The population dynamics of molecules, cells, and organisms are governed by a number of unknown forces. In the last decade, population dynamics have predominantly been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to capture important dynamical properties, such as periodicity. In this work, we propose a change in perspective by considering dynamics that minimize a population-level action under a damped Wasserstein Lagrangian. By deriving the corresponding Hamiltonian equations of motion, we formalize Wasserstein Lagrangian Mechanics, a structured class of second-order dynamics that encompasses classical mechanics, quantum mechanics, and gradient flows. We then propose WLM as the first algorithm that learns these second-order dynamics from observed marginals, without specifying the Lagrangian. By directly learning the population mechanics, WLM can both forecast and interpolate unseen marginals, and outperforms existing gradient flow and flow matching methods across a wide range of dynamics, including vortex dynamics, embryonic development, and flocking.

Automated systems built on artificial intelligence (AI) are increasingly deployed across high-stakes domains, raising critical concerns about fairness and the perpetuation of demographic disparities that exist in the world. In this context, causal inference provides a principled framework for reasoning about fairness, as it links observed disparities to underlying mechanisms and aligns naturally with human intuition and legal notions of discrimination. Prior work on causal fairness primarily focuses on the standard machine learning setting, where a decision-maker constructs a single predictive mechanism $f_{\widehat Y}$ for an outcome variable $Y$, while inheriting the causal mechanisms of all other covariates from the real world. The generative AI setting, however, is markedly more complex: generative models can sample from arbitrary conditionals over any set of variables, implicitly constructing their own beliefs about all causal mechanisms rather than learning a single predictive function. This fundamental difference requires new developments in causal fairness methodology. We formalize the problem of causal fairness in generative AI and unify it with the standard ML setting under a common theoretical framework. We then derive new causal decomposition results that enable granular quantification of fairness impacts along both (a) different causal pathways and (b) the replacement of real-world mechanisms by the generative model's mechanisms. We establish identification conditions and introduce efficient estimators for causal quantities of interest, and demonstrate the value of our methodology by analyzing race and gender bias in large language models across different datasets.

Preprocessing screening is often the most expensive part of a near-infrared spectroscopy calibration workflow. It works because smoothing, derivatives, detrending and related filters change the spectral directions seen by PLS or Ridge regression, but a full external search repeatedly refits nearly the same linear model. This paper studies the case where that search can be collapsed into one calibration step. For strict linear preprocessing operators, the transformed PLS cross-covariance satisfies (X A^T)^T Y = A X^T Y, and Ridge regression depends on the operator-induced kernel X A^T A X^T. These identities allow a finite operator bank to be screened inside the model while retaining original-wavelength coefficients. Sample-adaptive or fitted corrections such as SNV, MSC, EMSC and ASLS remain fold-local branches, not absorbed into the algebra. The study uses the AOM benchmark cohort: 61 regression rows and 17 classification rows in the manifest. On the main regression denominator (N=32), plain compact-bank AOM-PLS records median RMSEP ratios of 0.991 against PLS-default and 0.990 against PLS-HPO; the selected ASLS-AOM-compact-cv5 branch records 0.985 and 1.002 on the same two references. The plain AOMRidge-global-compact-none baseline records 0.974 against Ridge-default and 0.984 against Ridge-HPO, while the selected AOMRidge-Blender-headline-spxy3 records 0.918 and 0.966. The selected classifier, AOM-PLS-DA-global-simpls-covariance, improves balanced accuracy by 0.159 on N=13 datasets with 12/13 wins. The runtime gap is the practical result: PLS-HPO takes a median total time of 710.81 s per run, whereas the selected AOM-PLS branch takes 1.63 s. Linear operator-adaptive calibration therefore gives comparable prediction quality to exhaustive preprocessing screening, with orders-of-magnitude less fitting time for PLS.

Medium-horizon Alzheimer's disease progression prediction is difficult because future clinical scores can remain tied to baseline severity, while biomarker histories are irregular and incompletely observed. We develop an anchor-based analysis of 24-month Clinical Dementia Rating Sum of Boxes (CDR-SB) change using harmonized Alzheimer's Disease Neuroimaging Initiative (ADNI) tables. Each labeled sample is anchored at a mild cognitive impairment visit, uses only clinical and biomarker history observed at or before that anchor, and defines the response as CDR-SB at the future visit closest to 24 months within an 18--30 month window minus anchor CDR-SB. The analytic cohort contains 2,600 labeled anchors from 858 participants and 7,276 longitudinal rows. We propose a residual gap-aware transformer that combines a mixed-effects statistical reference with transformer-based residual learning from pre-anchor clinical and biomarker histories. The model uses participant-level random intercepts in the mixed-effects reference, observation-level triplet tokenization for irregular histories, and a learned nonnegative time-gap penalty inside self-attention. We compare the proposed model with a Bayesian-information-criterion-selected linear mixed-effects baseline, GRU-D, and STraTS under repeated participant-level train--test splits. Across five participant-level random seeds, the proposed model achieves the best mean test performance across all reported metrics, reducing MSE by 13.1% and increasing prediction--observation correlation by 26.4% relative to the mixed-effects baseline. It also improves over both GRU-D and STraTS in mean error and correlation. These results show that statistical anchoring and gap-aware residual learning provide a useful structure for medium-horizon Alzheimer's disease progression prediction.

Large language models (LLMs) are increasingly used as automated evaluators of AI systems, including in high-stakes applications. In this role, LLMs are used to generate judgments about the quality, appropriateness, or even safety of model outputs. This approach is motivated by practical constraints. Expert human ratings are costly and difficult to scale, whereas LLM ratings can be produced quickly at low cost. However, current approaches to deploying LLM evaluators are ad hoc, typically limited to reporting agreement metrics between human and LLM judges as a justification for substitution of human ratings, and lack a formal basis for study design. This paper (1) shifts the role of the LLM judge from substitutive to auxiliary, and (2) formulates the LLM-as-a-judge paradigm as one of augmenting human evaluation through a two-stage sampling design, where LLM evaluations are measured for all observations at the first stage and human ratings are partially observed for a subsample at the second stage. We propose to use a doubly robust estimator from the missing data literature, which takes advantage of the robustness property against the prediction model, since the missingness model is known by design. Using the asymptotic variance of this estimator, we propose how sample sizes of human and LLM ratings can be determined to achieve a targeted level of power. We also show that a study can be efficiently designed by allocating more human ratings for types of evaluations where the predictability of LLM ratings is not high. To the best of our knowledge, there is very little guidance on how much human oversight should be retained when validating benchmarks.

We present TailedTS, a large-scale benchmark dataset derived from Wikipedia hourly page view observations throughout 2024, specifically designed to test time series forecasting models under heavy-tailed, zero-inflated, and non-Gaussian conditions. The dataset comprises approximately 24.69 billion data points spanning roughly 3 million unique Wikipedia pages per month, stored in high-efficiency Apache Parquet format. Wikipedia traffic follows a pronounced power-law distribution where roughly 5% of pages account for over 70% of total page views, creating a natural and rigorous testbed for model robustness against extreme volatility that are absent from or underrepresented in existing benchmarks such as M4, M5, and UCI electricity datasets. TailedTS enables several research tasks. First, we introduce a periodicity quantification framework based on sparse autoregression with sparsity and non-negativity constraints, revealing that frequently-viewed pages exhibit significantly weaker periodic structure than their less-viewed counterparts, showing direct implications for server allocation and traffic forecasting on large digital platforms. Second, we provide standardized prediction benchmarks evaluated under a suite of non-Gaussian loss functions, including $\ell_1$-norm, Huber, quantile, and $\ell_p$-norm losses, demonstrating that standard Gaussian-based estimators degrade substantially on high-volume page categories, while robust alternatives provide consistent gains across all traffic scales. TailedTS is publicly available at https://doi.org/10.5281/zenodo.17070469.

Diffusion and flow-based models are ubiquitously used for generative modelling and density estimation. They admit a deterministic probability flow ordinary differential equation (PF-ODE), analogous to continuous normalizing flows (CNFs), which describes the transport of the probability mass. Obtaining the likelihood from these models is of interest to many workflows, especially Bayesian analysis, and requires solving the trace of the Jacobian to compute the divergence of the learned PF-ODE, which is either $\mathcal{O}(D^2)$ to compute exactly or $\mathcal{O}(D)$ with a noisy estimate. We introduce StAD, a new distillation method to predict and learn the divergence of the PF-ODE using the Langevin-Stein operator without ever computing the Jacobian. We show that our method is competitive with the Hutchinson and Hutch++ on CIFAR-10, ImageNet and other density estimation tasks, consistently improving the variance and speed of the likelihood predictions compared to the Hutchinson. We additionally show our method will generalize to a varied class of generative models, and show that under some regularity conditions these learned vector fields can be made to satisfy the Stein class.

Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are accompanied by reliable uncertainty estimates. While deep learning methods provide both scalable and accurate models for spatial predictions, there remains no clear consensus for addressing uncertainty quantification in spatial deep learning. Monte Carlo (MC) dropout has become a popular approach for uncertainty quantification, yet existing implementations typically focus on tuning the dropout rate while fixing other influential hyperparameters, such as weight decay and the predictive standard deviation multiplier, often through ad-hoc or manual tuning. We propose a cubing-based diagnostic framework that recursively partitions the hyperparameter space to identify stable regions where MC dropout yields well-calibrated predictive intervals. The approach evaluates hyperparameter regions using scoring rules relative to a statistical baseline model, which serves as a calibration anchor. Through a simulation study spanning multiple spatial dependence regimes as well as a large remotely-sensed land surface temperature dataset, we demonstrate that our approach produces competitive or superior predictive intervals compared to the baseline model. Our methodology provides practitioners with a systematic procedure for incorporating uncertainty quantification into spatial deep learning models.

Time-to-event data is widespread across the life sciences and engineering, but it is typically encountered together with censoring, which complicates the application of standard machine learning methods. Deep Cox models have emerged as a popular method for analyzing time-to-event data because they gracefully handle censoring and can be used with unstructured data such as clinical text reports, genomic sequences, and pathology images. However, their predicted survival probabilities are often poorly calibrated, thus limiting their practical utility. In this paper, we propose a novel post hoc calibration method for Deep Cox models that uses isotonic regression to refine predicted survival probabilities without affecting discriminative power. We establish favorable theoretical guarantees, including a double-robustness property and asymptotic calibration. Experiments on synthetic and real-world clinical data demonstrate the empirical effectiveness of our method.

Decision-makers frequently must choose a single action from a finite set of alternatives -- for example, physicians selecting a treatment, investors choosing a portfolio risk level, or judges determining sentences. To improve outcomes, policymakers often issue policy rules or guidelines to inform such choices. In this paper, I show how to generally derive policy rules from observational data in a multi-action framework under relatively weak assumptions about the underlying structure of the heterogeneous sampled population. Conditional average treatment effects (CATEs) are consistently estimated via a weighted K-means algorithm, assuming the outcome model is correctly specified within each homogeneous subgroup. Feasible policy rules are then implemented via a standard decision tree, allowing for both perfect and imperfect adherence to treatment. The methodology is applied to treatment options for Hepatitis C (HCV) among patients co-infected with human immunodeficiency virus (HIV), a setting in which no uniform guideline exists for modern pharmaceutical therapies. The results identify a subgroup of patients with approximately an 80% probability of spontaneous HCV clearance without treatment. Estimation results also show that reallocating treatments among treated individuals could have reduced total treatment costs by CAN$3.6-4.9 million while still increasing aggregate health benefits relative to the status quo. These findings demonstrate that the proposed approach can generate improved, data-driven treatment guidelines for the management of HIV/HCV co-infected patients.