sets that have a guarantee of marginal validity for finite samples with minimal distributional assumptions. This is a property that makes conformal predictors useful for machine learning tasks where we require reliable predictions. It would also be desirable to achieve conditional validity in the same setting, in the sense that validity of the prediction intervals remains valid regardless of conditioning on any particular property of the object of the prediction. Unfortunately, it has been shown that such conditional validity is impossible to guarantee for non-trivial prediction problems for finite samples. In this article, instead of trying to achieve a strong conditional validity result, the weaker goal of achieving an approximation to conditional validity is considered. A new algorithm is introduced to do this by iteratively adjusting a conformity measure to deviations from object conditional validity measured in the training data. Along with some theoretical results, experimental results are provided for three data sets that demonstrate (1) in real world machine learning tasks, lack of conditional validity is a measurable problem and (2) that the proposed algorithm is effective at alleviating this problem.