Adaptive Conformal Inference by Betting (2412.19318v1)

Abstract: Conformal prediction is a valuable tool for quantifying predictive uncertainty of machine learning models. However, its applicability relies on the assumption of data exchangeability, a condition which is often not met in real-world scenarios. In this paper, we consider the problem of adaptive conformal inference without any assumptions about the data generating process. Existing approaches for adaptive conformal inference are based on optimizing the pinball loss using variants of online gradient descent. A notable shortcoming of such approaches is in their explicit dependence on and sensitivity to the choice of the learning rates. In this paper, we propose a different approach for adaptive conformal inference that leverages parameter-free online convex optimization techniques. We prove that our method controls long-term miscoverage frequency at a nominal level and demonstrate its convincing empirical performance without any need of performing cumbersome parameter tuning.

• The paper introduces a parameter-free approach for conformal inference that eliminates the need for hyperparameter tuning.
• It leverages coin betting strategies to adaptively adjust prediction intervals in online settings with non-exchangeable data.
• Empirical tests demonstrate robust coverage with sub-linear regret, offering competitive performance against tuned methods.

Adaptive Conformal Inference by Betting: A Parameter-Free Approach

The paper "Adaptive Conformal Inference by Betting" addresses the challenge of producing reliable predictive uncertainty estimates for machine learning models in non-exchangeable data environments. The authors introduce a novel, parameter-free method for adaptive conformal inference that circumvents the hyperparameter sensitivity issues present in previous methodologies. This approach leverages parameter-free optimization techniques, particularly those grounded in coin betting, to adaptively calibrate prediction intervals in an online setting.

Problem Context

Traditional conformal predictors assume exchangeability in the data, which may not hold in many real-world applications, such as time-series analysis or scenarios involving distribution shifts. To address this, adaptive conformal inference techniques have been developed that optimize the pinball loss via online gradient methods. However, these methods require careful calibration of hyperparameters like the learning rate, which can introduce performance variability and complicate the tuning process.

Proposed Methodology

The authors propose a parameter-free approach for adaptive conformal inference by employing coin-betting algorithms. The primary goal is to construct prediction sets with long-term miscoverage rates aligning with a desired nominal level (denoted by α), without assumptions about the data generating process. The approach produces prediction intervals by dynamically adjusting a parameter (radius) without the need for pre-specified learning rates or grids thereof.

Key to this method is the framing of conformal inference as a quantile learning problem addressed through pinball loss optimization. By optimizing quantiles of prediction errors online, the method adjusts prediction intervals to maintain coverage rates at α. The coin-betting strategy ensures sub-linear regret bounds, guaranteeing competitive performance relative to any fixed prediction interval.

Theoretical Contributions

The authors derive theoretical guarantees for their method, demonstrating that the long-term miscoverage rate converges to the nominal level given bounded nonconformity scores. The approach’s robustness in maintaining desired coverage without manual tuning distinguishes it from previous gradient-based methods, which often require extensive parameter tuning to achieve similar reliability.

Empirical Evaluation

Experimental results confirm the efficacy of the proposed method across various settings, including changepoint detection scenarios and time series forecasting. The method's performance closely aligns with optimally tuned online gradient descent (OGD) methods, yet it offers the advantage of tuning-free implementation. This empirical validation covers both synthetic data and real-world datasets, showcasing the method’s adaptability to different data dynamics.

Implications and Future Directions

This work holds significant practical implications for using machine learning in dynamic and uncertain environments where data distributions may change over time. The parameter-free nature of this approach simplifies deployment in real-world applications, potentially reducing overhead in model maintenance and adaptation.

In future developments, this methodology could be extended to settings involving multivariate response models or complex data structures, such as graph-based data or reinforced learning contexts. Additionally, exploring the integration of this parameter-free conformal inference with deep learning models could yield further insights into scaling the technique for highly non-linear and high-dimensional data.

Conclusion

The paper presents a substantial advancement in conformal prediction methodology by proposing a parameter-free adaptive approach. This method eliminates the need for cumbersome hyperparameter tuning while ensuring robust uncertainty quantification, thus enhancing the applicability of conformal predictions in diverse and challenging data environments.