Conformal prediction (CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick (PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provides extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques.

Modern data analysis increasingly requires flexible conditional inference P(X_B | X_A) where (X_A, X_B) is an arbitrary partition of observed variable X. Existing conditional inference methods lack this flexibility as they are tied to a fixed conditioning structure and cannot perform new conditional inference once trained. To solve this, we propose a Bayesian generative modeling (BGM) approach for arbitrary conditional inference without retraining. BGM learns a generative model of X through an iterative Bayesian updating algorithm where model parameters and latent variables are updated until convergence. Once trained, any conditional distribution can be obtained without retraining. Empirically, BGM achieves superior prediction performance with well calibrated predictive intervals, demonstrating that a single learned model can serve as a universal engine for conditional prediction with uncertainty quantification. We provide theoretical guarantees for the convergence of the stochastic iterative algorithm, statistical consistency and conditional-risk bounds. The proposed BGM framework leverages the power of AI to capture complex relationships among variables while adhering to Bayesian principles, emerging as a promising framework for advancing various applications in modern data science. The code for BGM is freely available at https://github.com/liuq-lab/bayesgm.

This paper introduces a boosted conformal procedure designed to tailor conformalized prediction intervals toward specific desired properties, such as enhanced conditional coverage or reduced interval length. We employ machine learning techniques, notably gradient boosting, to systematically improve upon a predefined conformity score function. This process is guided by carefully constructed loss functions that measure the deviation of prediction intervals from the targeted properties. The procedure operates post-training, relying solely on model predictions and without modifying the trained model (e.g., the deep network). Systematic experiments demonstrate that starting from conventional conformal methods, our boosted procedure achieves substantial improvements in reducing interval length and decreasing deviation from target conditional coverage.

Large language models (LLMs) are increasingly used as evaluators in lieu of humans. While scalable, their judgments are noisy due to imperfect specificity and sensitivity of LLMs, leading to biased accuracy estimates. Although bias-correction methods exist, they are underutilized in LLM research and typically assume exact knowledge of the model's specificity and sensitivity. Furthermore, in general we only have estimates of these values and it is not well known how to properly construct confidence intervals using only estimates. This work presents a simple plug-in framework that corrects such bias and constructs confidence intervals reflecting uncertainty from both test and calibration dataset, enabling practical and statistically sound LLM-based evaluation. Additionally, to reduce uncertainty in the accuracy estimate, we introduce an adaptive algorithm that efficiently allocates calibration sample sizes.

Online conformal prediction (OCP) wraps around any pre-trained predictor to produce prediction sets with coverage guarantees that hold irrespective of temporal dependencies or distribution shifts. However, standard OCP faces two key limitations: it operates in the output space using simple nonconformity (NC) scores, and it treats all historical observations uniformly when estimating quantiles. This paper introduces attention-based feature OCP (AFOCP), which addresses both limitations through two key innovations. First, AFOCP operates in the feature space of pre-trained neural networks, leveraging learned representations to construct more compact prediction sets by concentrating on task-relevant information while suppressing nuisance variation. Second, AFOCP incorporates an attention mechanism that adaptively weights historical observations based on their relevance to the current test point, effectively handling non-stationarity and distribution shifts. We provide theoretical guarantees showing that AFOCP maintains long-term coverage while provably achieving smaller prediction intervals than standard OCP under mild regularity conditions. Extensive experiments on synthetic and real-world time series datasets demonstrate that AFOCP consistently reduces the size of prediction intervals by as much as $88\%$ as compared to OCP, while maintaining target coverage levels, validating the benefits of both feature-space calibration and attention-based adaptive weighting.

General-purpose foundation models for neural time series can help accelerate neuroscientific discoveries and enable applications such as brain computer interfaces (BCIs). A key component in scaling these models is population-level representation learning, which leverages information across channels to capture spatial as well as temporal structure. Population-level approaches have recently shown that such representations can be both efficient to learn on top of pretrained temporal encoders and produce useful representations for decoding a variety of downstream tasks. However, these models remain sensitive to mismatches in preprocessing, particularly on time-scales, between pretraining and downstream settings. We systematically examine how time-scale mismatches affects generalization and find that existing representations lack invariance. To address this, we introduce Time-scale Augmented Pretraining (TSAP), which consistently improves robustness to different time-scales across decoding tasks and builds invariance in the representation space. These results highlight handling preprocessing diversity as a key step toward building generalizable neural foundation models.

This paper introduces a boosted conformal procedure designed to tailor confor-malized prediction intervals toward specific desired properties, such as enhanced conditional coverage or reduced interval length. We employ machine learning techniques, notably gradient boosting, to systematically improve upon a predefined conformity score function. This process is guided by carefully constructed loss functions that measure the deviation of prediction intervals from the targeted properties. The procedure operates post-training, relying solely on model predictions and without modifying the trained model (e.g., the deep network). Systematic experiments demonstrate that starting from conventional conformal methods, our boosted procedure achieves substantial improvements in reducing interval length and decreasing deviation from target conditional coverage.

Conformal Prediction (CP) is a distribution-free framework for constructing statistically rigorous prediction sets. While popular variants such as CD-split improve CP's efficiency, they often yield prediction sets composed of multiple disconnected subintervals, which are difficult to interpret. In this paper, we propose SCD-split, which incorporates smoothing operations into the CP framework. Such smoothing operations potentially help merge the subintervals, thus leading to interpretable prediction sets. Experimental results on both synthetic and real-world datasets demonstrate that SCD-split balances the interval length and the number of disconnected subintervals. Theoretically, under specific conditions, SCD-split provably reduces the number of disconnected subintervals while maintaining comparable coverage guarantees and interval length compared with CD-split.