Probabilistic Conformal Prediction with Approximate Conditional Validity
This work addresses the need for more reliable statistical inference in applications requiring conditional coverage, representing an incremental improvement over existing conformal prediction methods.
The paper tackles the problem of generating prediction sets with only marginal coverage guarantees by developing a method that achieves approximately conditional coverage, crucial for practical applications, and shows through simulations that it consistently outperforms existing approaches in conditional coverage.
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and probabilistic conformal prediction, usually provide only a marginal coverage guarantee. In contrast, our approach extends these frameworks to achieve approximately conditional coverage, which is crucial for many practical applications. Our prediction sets adapt to the behavior of the predictive distribution, making them effective even under high heteroscedasticity. While exact conditional guarantees are infeasible without assumptions on the underlying data distribution, we derive non-asymptotic bounds that depend on the total variation distance of the conditional distribution and its estimate. Using extensive simulations, we show that our method consistently outperforms existing approaches in terms of conditional coverage, leading to more reliable statistical inference in a variety of applications.