Prediction under label shift becomes nonstandard when responses are censored. In a two-sided censored Gaussian model, latent values below $L$ and above $U$ are recorded at the boundary values, so the observed predictive distribution is mixed, with atoms at $L$ and $U$ and a continuous density on $(L,U)$. In this paper we develop conformal Bayes for this mixed-space setting by combining posterior predictive tilting with weighted conformal calibration. Under a two-sided Tobit Gaussian Bayesian prediction head with a Laplace posterior approximation, the tilted predictive distribution has left-atom, interior, and right-atom components, with a three-term closed-form normalizer. The resulting prediction set is a mixed highest density region that can combine boundary atoms with an interior interval and can reduce to atom-only sets under strong censoring. The main technical issue is that latent label shift does not directly give an ordinary density ratio on the observed censored scale. A latent exponential tilt induces tail-averaged atom weights at the censored boundaries, while the interior ratio remains density based. This yields a mixed observed-space calibration weight with two atom ratios and one interior density ratio. The weight corrects the calibration measure, while predictive tilting gives target-adapted mixed-HDR geometry. Synthetic experiments show that weighted tilted conformal Bayes restores marginal coverage with smaller sets than weighted source-score calibration, while revealing a trade-off between marginal coverage and component-wise behavior across atoms and interior observations.

Aqueous solubility is a key property in early-stage drug discovery, but most predictive models merge physicochemical descriptors and molecular graph information into a single representation, obscuring whether a prediction is driven by global chemistry, molecular structure, or both. We present an additive deep-learning framework that keeps these two sources of information separate throughout training: physicochemical descriptors are encoded by a multilayer perceptron (the chemical branch) and molecular graph topology by a graph neural network (the structural branch), with the two outputs combined only at the prediction stage through an additive model with an optional multiplicative interaction. This design provides a direct decomposition of chemical and structural components that can be examined separately after training. Furthermore, pretraining on the larger AqSolDB dataset and fine-tuning on the smaller BigSolDB2 dataset substantially improve accuracy and reduce run-to-run variations, indicating generalizability of the learned features from the data-rich settings. We further interpret the fitted model using best linear projections of the branch outputs, molecule-level embedding summaries across solubility classes, and atom-level GNNExplainer masks aggregated over functional groups. These analyses show that the chemical branch aligns with familiar physicochemical descriptors, while the structural branch captures graph-topological and functional-group patterns associated with solubility. Across both datasets, the framework attains competitive predictive performance while making the distinct roles of chemical and structural information more transparent.

Knowing which training examples drive outputs is fundamental to auditing, correcting, and understanding language models, yet for modern LLMs this remains expensive, approximate, and largely post-hoc. Standard language models generate tokens through a dense network pathway, causing training data's influence to be distributed across parameters rather than organized along explicit, traceable components. We introduce a prototype language model architecture, Prototypes for Interpretable Sequence Modeling (PRISM), that forms each prediction via a sparse, non-negative mixture of learned prototypes, trained with clustering objectives that anchor each prototype to coherent neighborhoods of training examples. Across architectures from 130M to 1.6B parameters trained on up to 50B tokens, prototype language models either surpass or remain within 2.5 percentage points on average downstream accuracy of matched dense baselines. We show that sparse prototype structure localizes curvature in the loss landscape, yielding a more tractable Hessian and enabling training data attribution that is ~500x faster than post hoc baselines when consuming equivalent memory. Calibrating linear prototype controllers can improve downstream accuracy by roughly 3 points while tracing those corrections back to training neighborhoods, and targeted prototype suppression can remove model behaviors without finetuning or measurable loss in generation quality.

Safety classifiers deployed in production operate under a stationarity assumption that fails silently: when input distributions drift, accuracy degrades with no error signal until ground-truth labels arrive. We present an online monitor that detects distributional shift in classifier scores via a sliding-window KS statistic with empirically calibrated alarm thresholds. In a pre-registered factorial evaluation (4 classifiers $\times$ 5 shift conditions $\times$ 20 seeds $\times$ 2 window sizes; 800 cells), the monitor achieves 86.6% valid detection (mean latency 39.5 steps) across synthetic-onset, real-jailbreak, and adversarial regimes; a classifier $\times$ shift interaction ($η^2 = 0.185$) shows that monitoring must be tuned per classifier. Attempting to recover post-detection coverage via weighted conformal prediction exposes a failure mode: density-ratio estimation collapses for generative classifiers because logistic regression separates source from target perfectly in 3584-4096-dimensional embedding space, clipping all importance weights to zero; projecting to $\leq 32$ dimensions restores coverage. We then extend the framework to gradient-based evasion and give the first threat-model characterisation of score-disagreement monitoring as a canary. We falsify three assumptions: that architectural diversity drives the signal (false, $η^2 = 0.011$), that it is generic out-of-distribution detection (false, GCG-specific, $p < 10^{-12}$), and that an adaptive attacker can suppress it (false while the canary is confident). We derive the exact security boundary, a confidence-gated equilibrium at which a monitor-aware attacker stalls at gap $= 1/(2λ)$, and provide a calibration-free scan martingale achieving false-alarm rate $\leq 1\%$ across all classifiers with no per-model tuning.

While conformal prediction provides a general framework for uncertainty quantification in predictive inference, its application is often limited by computational cost. Recent methods, including Jackknife+ and Jackknife-minmax, achieve faster computation by trading a slight loss of efficiency relative to full conformal prediction, but still requires computing leave-one-out refits for all observations. In this paper, we further accelerate conformal prediction by incorporating approximate leave-one-out (ALO) estimators, and establish asymptotic coverage and efficiency. While our proof draws on methods developed for analyzing the consistency of ALO cross-validation risk estimators in high-dimensional statistics, it requires adaptations to handle conformal prediction, where leave-$i$-out residuals are needed for predictions at $x_{n+1}$ rather than just at the training covariate $x_i$. Simulation results validate our theoretical findings, showing that the ALO-based methods achieve coverage and efficiency comparable to the exact methods, while significantly reducing the runtime.

Conformal prediction and its variants, including the split conformal prediction, provide a distribution-free framework for uncertainty quantification by constructing prediction intervals or sets with finite-sample coverage guarantees. The statistical efficiency of these intervals depends critically on how the data are split into training and calibration samples. Despite its practical importance, a principled characterization of the training-calibration split that minimizes prediction interval length while maintaining coverage has remained largely unresolved. In this paper, we develop a theoretical framework for optimal data splitting in split conformal prediction. We first analyze the problem in a general setting and derive analytical characterizations of the length-optimal split ratio under both symmetric and asymmetric regimes. We then show how the general results specialize to several commonly used regression settings, including linear regression, nonparametric regression, and neural networks, thereby demonstrating the scope of the framework. We also describe a data-based method for selecting the optimal proportion. Our analysis clarifies how model-related features govern the optimal allocation of samples between training and calibration and provides principled guidance for constructing shorter prediction intervals. Experiments on both synthetic and real-world datasets demonstrate the applicability of the proposed methodology across a variety of practical scenarios.

Prediction sets should have high coverage to be useful, but some coverage notions are more practically relevant than others. In the classification setting, class-conditional coverage requires that the prediction set (i.e., the set of candidate labels for a new test point) must achieve the target accuracy level within each class, which may be challenging to satisfy when many classes are rare and have few calibration points. At the other extreme, marginal coverage requires only that coverage holds on average over the distribution of all classes, which can lead to low-probability labels being essentially ignored. To find a middle ground, recent work has introduced macro-coverage, defined as the unweighted average of class-conditional coverages. Macro-coverage offers a compromise between marginal coverage and class-conditional coverage that is particularly appropriate for long-tailed settings. In this work, we show that label-weighted conformal prediction can be used to produce prediction sets with a finite-sample macro-coverage guarantee, and more generally a guarantee on a family of generalized macro-coverage objectives that aggregate coverage at the level of arbitrary class groupings and take a weighted average. We further characterize the form of the smallest prediction sets satisfying a given generalized macro-coverage objective and propose a corresponding conformal score function. We validate our theoretical results on two large-scale image classification datasets.

Predictive models are increasingly embedded in operational decision-making, yet standard explanation methods typically explain forecasts rather than the decisions those forecasts induce. This distinction is important in predict-then-optimize systems: large forecast changes may leave the optimizer's action unchanged, while small changes can alter the selected decision and its realized value. We propose Decision Value Attribution (DVA), a Shapley-based framework for attributing the value of a fixed prediction--optimization pipeline. The framework defines cooperative games whose payoff is the downstream decision value, allowing the players to be information sources, optimization or design parameters, or both. We present three variants: InfoDVA attributes value to features, DesignDVA attributes value to operational configurations, and Decision-Value Interactions (DVI) quantifies how information and design jointly create value. We further distinguish post-DVA, which evaluates decisions using realized outcomes, from pre-DVA, which evaluates decisions under the model's full prediction. This separation turns attribution into a decision-level diagnostic of whether the model's operational beliefs align with realized performance. The resulting attributions are expressed in the units of the operational objective and decompose the gain or loss relative to a baseline. Case studies in electricity storage arbitrage and emergency medical service coverage show that predictive explanations can be poor proxies for operational value, that DVA can guide targeted information-control interventions, and that optimization configurations determine when predictive information is decision-relevant.

Predicting the aerodynamic performance (e.g. lift, drag, and moment coefficients) of an aircraft is challenging -- computational models are biased and direct simulations are prohibitive. A pragmatic way to overcome this limitation is by calibrating low-fidelity computational predictions with experimental measurements. This, however, requires calibrating against \emph{sparse} measurements contaminated with \emph{uncertainty} in both the control inputs and the measured aerodynamic response. We develop a methodology to address this problem based on Gaussian process surrogates and the classical Kennedy-O'Hagan calibration. A surrogate model learned on abundant-but-cheap low-fidelity data is calibrated with a sparse set of measurement data. Crucialy, we develop a Bayesian latent Gaussian process based approach that marginalizes the calibrated surrogate model over the input uncertainty, while also matching the marginal mean and variance of the measured output uncertainty. Once calibrated, our surrogate model predicts the uncertainty in aerodynamic coefficients with very high accuracy, including at extrapolative input settings. We validate our calibrated surrogate model predictions against measurement data with \emph{true} uncertainty intervals to demonstrate that the model places $94.2-95.8\%$ of its predictive samples inside the released $95\%$ truth intervals, with endpoint cumulative probabilities very close to the nominal 0.025 and 0.975 levels.

This work presents a new bidirectional autoregressive latent diffusion approach for predicting the evolution of multiple fields (mass density, pressure, velocity, and magnetic field components) for magnetohydrodynamics. We show that this bidirectional flow can be used as a self-supervised consistency metric for uncertainty and error estimation, which enables the model to estimate test-time uncertainty and error without access to ground truth, by comparing how closely flowing forwards and backwards in time returns to the same predicted fields. We also demonstrate this methods's potential to serve as a non-invasive plasma diagnostic, and show how adaptive feedback can be used to make the model more robust based on sparse diagnostics or limited views/measurements.