We study models for human-AI teaming through the lens of statistical calibration. We assume the team consists of an AI model and human -- both of which are calibrated with respect to some partitioning of the feature space -- and expose how the calibration assumptions propagate into the teaming framework. In particular, we consider frameworks that either (i) combine human and model predictions or (ii) delegate prediction responsibility to either a human or model. We show via theoretical and empirical results that existing methods for combination do not preserve the human's degree of calibration. Methods for delegation (by the very act of delegation) preserve calibration of the downstream predictors but shift the burden onto the rejector meta-model that decides who predicts. The rejector must be calibrated finely enough to locate where each member is superior, a demand that grows with the human's expertise and becomes unattainable when the human relies on information the system cannot observe.

Parameter-efficient fine-tuning of large language models (LLMs) can exhibit problematic memorization of individual training examples. Empirical privacy auditing (EPA) quantifies this risk by measuring realistic data leakage on membership inference (MI) or reconstruction attacks. A key challenge in EPA is designing ``canary'' examples that are mixed with the privacy-sensitive training data. We propose generating synthetic canaries via high-temperature sampling ($T \geq 0.8$) from LLMs, using prompts tailored to the privacy-sensitive training data. These canaries act as high-influence outliers, ensuring high identifiability and hence strong audits. Further, since the canaries are themselves non-private, they are inspectable and can be inserted with repetition without jeopardizing the privacy of the real data. An important use of models fine-tuned on privacy-sensitive data is the generation of synthetic data. This also comes with privacy risk. We introduce a powerful synthetic data audit based on fine-tuning an auxiliary model on the synthetic data. Auditing the auxiliary model for the original canaries then provides a strong estimate of the privacy leakage through the synthetic data. Finally, leveraging our strong auditing methodologies, we perform a systematic investigation into the interacting effects of model capacity and canary entropy on memorization.

Despite its importance to applications in protein design, predicting protein properties like binding affinity and thermostability from sparse experimental data remains a significant challenge. Accordingly, we introduce a class of sequence kernels that exploit evolutionary substitution matrices as well as local linearity and demonstrate that the resulting Gaussian processes provide data-efficient models of protein property landscapes, frequently outperforming alternatives that rely on foundation model embeddings. Furthermore--by learning what are in effect structure-aware substitution matrices--we show that our kernels can readily incorporate structural information from foundation models. We demonstrate that these structure-conditioned kernels are well suited to multi-task learning across multiple protein property landscapes and can decisively outperform local supervised learning methods.

The Gromov--Wasserstein (GW) distance provides a framework for comparing metric measure spaces, regardless of their underlying structure or geometry. For network-based data, it enables direct comparisons of graphs with different numbers of nodes, without requiring an embedding or other abstraction. Furthermore, through a variant of GW known as fused Gromov--Wasserstein (fGW), it is also possible to incorporate node features in addition to graph structure. In this work, we implement $k$-nearest neighbors ($k$-NN) classification using the GW and fGW distances. We prove the universal consistency of the GW-$k$-NN classifier on the space of equivalence classes of metric measure spaces with finite support and uniform probability measure. By viewing graphs as finitely supported metric measure spaces equipped with the pairwise distance metric and a uniform probability measure on the nodes, we obtain universal consistency of GW-$k$-NN for the space of graphs. Likewise for fGW-$k$-NN, we prove universal consistency on the space of weak isomorphism classes of structured objects consisting of metric measure spaces with finite support and uniform probability measure and feature maps into Euclidean space, thus establishing universal consistency on the space of node-attributed graphs. Our numerical experiments show that GW-$k$-NN and fGW-$k$-NN consistently perform well across multiple graph datasets, suggesting that metric classifiers such as $k$-NN work well in the GW framework.

Post-training Large Language Models (LLMs) for reasoning typically focuses on deductive tasks such as mathematics and coding where correctness is verifiable. Yet, many real-world reasoning problems are inductive: agents must infer uncertain beliefs from sparse, ambiguous observations. There are challenges to using standard fine-tuning methods for inductive reasoning, including difficulties in curating large-scale, high-quality labeled datasets and in handling targets that are inherently distributional. In this work, we introduce a novel approach, called Program-based Posterior Training (PPT), to address these limitations: we use an LLM to generate diverse open-world scenarios as probabilistic programs, run probabilistic inference to produce distributional target responses to queries, and then fine-tune on these probabilistic soft labels. Using this approach, we fine-tune LLMs on 10,000 programmatically generated scenarios and evaluate on held-out motifs, humanlabeled judgments, and external benchmarks. Overall, PPT substantially improves estimation accuracy on held-out inductive tasks, increases alignment with human judgments, and transfers to external benchmarks for estimation and calibration. Additionally, the gains in raw calibration are not subsumed by post-hoc temperature scaling, showing that the models have more deeply internalized uncertainty compared to output rescaling. Together, these results suggest that probabilisticprogram-mediated fine-tuning is a promising approach for post-training LLMs to reliably perform approximate inductive inference.

Non-alcoholic fatty liver disease (NAFLD) affects roughly 25% of global adults, posing substantial hepatic and cardiovascular risks. Yet, population-level screening tools remain inadequate. We present Method, a machine-learning framework for NAFLD risk prediction coupling gradient-boosted decision trees with conformal prediction to yield calibrated, distribution-free coverage guarantees on individual risk estimates. It integrates a mutual-information-based stability selection procedure to identify a compact, clinically interpretable feature subset via bootstrap resampling, constructing prediction sets whose marginal coverage provably exceeds a user-specified confidence level. We evaluated Method on a multicenter cohort from Guangzhou, China (primary n=2,187; external validation n=412) using 78 candidate features across demographics, metabolic biomarkers, and lifestyle factors. Method achieves an AUROC of 0.912 internally and 0.891 externally, outperforming deep neural networks, TabNet, support vector machines, and logistic regression. Conformal prediction sets achieve 91.3% empirical coverage at the 90% nominal level. A three-tier risk stratification derived from these scores separates the population into distinct groups, with the high-risk subgroup showing a 12-month progression rate 4.7 times that of the low-risk tier. The selected features -- notably waist circumference, ALT, GGT, triglycerides, fasting glucose, and BMI -- align with established metabolic risk factors, providing biological plausibility.

We develop a decision-calibrated conformal framework for pacing decisions in streaming advertising. Pacing depends on uncertain future inventory, demand pressure, incremental response, and member-experience load. Instead of calibrating a generic forecast residual, the framework measures forecast error by its largest impact on the policies that could actually be deployed. The main theorem shows that the proposed score is the smallest valid uncertainty measure that uniformly protects all deployable pacing policies. Geometrically, it is the support function of the signed policy sensitivity set. Split conformal calibration gives finite-sample coverage for this score. A high-dimensional separation theorem shows that traditional residual calibration can be arbitrarily more conservative by paying for nuisance inventory dimensions, and a robust pacing result combines inventory, response, and experience uncertainty. On public-data-calibrated pacing replays built from Criteo Uplift and KuaiRand datasets, traditional conformal pacing remains unresolved with high residual radii of 7236.7 on Criteo and 4629.4 on KuaiRand. With the proposed decision calibration approach, the uncertainty radii are reduced to 18.4 and 278.6 respectively, with separate margins for value, delivery, budget, and member load. On Criteo, the proposed method certifies a less aggressive pacing policy than the point-forecast baseline, and reduces held-out any-violation rate from 16.7% to 3.3%, with zero budget and member-load violations. On KuaiRand, the choice remains unresolved. In a nutshell, the paper establishes that forecasts, response estimates, and member-experience models should be judged by whether they shrink the uncertainty that the pacing decision uses, as this leads to confident decisions that are not overly conservative.

We study the generalization of ridge-regularized nonlinear least-squares models via on-average algorithmic stability, deriving error bounds for local minimizers in terms of a data-dependent effective dimension that reflects the geometry of the gradient model at the trained parameters, through the empirical Jacobian Gram matrix and a residual-curvature term. In the linear case, where the curvature term vanishes, this recovers the classical effective dimension of the Jacobian kernel covariance, but evaluated at the trained model rather than at initialization as is typical in neural tangent kernel analyses. We further bound this effective dimension via covering complexity of the gradient features, leading to guarantees that depend on learned geometry rather than parameter count. In particular, for manifold-supported data and piecewise Lipschitz Jacobians, the bounds scale with intrinsic dimension, while for one-hidden-layer ReLU networks, the mechanism can be made explicit through counts of activation-stable regions. Experiments on synthetic manifolds, clustered distributions, and benchmark datasets illustrate trained-Jacobian compression, the tightness of the residual-curvature linearization, and agreement between the stability bound and observed generalization gaps. A key feature of our bounds is the simplicity of their derivation, which follows from first principles using the Brascamp-Lieb inequality under strongly log-concave noise.

The lack of fine-grained, large-scale datasets on water availability presents a critical barrier to applying machine learning (ML) for agricultural water management. Since there are multiple natural and anthropogenic factors that influence water availability, incorporating diverse multimodal features can significantly improve modeling performance. However, integrating such heterogeneous data is challenging due to spatial misalignments, inconsistent formats, semantic label ambiguities, and class imbalances. To address these challenges, we introduce IRRISIGHT, a large-scale, multimodal dataset spanning 20 U.S. states. It consists of 1.4 million pixel-aligned 224 224 patches that fuse satellite imagery with rich environmental attributes. We develop a robust geospatial fusion pipeline that aligns raster, vector, and point-based data on a unified 10m grid, and employ domain-informed structured prompts to convert tabular attributes into natural language. With irrigation type classification as a representative problem, the dataset is AI-ready, offering a spatially disjoint train/test split and extensive benchmarking with both vision and vision-language models.

With the 2026 FIFA World Cup about to get under way, many fans in England and Scotland are honing their strategy to balance late kick-offs with work the next morning. Matches are happening across the US, Canada and Mexico, with England's group games starting at 2100 and 2200 BST and Scotland's even later at 2300 and 0200. Some football fans have already strategically booked annual leave around potential knockout fixtures. Others are hoping to negotiate flexible working - later starts or working from home after late-night matches. Scotland fan Cameron Rae has already booked the Monday after the Haiti game off work so he can attend a Tartan Army fan zone at his local town hall, complete with a bar and DJ running until 4am.