Asymmetric conformal prediction with penalized kernel sum-of-squares

Conformal prediction (CP) is a distribution-free method to construct reliable prediction intervals that has gained significant attention in recent years. Despite its success and various proposed extensions, a significant practical feature which has been overlooked in previous research is the potential skewed nature of the noise, or of the residuals when the predictive model exhibits bias. In this work, we leverage recent developments in CP to propose a new asymmetric procedure that bridges the gap between skewed and non-skewed noise distributions, while still maintaining adaptivity of the prediction intervals. We introduce a new statistical learning problem to construct adaptive and asymmetric prediction bands, with a unique feature based on a penalty which promotes symmetry: when the penalty intensity varies, the intervals smoothly change from symmetric to asymmetric ones. This statistical learning problem is based on reproducing kernel Hilbert spaces and the recently introduced kernel sum-of-squares framework. First, we establish representer theorems to make our problem tractable in practice, and derive dual formulations which are essential for scalability to larger datasets. Second, the intensity of the penalty is chosen using a novel data-driven method which automatically identifies the symmetric nature of the noise. We show that consenting to some asymmetry can let the learned prediction bands better adapt to small sample regimes, outliers or biased predictive models. Finally, our experiments illustrate the efficiency of such penalized kernel sum-of-squares to construct adaptive prediction bands.

Machine learning models usually output a single prediction, for instance tomorrow's temperature will be 15°C. In many applications, we also need a range of plausible values, for example "between 14°C and 16°C with 90% probability". Building such ranges with mathematical guarantees is well-studied, but most existing methods assume the uncertainty is symmetric around the prediction. Often it isn't: if a heat spike is more plausible than a cold front, [14°C, 18°C] is more honest than [13°C, 17°C], even though the best guess remains 15°C. Existing methods commit to either symmetric or asymmetric ranges from the start, without checking which the data actually needs. We propose a new method that smoothly interpolates between the two and automatically detects, from the data alone, how asymmetric the range should be. Surprisingly, even when the data is symmetric, allowing a small amount of asymmetry can produce tighter and more reliable ranges, especially when training data is scarce or the underlying prediction model is biased. The result is tighter, more faithful uncertainty estimates. This is especially valuable in high-stakes applications, where decisions rely on knowing how wrong a prediction could be.