#01Nov 10, 2026
stat.ME
One Curve, Different Weights: AUC, the Brier Score, Decision-Weighted AUC, and the Policy Youden Index
Yegor Baranovski
AUC and the Brier score are standard summaries of a binary risk score, yet they can rank models differently. We introduce a weighted AUC, AUC$_π$, which weights each pair of observations by how differently a decision maker with probability of acting $π$ treats them. We show that all three are built on weighted averages of one curve, the Youden index $J(t) = \mathrm{TPR}(t) - \mathrm{FPR}(t)$ across cutoffs $t$, and that the averages differ in the weights they put on the cutoffs. Each weights a cutoff by how much something rises across it: for AUC, the distribution of all scores; for the Brier score, the true probability $\mathbb{E}[Y \mid S]$; for AUC$_π$, the decision maker's probability of acting. Up to normalization, AUC$_π$ is the Brier skill score of the ideal forecast with its weight moved to the cutoffs the decision maker cares about. We also show that weighting pairs by $|π(s) - π(s')|$ is, up to scale, the only pair weight fixed in advance that makes a pair-weighted AUC an average of the Youden curve for every score distribution. As a ranking measure, AUC weights every model the same way. Hand (2009) shows that it can also be read as an average over cost thresholds, and in that reading each model weights the thresholds differently. The numerator of AUC$_π$, which we call the policy Youden index, is the expected share of class 1 a fixed policy acts on minus the expected share of class 0. It judges every model by the same policy and so avoids this; the full ratio AUC$_π$ does not.
#02Nov 10, 2026
cs.AI
Contrastive Discovery: Open-Ended Scientific Discovery over Competing Explanations
Ziang Liu, James J. Kim, Yijia Dai and 1 more
LLM agents are increasingly used for open-ended, data-driven scientific discovery, yet most of them evaluate hypotheses pointwise, testing an empirical claim $h$ only against its complement $\neg h$. When evidence rejects $h$, the agent learns that one explanation is unlikely but not which alternative the evidence supports. To recover that alternative, we introduce Contrastive Discovery, which replaces the single hypothesis with a contrast set, a scientific question paired with mutually exclusive and collectively exhaustive competing explanations. Each experiment is scored by how its evidence redistributes belief across the set, and the question is resolved when belief concentrates on one explanation. Because contrast sets change only the unit an agent proposes and scores, an existing agent can use them to re-evaluate evidence it has already collected or to guide its search. Across six domains, $89\%$ of the pointwise candidates with the largest belief shifts are rejections. On the same evidence, contrast sets resolve $73\%$ of these candidates to a specific alternative. When contrast sets guide search, the agent resolves $67\%$ more questions than pointwise surprisal under the same experiment budget. In a blinded study, $38$ human experts chose the same explanation on $78\%$ of resolved questions and on $82\%$ of questions where the pointwise agent rejected its hypothesis and stopped. Together, these results support explicit competing explanations as a way for discovery agents to resolve more scientific questions from the same evidence and validation budget.
#03Nov 10, 2026
stat.ML
A Theory of Cross-Validation Variance
Nathaniel S. O'Connell, Jaime L. Speiser
Cross-validation estimates predictive performance by repeatedly splitting the data into training and validation sets, fitting the model on the first and evaluating it on the second. Every observation influences the estimate in two roles, through its own evaluation when it is held out and through the models it helps fit when it trains. The random splits determine its weight in each role. From this representation, we prove an exact finite-sample identity for the variance of the cross-validated estimate. For a given splitting scheme with a common training set size, the variance is a function of these weights, with constants of the model, the metric, and the population. It covers metrics averaged over observations, such as mean squared error, and over case--control pairs, such as the AUC. The identity shows which schemes to use. The variance decomposes into sampling variance, which depends only on the training size, and variance due to the random fold splitting, which arises when the weights change from one draw of the splits to the next. K-fold cross-validation, whose weights are equal across observations by design, is therefore variance optimal at first order; Monte Carlo and bootstrap cross-validation are not. The first-order variance of K-fold does not depend on K, and under reasonable conditions on the model leave-one-out has the smallest variance of any K-fold scheme. For the AUC the same holds for leave-pair-out, which evaluates every case--control pair. Finally, we show the cross-validated estimate is asymptotically normal with the identity's full variance. Together, these results provide a general theoretical foundation for inference on cross-validated performance and establish principles for selecting variance-optimal cross-validation designs.
#04Nov 10, 2026
cs.LG
Accurate predictions of properties of energetic materials with tabular foundation models
Vagn Krister Nes Glomsrud, Mathias Bynke, Lars Henry Berge Olsen and 1 more
We use TabPFN, a recently developed tabular foundation model, to predict three properties of energetic materials: impact sensitivity, decomposition temperature and crystal density. Without any hyperparameter tuning, TabPFN outperforms the best published models for all three properties. It also substantially outperforms a wide range of established machine-learning models, including tuned gradient boosting (XGBoost), random forests and Gaussian processes. This holds both when the models are given hand-crafted molecular descriptors and when they are given learned representations from Chemprop's message-passing neural network. In particular, for all three properties, TabPFN applied to Chemprop's own embedding is more accurate than Chemprop's predictions. TabPFN is also among the fastest models we consider, more than an order of magnitude faster than XGBoost. As TabPFN predicts the entire distribution of the target rather than just a single value, it offers built-in uncertainty quantification, which we compare with the empirical distributions of compounds with repeated measurements. Finally, we interpret the predictions using Shapley values, which rank the features by their importance.
#05Nov 10, 2026
cs.CV
UGG: Unified Generative Geometry Model
Amani Kiruga, Zhiyi Li, Ruojin Cai and 4 more
Understanding 4D scenes is a core challenge in visual intelligence, requiring models to jointly capture scene geometry, appearance, and dynamics from partial observations. However, existing approaches are subdivided into feedforward models for direct geometric prediction, and generative models for visual synthesis. We introduce UGG, a unified framework for 4D scene understanding that jointly models RGB video and geometric representations such as depth and camera pose. By assigning different noise levels across modalities and time, UGG formulates visual generation and geometric prediction as conditional completion within a single generative model. This flexible formulation enables the model to learn from diverse, heterogeneous datasets with different subsets of geometric and visual annotations. Furthermore, our generative formulation enables inference-time search over multiple plausible scene hypotheses, using geometric evidence extracted from observed RGB frames to improve geometric prediction without ground truth geometry. We demonstrate UGG's effectiveness over non-unified baselines across camera-controlled video generation, depth estimation, and camera pose prediction, including in challenging sparse observation settings. Code and visualizations are available at https://ugg-model.github.io/