Negative impact of heavy-tailed uncertainty and error distributions on the reliability of calibration statistics for machine learning regression tasks
Average calibration of the (variance-based) prediction uncertainties of machine learning regression tasks can be tested in two ways: one is to estimate the calibration error (CE) as the difference between the mean absolute error (MSE) and the mean variance (MV); the alternative is to compare the mean squared z-scores (ZMS) to 1. The problem is that both approaches might lead to different conclusions, as illustrated in this study for an ensemble of datasets from the recent machine learning uncertainty quantification (ML-UQ) literature. It is shown that the estimation of MV, MSE and their confidence intervals becomes unreliable for heavy-tailed uncertainty and error distributions, which seems to be a frequent feature of ML-UQ datasets. By contrast, the ZMS statistic is less sensitive and offers the most reliable approach in this context, still acknowledging that datasets with heavy-tailed z-scores distributions should be considered with great care. Unfortunately, the same problem is expected to affect also conditional calibrations statistics, such as the popular ENCE, and very likely post-hoc calibration methods based on similar statistics. Several solutions to circumvent the outlined problems are proposed.
Code (1)
Tasks
regressionUncertainty QuantificationSimilar Papers 제목 키워드 기반
Catastrophic Goodhart: regularizing RLHF with KL divergence does not mitigate heavy-tailed reward misspecification
When applying reinforcement learning from human feedback (RLHF), the reward is learned from data and, therefore, always has some error. It is common to mitigate this by regularizing the policy with KL divergence from a b…
Maximum Likelihood Uncertainty Estimation: Robustness to Outliers
We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well…
Depth EstimationMonocular Depth EstimationregressionBest-of-Both-Worlds for Heavy-Tailed Markov Decision Processes
We investigate episodic Markov Decision Processes with heavy-tailed losses (HTMDPs). Existing approaches for HTMDPs are conservative in stochastic environments and lack adaptivity in adversarial regimes. In this work, we…
Robust Offline Reinforcement learning with Heavy-Tailed Rewards
This paper endeavors to augment the robustness of offline reinforcement learning (RL) in scenarios laden with heavy-tailed rewards, a prevalent circumstance in real-world applications. We propose two algorithmic framewor…
Offline RLOff-policy evaluationreinforcement-learningReinforcement Learning+1Stability and Generalization of Nonconvex Optimization with Heavy-Tailed Noise
The empirical evidence indicates that stochastic optimization with heavy-tailed gradient noise is more appropriate to characterize the training of machine learning models than that with standard bounded gradient variance…
Stochastic Optimization