We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables. Our approach builds on conformal prediction, a powerful framework to construct prediction sets that are valid under the i.i.d assumption. Importantly, naively applying conformal prediction does not provide reliable predictions in this setting, due to the distribution shift induced by the corruptions. To account for the distribution shift, we assume access to privileged information (PI). The PI is formulated as additional features that explain the distribution shift, however, they are only available during training and absent at test time.We approach this problem by introducing a novel generalization of weighted conformal prediction and support our method with theoretical coverage guarantees. Empirical experiments on both real and synthetic datasets indicate that our approach achieves a valid coverage rate and constructs more informative predictions compared to existing methods, which are not supported by theoretical guarantees.

We study fair machine learning (ML) under predictive uncertainty to enable reliable and trustworthy decision-making. The seminal work of'equalized coverage' proposed an uncertainty-aware fairness notion. However, it does not guarantee equal coverage rates across more fine-grained groups (e.g., low-income females) conditioning on the true label and is biased in the assessment of uncertainty. To tackle these limitations, we propose a new uncertainty-aware fairness -- Equal Opportunity of Coverage (EOC) -- that aims to achieve two properties: (1) coverage rates for different groups with similar outcomes are close, and (2) the coverage rate for the entire population remains at a predetermined level. Further, the prediction intervals should be narrow to be informative. We propose Binned Fair Quantile Regression (BFQR), a distribution-free post-processing method to improve EOC with reasonable width for any trained ML models. It first calibrates a hold-out set to bound deviation from EOC, then leverages conformal prediction to maintain EOC on a test set, meanwhile optimizing prediction interval width. Experimental results demonstrate the effectiveness of our method in improving EOC.

Autonomous aerial vehicles (AAVs) have played a pivotal role in coverage operations and search missions. Recent advances in large language models (LLMs) offer promising opportunities to augment AAV intelligence. These advances help address complex challenges like area coverage optimization, dynamic path planning, and adaptive decision-making. However, the absence of physical grounding in LLMs leads to hallucination and reproducibility problems in spatial reasoning and decision-making. To tackle these issues, we present Skypilot, an LLM-enhanced two-stage framework that grounds language models in physical reality by integrating monte carlo tree search (MCTS). In the first stage, we introduce a diversified action space that encompasses generate, regenerate, fine-tune, and evaluate operations, coupled with physics-informed reward functions to ensure trajectory feasibility. In the second stage, we fine-tune Qwen3-4B on 23,000 MCTS-generated samples, achieving substantial inference acceleration while maintaining solution quality. Extensive numerical simulations and real-world flight experiments validate the efficiency and superiority of our proposed approach. Detailed information and experimental results are accessible at https://sky-pilot.top.

We develop a method to generate prediction sets with a guaranteed coverage rate that is robust to corruptions in the training data, such as missing or noisy variables.

The inequality trivially holds for α 0. 5, so we only focus on the case when α < 0. 5. If the nonconformity score's rank has no temporal dependence, we have Remarks The alternative update rule in Eq. 37 is not just used to prove Theorem 4.4. This is because Eq. 37 does not become more conservative on average Note that with Eq. 9, we have a T α + α + γ γT (47) By taking the limit of both sides, we are done. The task is to predict the (allowed) claim amount for the next visit. It has hourly temperature and electricity load data for one utility.

We give both theory and an extensive set of empirical evaluations.