Papers

Random Forests (RF) are among the most powerful and widely used predictive models for centralized tabular data, yet few methods exist to adapt them to the federated learning setting. Unlike most federated learning approaches, the piecewise-constant nature of RF prevents exact gradient-based optimization. As a result, existing federated RF implementations rely on unprincipled heuristics: for instance, aggregating decision trees trained independently on clients fails to optimize the global impurity criterion, even under simple distribution shifts. We propose FedForest, a new federated RF algorithm for horizontally partitioned data that naturally accommodates diverse forms of client data heterogeneity, from covariate shift to more complex outcome shift mechanisms. We prove that our splitting procedure, based on aggregating carefully chosen client statistics, closely approximates the split selected by a centralized algorithm. Moreover, FedForest allows splits on client indicators, enabling a non-parametric form of personalization that is absent from prior federated random forest methods. Empirically, we demonstrate that the resulting federated forests closely match centralized performance across heterogeneous benchmarks while remaining communication-efficient.

For randomized controlled trials to be conclusive, it is important to set the target sample size accurately at the design stage. Comparing two normal populations, the sample size calculation requires specification of the variance other than the treatment effect and misspecification can lead to underpowered studies. Blinded sample size re-estimation is an approach to minimize the risk of inconclusive studies. Existing methods proposed to use the total (one-sample) variance that is estimable from blinded data without knowledge of the treatment allocation. We demonstrate that, since the expectation of this estimator is greater than or equal to the true variance, the one-sample variance approach can be regarded as providing an upper bound of the variance in blind reviews. This worst-case evaluation can likely reduce a risk of underpowered studies. However, blinded reviews of small sample size may still lead to underpowered studies. We propose a refined method accounting for estimation error in blind reviews using an upper confidence limit of the variance. A similar idea had been proposed in the setting of external pilot studies. Furthermore, we developed a method to select an appropriate confidence level so that the re-estimated sample size attains the target power. Numerical studies showed that our method works well and outperforms existing methods. The proposed procedure is motivated and illustrated by recent randomized clinical trials.

Accurate estimation of tacrolimus exposure, quantified by the area under the concentration-time curve (AUC), is essential for precision dosing after renal transplantation. Current practice relies on population pharmacokinetic (PopPK) models based on nonlinear mixed-effects (NLME) methods. However, these models depend on rigid, pre-specified assumptions and may struggle to capture complex, patient-specific dynamics, leading to model misspecification. In this study, we introduce a novel data-driven alternative based on Latent Ordinary Differential Equations (Latent ODEs) for tacrolimus AUC prediction. This deep learning approach learns individualized pharmacokinetic dynamics directly from sparse clinical data, enabling greater flexibility in modeling complex biological behavior. The model was evaluated through extensive simulations across multiple scenarios and benchmarked against two standard approaches: NLME-based estimation and the iterative two-stage Bayesian (it2B) method. We further performed a rigorous clinical validation using a development dataset (n = 178) and a completely independent external dataset (n = 75). In simulation, the Latent ODE model demonstrated superior robustness, maintaining high accuracy even when underlying biological mechanisms deviated from standard assumptions. Regarding experiments on clinical datasets, in internal validation, it achieved significantly higher precision with a mean RMSPE of 7.99% compared with 9.24% for it2B (p < 0.001). On the external cohort, it achieved an RMSPE of 10.82%, comparable to the two standard estimators (11.48% and 11.54%). These results establish the Latent ODE as a powerful and reliable tool for AUC prediction. Its flexible architecture provides a promising foundation for next-generation, multi-modal models in personalized medicine.

We study the relation between the total variation (TV) and Hellinger distances between two Gaussian location mixtures. Our first result establishes a general upper bound: for any two mixing distributions supported on a compact set, the Hellinger distance between the two mixtures is controlled by the TV distance raised to a power $1-o(1)$, where the $o(1)$ term is of order $1/\log\log(1/\mathrm{TV})$. We also construct two sequences of mixing distributions that demonstrate the sharpness of this bound. Taken together, our results resolve an open problem raised in Jia et al. (2023) and thus lead to an entropic characterization of learning Gaussian mixtures in total variation. Our inequality also yields optimal robust estimation of Gaussian mixtures in Hellinger distance, which has a direct implication for bounding the minimax regret of empirical Bayes under Huber contamination.

Clustering functional data in the presence of phase variation is challenging, as temporal misalignment can obscure intrinsic shape differences and degrade clustering performance. Most existing approaches treat registration and clustering as separate tasks or rely on restrictive parametric assumptions. We present NeuralFLoC, a fully unsupervised, end-to-end deep learning framework for joint functional registration and clustering based on Neural ODE-driven diffeomorphic flows and spectral clustering. The proposed model learns smooth, invertible warping functions and cluster-specific templates simultaneously, effectively disentangling phase and amplitude variation. We establish universal approximation guarantees and asymptotic consistency for the proposed framework. Experiments on functional benchmarks show state-of-the-art performance in both registration and clustering, with robustness to missing data, irregular sampling, and noise, while maintaining scalability. Code is available at https://anonymous.4open.science/r/NeuralFLoC-FEC8.

Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-\alpha$ coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the $(1-\alpha)$-pinball loss. Our first contribution is to identify linearized regret as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions in highdimensional spaces, the efficiency of importance sampling critically depends on the choice of the proposal distribution. In this paper, we propose a novel adaptive scheme for the construction of efficient proposal distributions. Our algorithm promotes efficient exploration of the target distribution by combining global sampling mechanisms with a delayed weighting procedure. The proposed weighting mechanism plays a key role by enabling rapid resampling in regions where the proposal distribution is poorly adapted to the target. Our sampling algorithm is shown to be geometrically convergent under mild assumptions and is illustrated through various numerical experiments.

Group Relative Policy Optimization (GRPO) has recently emerged as a practical recipe for aligning large language models with verifiable objectives. However, under sparse terminal rewards, GRPO often stalls because rollouts within a group frequently receive identical rewards, causing relative advantages to collapse and updates to vanish. We propose self-hint aligned GRPO with privileged supervision (SAGE), an on-policy reinforcement learning framework that injects privileged hints during training to reshape the rollout distribution under the same terminal verifier reward. For each prompt $x$, the model samples a compact hint $h$ (e.g., a plan or decomposition) and then generates a solution $\tau$ conditioned on $(x,h)$. Crucially, the task reward $R(x,\tau)$ is unchanged; hints only increase within-group outcome diversity under finite sampling, preventing GRPO advantages from collapsing under sparse rewards. At test time, we set $h=\varnothing$ and deploy the no-hint policy without any privileged information. Moreover, sampling diverse self-hints serves as an adaptive curriculum that tracks the learner's bottlenecks more effectively than fixed hints from an initial policy or a stronger external model. Experiments over 6 benchmarks with 3 LLMs show that SAGE consistently outperforms GRPO, on average +2.0 on Llama-3.2-3B-Instruct, +1.2 on Qwen2.5-7B-Instruct and +1.3 on Qwen3-4B-Instruct. The code is available at https://github.com/BaohaoLiao/SAGE.

We introduce functional adaptive shrinkage (FASH), an empirical Bayes method for joint analysis of observation units in which each unit estimates an effect function at several values of a continuous condition variable. The ideas in this paper are motivated by dynamic expression quantitative trait locus (eQTL) studies, which aim to characterize how genetic effects on gene expression vary with time or another continuous condition. FASH integrates a broad family of Gaussian processes defined through linear differential operators into an empirical Bayes shrinkage framework, enabling adaptive smoothing and borrowing of information across units. This provides improved estimation of effect functions and principled hypothesis testing, allowing straightforward computation of significance measures such as local false discovery and false sign rates. To encourage conservative inferences, we propose a simple prior- adjustment method that has theoretical guarantees and can be more broadly used with other empirical Bayes methods. We illustrate the benefits of FASH by reanalyzing dynamic eQTL data on cardiomyocyte differentiation from induced pluripotent stem cells. FASH identified novel dynamic eQTLs, revealed diverse temporal effect patterns, and provided improved power compared with the original analysis. More broadly, FASH offers a flexible statistical framework for joint analysis of functional data, with applications extending beyond genomics. To facilitate use of FASH in dynamic eQTL studies and other settings, we provide an accompanying R package at https: //github.com/stephenslab/fashr.

Evaluating mathematical reasoning in LLMs is constrained by limited benchmark sizes and inherent model stochasticity, yielding high-variance accuracy estimates and unstable rankings across platforms. On difficult problems, an LLM may fail to produce a correct final answer, yet still provide reliable pairwise comparison signals indicating which of two candidate solutions is better. We leverage this observation to design a statistically efficient evaluation framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains. Treating these comparison signals as control variates, we develop a semiparametric estimator based on the efficient influence function (EIF) for the setting where auxiliary reasoning chains are observed. This yields a one-step estimator that achieves the semiparametric efficiency bound, guarantees strict variance reduction over naive sample averaging, and admits asymptotic normality for principled uncertainty quantification. Across simulations, our one-step estimator substantially improves ranking accuracy, with gains increasing as model output noise grows. Experiments on GPQA Diamond, AIME 2025, and GSM8K further demonstrate more precise performance estimation and more reliable model rankings, especially in small-sample regimes where conventional evaluation is pretty unstable.

It is increasingly common for data to possess intricate structure, necessitating new models and analytical tools. Graphs, a prominent type of structure, can encode the relationships between any two entities (nodes). However, graphs neither allow connections that are not dyadic nor permit relationships between sets of nodes. We thus turn to simplicial complexes for connecting more than two nodes as well as modeling relationships between simplices, such as edges and triangles. Our data then consist of signals lying on topological spaces, represented by simplicial complexes. Much recent work explores these topological signals, albeit primarily through deterministic formulations. We propose a probabilistic framework for random signals defined on simplicial complexes. Specifically, we generalize the classical notion of stationarity. By spectral dualities of Hodge and Dirac theory, we define stationary topological signals as the outputs of topological filters given white noise. This definition naturally extends desirable properties of stationarity that hold for both time-series and graph signals. Crucially, we properly define topological power spectral density (PSD) through a clear spectral characterization. We then discuss the advantages of topological stationarity due to spectral properties via the PSD. In addition, we empirically demonstrate the practicality of these benefits through multiple synthetic and real-world simulations.

Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as distinct phenomena, this paper introduces a unified statistical inference framework that bridges these contexts, treating the former as a special case of the latter. Our contribution is two-fold. First, we put forward the Repeated Risk Minimization (RRM) procedure for estimating the performative stability, and establish a rigorous inferential theory for admitting its asymptotic normality and confirming its asymptotic efficiency. Second, for the performative optimality, we introduce a novel two-step plug-in estimator that integrates the idea of Recalibrated Prediction Powered Inference (RePPI) with Importance Sampling, and further provide formal derivations for the Central Limit Theorems of both the underlying distributional parameters and the plug-in results. The theoretical analysis demonstrates that our estimator achieves the semiparametric efficiency bound and maintains robustness under mild distributional misspecification. This work provides a principled toolkit for reliable estimation and decision-making in dynamic, performative environments.

Machine unlearning, the ability to erase the effect of specific training samples without retraining from scratch, is critical for privacy, regulation, and efficiency. However, most progress in unlearning has been empirical, with little theoretical understanding of when and why unlearning works. We tackle this gap by framing unlearning through the lens of asymptotic linear stability to capture the interaction between optimization dynamics and data geometry. The key quantity in our analysis is data coherence which is the cross sample alignment of loss surface directions near the optimum. We decompose coherence along three axes: within the retain set, within the forget set, and between them, and prove tight stability thresholds that separate convergence from divergence. To further link data properties to forgettability, we study a two layer ReLU CNN under a signal plus noise model and show that stronger memorization makes forgetting easier: when the signal to noise ratio (SNR) is lower, cross sample alignment is weaker, reducing coherence and making unlearning easier; conversely, high SNR, highly aligned models resist unlearning. For empirical verification, we show that Hessian tests and CNN heatmaps align closely with the predicted boundary, mapping the stability frontier of gradient based unlearning as a function of batching, mixing, and data/model alignment. Our analysis is grounded in random matrix theory tools and provides the first principled account of the trade offs between memorization, coherence, and unlearning.

We develop a Bayesian methodology for numerical solution of the incompressible Navier–Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier–Stokes dynamics as a state-space model and to view numerical solution as posterior computation: priors encode physical structure and modeling error, and the solver outputs a distribution over states and quantities of interest rather than a single trajectory. In two dimensions, stochastic representations (Feynman–Kac and stochastic characteristics for linear advection–diffusion with prescribed drift) motivate Monte Carlo solvers and provide intuition for uncertainty propagation. In three dimensions, we formulate stochastic Navier–Stokes models and describe particle-based and ensemble-based Bayesian workflows for uncertainty propagation in spectral discretizations. A key computational advantage is that parameter learning can be performed stably via particle learning: marginalization and resample–propagate (one-step smoothing) constructions avoid the weight-collapse that plagues naive sequential importance sampling on static parameters. When partial observations are available, the same machinery supports sequential observational updating as an additional capability. We also discuss non-Gaussian (heavy-tailed) error models based on normal variance-mean mixtures, which yield conditionally Gaussian updates via latent scale augmentation.

Clustered data, which arise when observations are nested within groups, are incredibly common in clinical, education, and social science research. Traditionally, a linear mixed model, which includes random effects to account for within-group correlation, would be used to model the observed data and make new predictions on unseen data. Some work has been done to extend the mixed model approach beyond linear regression into more complex and non-parametric models, such as decision trees and random forests. However, existing methods are limited to using the global fixed effects for prediction on data from out-of-sample groups, effectively assuming that all clusters share a common outcome model. We propose a lightweight sum-of-trees model in which we learn a decision tree for each sample group. We combine the predictions from these trees using weights so that out-of-sample group predictions are more closely aligned with the most similar groups in the training data. This strategy also allows for inference on the similarity across groups in the outcome prediction model, as the unique tree structures and variable importances for each group can be directly compared. We show our model outperforms traditional decision trees and random forests in a variety of simulation settings. Finally, we showcase our method on real-world data from the sarcoma cohort of The Cancer Genome Atlas, where patient samples are grouped by sarcoma subtype.

Masked diffusion models have emerged as a powerful framework for text and multimodal generation. However, their sampling procedure updates multiple tokens simultaneously and treats generated tokens as immutable, which may lead to error accumulation when early mistakes cannot be revised. In this work, we revisit existing self-correction methods and identify limitations stemming from additional training requirements or reliance on misaligned likelihood estimates. We propose a training-free self-correction framework that exploits the inductive biases of pre-trained masked diffusion models. Without modifying model parameters or introducing auxiliary evaluators, our method significantly improves generation quality on text-to-image generation and multimodal understanding tasks with reduced sampling steps. Moreover, the proposed framework generalizes across different masked diffusion architectures, highlighting its robustness and practical applicability. Code can be found in https://github.com/huge123/FreeCorrection.

Many ideas in modern control and reinforcement learning treat decision-making as inference: start from a baseline distribution and update it when a signal arrives. We ask when this can be made literal rather than metaphorical. We study the special case where a KL-regularized soft update is exactly a Bayesian posterior inside a single fixed probabilistic model, so the update variable is a genuine channel through which information is transmitted. In this regime, behavioral change is driven only by evidence carried by that channel: the update must be explainable as an evidence reweighing of the baseline. This yields a sharp identification result: posterior updates determine the relative, context-dependent incentive signal that shifts behavior, but they do not uniquely determine absolute rewards, which remain ambiguous up to context-specific baselines. Requiring one reusable continuation value across different update directions adds a further coherence constraint linking the reward descriptions associated with different conditioning orders.

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation $\sigma^2 \mapsto \kappa(\sigma^2)$, explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: anisotropy across eigenmodes, inhomogeneity across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.

Urban land use and building intensity are often planned without a direct, auditable link to network accessibility, limiting ex-ante policy evaluation. This study asks whether multi-radius street centralities can be elevated from diagnosis to design lever to allocate land use and floor area in a transparent, optimization-ready workflow. We introduce a three-stage pipeline that connects configuration to program and intensity. First, multi-radius accessibility is computed on the street network and translated to blocks to provide scale-legible measures of reach. Second, these measures structure nested service basins that guide a rule-based placement of land uses with explicit priorities and minimum parcel footprints, ensuring reproducibility. Third, within each use, floor-area ratio (FAR) is assigned by an accessibility-weighted linear model that satisfies global construction totals while anchoring the average FAR, thereby tilting height toward better-connected blocks without pathological extremes. The framework supports multi-objective policy search via sampling and Pareto screening. Applied to a real urban district, the workflow reproduces corridor-biased commercial siting and industrial belts while concentrating intensity on highly connected blocks. Policy sampling via multi-objective screening yields Pareto-efficient plans that reconcile accessibility gains with deviations from target land-share and construction-share structures. The contribution is twofold: methodologically, it translates familiar space-syntax measures into cluster-aware, rule-governed land-use and FAR assignment with explicit guarantees (scale-legible radii, parcel minima, and an average-FAR anchor). Practically, it offers planners a transparent instrument for counterfactual testing and negotiated trade-offs at neighborhood/district/city scales.

This paper introduces a new two-parameter distribution, referred to as the Shiha distribution, which provides a flexible model for skewed lifetime data with either heavy or light tails. The proposed distribution is applicable to various fields, including reliability engineering, environmental studies, and related areas. We derive its main statistical properties, including the moment generating function, moments, hazard rate function, quantile function, and entropy. The stress–strength reliability parameter is also derived in closed form. A simulation study is conducted to evaluate its performance. Applications to several real data sets demonstrate that the Shiha distribution consistently provides a superior fit compared with established competing models, confirming its practical effectiveness for lifetime data analysis.

Teaching data science presents unique challenges and opportunities that cannot be fully addressed by simply borrowing pedagogical strategies from its parent disciplines of statistics and computer science. Here, we present ten simple rules for teaching data science, developed and refined by leading educators in the community and successfully applied in our own data science classrooms.

We consider the functional regression model with multivariate response and functional predictors. Compared to fitting each individual response variable separately, taking advantage of the correlation between the response variables can improve the estimation and prediction accuracy. Using information in both functional predictors and multivariate response, we identify the optimal decomposition of the coefficient functions for prediction in population level. Then we propose methods to estimate this decomposition and fit the regression model for the situations of a small and a large number $p$ of functional predictors separately. For a large $p$, we propose a simultaneous smooth-sparse penalty which can both make curve selection and improve estimation and prediction accuracy. We provide the asymptotic results when both the sample size and the number of functional predictors go to infinity. Our method can be applied to models with thousands of functional predictors and has been implemented in the R package FRegSigCom.

Pre-training on a source task is usually expected to facilitate fine-tuning on similar downstream problems. In this work, we mathematically show that this naive intuition is not always true: excessive pre-training can computationally slow down fine-tuning optimization. We study this phenomenon for low-rank adaptation (LoRA) fine-tuning on single-index models trained under one-pass SGD. Leveraging a summary statistics description of the fine-tuning dynamics, we precisely characterize how the convergence rate depends on the initial fine-tuning alignment and the degree of non-linearity of the target task. The key take away is that even when the pre-training and downstream tasks are well aligned, strong pre-training can induce a prolonged search phase and hinder convergence. Our theory thus provides a unified picture of how pre-training strength and task difficulty jointly shape the dynamics and limitations of LoRA fine-tuning in a nontrivial tractable model. On the practical side, we empirically show that our theoretical findings extend beyond our toy model and remain relevant in the context of a vision-transformer model trained on real data.

Discovering causal structures from multivariate time series is a key problem because interactions span across multiple lags and possibly involve instantaneous dependencies. Additionally, the search space of the dynamic graphs is combinatorial in nature. In this study, we propose Stable Causal Dynamic Differentiable Discovery (SC3D), a two-stage differentiable framework that jointly learns lag-specific adjacency matrices and, if present, an instantaneous directed acyclic graph (DAG). In Stage 1, SC3D performs edge preselection through node-wise prediction to obtain masks for lagged and instantaneous edges, whereas Stage 2 refines these masks by optimizing a likelihood with sparsity along with enforcing acyclicity on the instantaneous block. Numerical results across synthetic SVAR systems, nonlinear and chaotic benchmarks, nonstationary dynamics and real-world datasets demonstrate that SC3D achieves improved stability and more accurate recovery of both lagged and instantaneous causal structures compared to existing baselines.

Spatial omics maps molecular features within tissues to study their organization across biological contexts, including disease and development. Interpreting these maps requires distinguishing patterns from noise and comparing them across samples. Yet pattern detection remains unresolved, and comparisons based on regional summaries lose spatial detail. Here we show that spatial frequency provides a common basis for detecting and comparing these patterns. Our framework, SONIC, unifies spatial detection tests through a common quadratic form, establishes conditions for reliable detection and explains how kernel choice determines sensitivity to different spatial patterns. It also separates changes in spatial organization from changes in overall abundance without aligning tissues. Fast, memory-efficient algorithms make detection and comparison practical across large datasets. Applying SONIC, we identify plaque-associated responses in Alzheimer's disease and differences in the spatial expression of blood-clotting genes between glioma subtypes. We further construct a gene-centric atlas that traces changes in spatial expression through mouse and human embryogenesis and supports retrieval of related patterns across species. These results extend spatial analysis from identifying individual patterns to following their changes across anatomically different tissues. Together, SONIC establishes a shared language for integrating molecular maps across studies and technologies.

Membership Inference Attacks (MIAs) aim to distinguish training points (members) from unseen data (non-members), and are widely used to quantify memorization and assess privacy risks. Standard MIA evaluation requires repeated retraining, which is computationally costly for large models. One-run (single training with randomized data inclusion) and zero-run (post hoc evaluation) methods are often used instead, but their statistical validity remains unclear. We address this gap by framing MIA evaluation as a causal inference problem, defining memorization as the causal effect of including a data point in the training set. This novel formulation reveals and formalizes key sources of bias in existing protocols: one-run methods suffer from interference between jointly included points, while zero-run evaluations are additionally confounded by distribution shift between member and non-member evaluation data. We derive causal analogues of standard MIA metrics and propose practical estimators for multi-run, one-run, and zero-run regimes with non-asymptotic consistency guarantees. We validate our approach in several settings, including pretrained and fine-tuned LLMs, showing that it enables reliable measurement of MIA performance without retraining and under distribution shift. Overall, our framework provides a principled foundation for privacy evaluation in modern AI systems.

Accurate and high-resolution estimation of land surface temperature (LST) is crucial in estimating evapotranspiration, a measure of plant water use and a central quantity in agricultural applications. In this work, we develop a novel statistical method for downscaling LST data obtained from NASA's ECOSTRESS mission, using high-resolution data from the Landsat 8 mission as a proxy for modeling agricultural field structure. Using the Landsat data, we identify the boundaries of agricultural fields through edge detection techniques, allowing us to capture the inherent block structure present in the spatial domain. We propose a block-diagonal Gaussian process (BDGP) model that captures the spatial structure of the agricultural fields, leverages independence of LST across fields for computational tractability, and accounts for the change of support present in ECOSTRESS observations. We use the resulting BDGP model to perform Gaussian process regression and obtain high-resolution estimates of LST from ECOSTRESS data, along with uncertainty quantification. Our results demonstrate the practicality of the proposed method in producing reliable high-resolution LST estimates, with potential applications in agriculture, urban planning, and climate studies.

There is growing interest in a hybrid control design for treatment evaluation, where a randomized controlled trial is augmented with external control data from a previous trial or a real world data source. The hybrid control design has the potential to improve efficiency but also carries the risk of introducing bias. The potential bias in a hybrid control study can be mitigated by adjusting for baseline covariates that are related to the control outcome. Existing methods that serve this purpose commonly assume that the internal and external control outcomes are exchangeable upon conditioning on a set of measured covariates. Possible violations of the exchangeability assumption can be addressed using a g-computation method with variable selection under a correctly specified outcome regression model. In this article, we note that a particular version of this g-computation method is protected against misspecification of the outcome regression model. This observation leads to a model-robust g-computation method that is remarkably simple and easy to implement, consistent and asymptotically normal under minimal assumptions, and able to improve efficiency by exploiting similarities between the internal and external control groups. The method is evaluated in a simulation study and illustrated using real data from HIV treatment trials.

AI agents increasingly execute procedural workflows as sequential action traces, which obscures latent concurrency and induces repeated step-by-step reasoning. We introduce BPOP, a Bayesianframework that infers a latent dependency partial order from noisy linearized traces. BPOP models traces as stochastic linear extensions of an underlying graph and performs efficient MCMC inference via a tractable frontier-softmax likelihood that avoids #P-hard marginalization over linear extensions. We evaluate on our open-sourced Cloud-IaC-6, a suite of cloud provisioning tasks with heterogeneous LLM-generated traces, and WFCommons scientific workflows. BPOP recover dependency structure more accurately than trace-only and process-mining baselines, and the inferred graphs support a compiled executor that prunes irrelevant context, yielding substantial reductions in token usage and execution time.

We propose a fundamental metric for measuring the distance between two distributions. This metric, referred to as the decision-focused (DF) divergence, is tailored to stochastic linear optimization problems in which the objective coefficients are random and may follow two distinct distributions. Traditional metrics such as KL divergence and Wasserstein distance are not well-suited for quantifying the resulting cost discrepancy, because changes in the coefficient distribution do not necessarily change the optimizer of the underlying linear program. Instead, the impact on the objective value depends on how the two distributions are coupled (aligned). Motivated by optimal transport, we introduce decision-focused distances under several settings, including the optimistic DF distance, the robust DF distance, and their entropy-regularized variants. We establish connections between the proposed DF distance and classical distributional metrics. For the calculation of the DF distance, we develop efficient computational methods. We further derive sample complexity guarantees for estimating these distances and show that the DF distance estimation avoids the curse of dimensionality that arises in Wasserstein distance estimation. The proposed DF distance provides a foundation for a broad range of applications. As an illustrative example, we study the interpolation between two distributions. Numerical studies, including a toy newsvendor problem and a real-world medical testing dataset, demonstrate the practical value of the proposed DF distance.