Papers

Treatment effects estimated from a randomized controlled trial are local not only to the study population but also to the time at which the trial was conducted. The literature on generalizing experimental findings to new populations is extensive, yet transporting effects across time has received far less attention, and even defining the target estimand is nonobvious. We formalize the transported average treatment effect under a separable temporal effects assumption, derive two identification strategies: replicated trials and common arm, and develop doubly robust, semiparametrically efficient estimators for each. Applied to a large archive of headline A/B tests, the common arm strategy is substantially more precise but exhibits systematic bias when the temporal factor depends on the gap between intervention and measurement rather than on measurement time alone, while the replicated trials strategy, which allows this dependence, tracks the ground truth more faithfully. Simulation studies investigate when each strategy is reliable and when it silently fails.

Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which additionally encode dependence across univariate marginals, have received less attention and pose computational and statistical challenges. In this work, we address these challenges with a new regression approach for multivariate distributional responses, in which distributions are modeled within the semiparametric nonparanormal family. By incorporating the nonparanormal transport (NPT) metric – an efficient closed-form surrogate for the Wasserstein distance – into the Fréchet regression framework, our approach decomposes the problem into separate regressions of marginal distributions and their dependence structure, facilitating both efficient estimation and granular interpretation of predictor effects. We provide theoretical justification for NPT, establishing its bi-Lipschitz equivalence to the Wasserstein distance and proving that it mitigates the curse of dimensionality. We further prove uniform convergence guarantees for regression estimators, both when distributional responses are fully observed and when they are estimated from empirical samples, attaining fast convergence rates comparable to the univariate case. The utility of our method is demonstrated via simulations and an application to continuous glucose monitoring data.

A matching platform is a system that matches participants of different types, such as companies and job-seekers. In such a platform, maximizing matches may concentrate assignments on popular participants, increasing dissatisfaction among others, and eventually causing churn, which reduces the platform's profit opportunities. To address this issue, we propose a novel online learning problem, Combinatorial Allocation Bandits (CAB), which incorporates the notion of *arm satisfaction*. In CAB, at each round, the learner observes feature vectors for $K$ arms and $N$ users, assigns users to arms, and observes feedback following a generalized linear model (GLM). Unlike prior work, the objective is to maximize arm satisfaction rather than the number of positive feedback. For CAB, we develop an upper confidence bound algorithm that uses an approximate optimization oracle and achieves an approximate regret upper bound, whose dependence on $d$, $T$, and $N$ matches the known lower bound for contextual combinatorial linear bandits up to logarithmic factors. We also analyze a Thompson sampling algorithm with a standard regret bound under an exact optimization oracle, and propose a cheaper one-pass variant retaining sublinear approximate regret under a self-concordance assumption. Experiments on synthetic data support the objective and show that CAB-UCB achieves higher cumulative satisfaction than baselines.

Many regulatory and analytic problems require that a prohibited variable influence a decision only through a designated allowable channel – a conditional-independence requirement that arises in path-specific fairness, the handling of classified information, and the regulation of trading on non-public information, among other settings. Such requirements may be enforced either stratum-by-stratum or, more commonly (and more efficiently), through a single averaged constraint on the conditional effect. We study the resulting enforcement problem from two perspectives. From the regulator's side, we formulate causal masking as a linear program and show that averaged-constraint optimization almost surely produces policies that violate the stratum-wise requirement while satisfying the averaged one exactly. The gains from masking grow with confounding and outcome heterogeneity, and detection requires precisely the conditional-independence tests that average constraints aim to avoid. From the optimizer's side, the same construction shows that masked policies recover most of the reward of unconstrained exploitation while being far harder to detect, making them attractive in any setting where the basis of decisions is itself sensitive. Together, these results argue that regulating direct dependence through averaged statistics on observed decisions is structurally limited, and that meaningful enforcement must operate at the level of the decision rule itself.

Many scientific applications involve mixed spatially indexed outcomes of heterogeneous types that are driven by shared latent mechanisms. Modeling such data is challenging due to complex, nonlinear, and potentially nonstationary spatial dependence, as well as the need for coherent joint inference across mixed outcome distributions. Existing multivariate mixed outcome models often rely on restrictive linear assumptions, while recent deep learning approaches emphasize predictive flexibility but typically lack coherent joint modeling and uncertainty quantification for spatial data. We develop MultiDeepGP, a scalable and statistically principled framework for joint modeling of multivariate mixed outcomes in spatial settings. The proposed approach introduces a shared latent spatial component that governs cross-outcome dependence while allowing outcome-specific distributions. Spatial dependence and nonlinear structure are captured through a deep latent representation, and uncertainty quantification is enabled via an efficient Monte Carlo-based inference strategy. This construction balances modeling flexibility with probabilistic interpretability and computational feasibility. The proposed method is evaluated through simulation studies designed to reflect key challenges in mixed outcome spatial modeling, as well as an application to georeferenced environmental and public health data from the African Great Lakes region. The results demonstrate that the proposed framework provides accurate joint prediction and reliable uncertainty quantification in complex spatial settings.

We study post-training linear autoregressive models with outcome and process rewards. Given a context $\boldsymbol{x}$, the model must predict the response $\boldsymbol{y} \in Y^N$, a sequence of length $N$ that satisfies a $\gamma$ margin condition, an extension of the standard separability to sequences. We prove that on test samples where the base model achieves a non-trivial likelihood $\alpha$, a variant of policy gradient (PG) can achieve likelihood $1 - \varepsilon$ with an essentially minimax optimal number of reward queries $\tilde{O}((\alpha^{-1} + \varepsilon^{-1})/\gamma^2)$. However, a barrier arises for going beyond the support of the base model. We prove that the overall expected error after post-training with outcome rewards is governed by a property of the base model called the Likelihood Quantile (LQ), and that variants of PG, while minimax optimal, may require a number of reward queries exponential in $N$ to go beyond this support, regardless of the pre-training algorithm. To overcome this barrier, we study post-training with a process reward model, and demonstrate how PG variants in this setting avoid the curse of dimensionality in $N$ via dependence on a token-level LQ. Along the way, we prove that under the margin condition, SGD with adaptive learning rate (LR) achieves a near optimal test error for statistical learning, and PG with adaptive LR achieves a near optimal number of mistakes for online learning while being computationally efficient whenever possible, both of which may be of independent interest.

Offline reinforcement learning (RL) aims to learn decision policies from a fixed batch of logged transitions, without additional environment interaction. Despite remarkable empirical progress, offline RL remains fragile under distribution shifts: value-based methods can overestimate the value of unseen actions, yielding policies that exploit model errors rather than genuine long-term rewards. We propose Bayesian Conservative Policy Optimization (BCPO), a unified framework that converts epistemic uncertainty into provably conservative policy improvement. BCPO maintains a hierarchical Bayesian posterior over environment/value models, constructs a credible lower bound (LCB) on action values, and performs policy updates under explicit KL regularization toward the behavior distribution. This yields an uncertainty-calibrated analogue of conservative policy iteration in the offline regime. We provide a finite-MDP theory showing that the pessimistic fixed point lower-bounds the true value function with high probability and that KL-controlled updates improve a computable return lower bound. Empirically, we verify the methodology on a real offline replay dataset for the CartPole benchmark obtained via the d3rlpy ecosystem, and report diagnostics that link uncertainty growth and policy drift to offline instability, motivating principled early stopping and calibration

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through samples generated by simulators or external datasets, while others admit tractable mathematical expressions or are specified through statistical assumptions about variable relationships. Developing inference methods that coherently integrate these heterogeneous sources of information remains an open challenge. In this paper, we propose a Two-Stage Normalizing Flows framework for approximating and sampling from such distributions. The method first learns the densities of components for which only samples are available, and then combines the outputs with the analytically specified terms to reconstruct the full target distribution in a second stage. The resulting model enables both point-wise density evaluation and efficient generation of representative samples, without requiring direct access to the full target density or joint samples from the complete model. We assess the proposed approach through simulation studies in joint density inference and Bayesian hierarchical models with inaccessible likelihoods. The proposed framework is able to accurately recover complex, highly nonlinear target structures using only partial information about the target density, providing stable and flexible approximations in settings where standard modeling assumptions do not hold (or when complete access to the target distribution is not available). Analysis of a large scale astronomy application highlights interesting differences between our method and existing approaches. Our normalizing flows procedure offers a robust and flexible approach to inference for intractable target distributions across both simulated and real-world applications.

Adaptive experiments are used extensively in online platforms, healthcare and biotechnology, and the social sciences. Often, the primary goal is not to precisely estimate a treatment effect but to demonstrate that at least one candidate intervention yields a positive effect, for some subpopulation and on some measured outcome. We formalize this objective as testing the global null in a threshold bandit framework, and develop two inference procedures that are valid under general adaptive sampling: one that pools information across promising arms, and one based on time-uniform multiple testing of individual arm means. To support the latter, we establish a moderate-deviations principle for the sequential $t$-statistic, justifying asymptotic confidence sequences in settings where the number of arms is large relative to the sample size. To illustrate how adaptive designs can target the proposed statistics, we recast experimental design as bandit optimization with an arm's reward given by its signal-to-noise ratio, and analyze an allocation rule for which we establish a logarithmic regret bound. We apply the methods in a simulation study of targeting unconditional cash transfer programs.

Medication adherence is essential to ensure treatment effectiveness, but too often in routine care non-adherence compromises the desired outcome. We explore longitudinal causal modelling using observational data to estimate the time-varying effects of continuous drug adherence measures on health outcomes over a sustained period. The goal of such analyses is to quantify the potential impact of interventions to improve adherence on long-term health. We consider two established longitudinal causal approaches designed to handle time-varying confounding under the “no unmeasured confounding” (NUC) assumption: G-estimation and inverse probability of treatment weighting (IPTW). In randomized controlled trial, NUC-based methods have been applied to address non-adherence as an intercurrent event, and instrumental variable (IV) extensions of G-estimation have also been introduced for settings where the NUC assumption may fail. We adapt these methods to observational data settings and illustrate their use for assessing how adherence over time impacts health outcomes. We align the causal parameters across methods and show they can target the same causal estimand: the average effect among treated individuals of full adherence versus zero adherence. We set out the identification conditions for IPTW and G-estimation under NUC, and for an IV-based extension that has specific utility when the NUC assumption is implausible. We assess the statistical properties, strengths and weaknesses of each approach through Monte Carlo simulations designed to reflect longitudinal studies with a continuous exposure. We demonstrate these methods by quantifying the effect of full statin adherence on LDL cholesterol control in 13,000 UK Biobank participants with linked primary care data.

As machine learning (ML) systems increasingly shape access to credit, jobs, and other opportunities, the fairness of algorithmic decisions has become a central concern. Yet it remains unclear when enforcing fairness constraints in these systems genuinely improves outcomes for affected groups or instead leads to "leveling down," making one or both groups worse off. We address this question in a unified, population-level (Bayes) framework for binary classification under prevalent group fairness notions. Our Bayes approach is distribution-free and algorithm-agnostic, isolating the intrinsic effect of fairness requirements from finite-sample noise and from training and intervention specifics. We analyze two deployment regimes for ML classifiers under common legal and governance constraints: attribute-aware decision-making (sensitive attributes available at decision time) and attribute-blind decision-making (sensitive attributes excluded from prediction). We show that, in the attribute-aware regime, fair ML necessarily (weakly) improves outcomes for the disadvantaged group and (weakly) worsens outcomes for the advantaged group. In contrast, in the attribute-blind regime, the impact of fairness is distribution-dependent: fairness can benefit or harm either group and may shift both groups' outcomes in the same direction, leading to either leveling up or leveling down. We characterize the conditions under which these patterns arise and highlight the role of "masked" candidates in driving them. Overall, our results provide structural guidance on when pursuing algorithmic fairness is likely to improve group outcomes and when it risks systemic leveling down, informing fair ML design and deployment choices.

We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. These eigenfunctions satisfy a transport-type partial differential equation (PDE) that we invert using three analytically grounded methods: (i) A Lions-type variational principle in a reproducing kernel Hilbert space (RKHS), (ii) convolution with a Green's function, and (iii) a resolvent operator constructed via Laplace transforms along characteristic flows. We prove that these three constructions yield identical kernels under mild smoothness and causality assumptions. We further show that the associated kernel eigenfunctions (Mercer modes) converge in L^2 to true Koopman eigenfunctions when the latter lie in the RKHS. Our approach is numerically realized through a mesh-free, convex optimization framework, enhanced with boundary regularization to handle eigenfunction blow-up. A multiple-kernel learning (MKL) scheme selects kernels automatically via residual minimization. Finally, we demonstrate that the same framework applies verbatim to a broader class of linear transport PDEs, including the advection, continuity, and Liouville equations. The unification of variational principles, Green's functions, and the method of characteristics enables the development of novel schemes for approximating eigenfunctions of transport equations, including those of the Koopman operator, and introduces a data-driven approach for learning kernels tailored to these approximations. Numerical experiments confirm the practical utility and robustness of the method.

Understanding interaction effects among variables is important for regression modeling in various applications. The conventional approach of quantifying interactions as the product of variables often lacks clear interpretability, especially in complex systems. The concept of conditional main effects (CME) provides a more intuitive and interpretable framework for capturing interaction effects by quantifying the effect of one variable conditional on the level of another. A recent method called cmenet further considered the bi-level selection of CMEs by leveraging their natural grouping structure (e.g., sibling and cousin groups) through penalization. However, there are several limitations in the cmenet method, including the coupling ability of penalties for within-group CMEs, lack of adaptiveness for between-group penalties, and restriction to linear models with continuous responses. To overcome these limitations, we propose an adaptive cmenet method for CME selection under the generalized linear model (GLM) framework. The proposed method considers a penalized likelihood approach with adaptive weights to enable effective bi-level variable selection, improving both between-group and within-group selection. An efficient algorithm for parameter estimation is also developed by employing an iteratively reweighted least squares procedure. The performance of the proposed method is evaluated by both simulation studies and real-data studies in gene association analysis.

In contextual bilateral trade under full feedback, the posted price does not affect which valuations are observed. We show that in this model such action-independent feedback removes the polynomial adaptation penalty familiar from heavy-tailed bandits: fully parameter-free algorithms attain the oracle minimax $T$-exponents up to logarithmic factors, with no knowledge of the moment order $p \in (1,2)$ or its scale $\sigma_p$, and – in the nonparametric case – none of the effective Hölder smoothness $\beta \in (0,1]$. The statistic that makes model selection possible is a paired squared-loss difference, whose noise-square term cancels exactly, leaving noise damped by the candidate gap. The resulting bilateral-trade regret rates are new. Trader valuations have bounded conditional densities and heavy tails – finite $p$-th moments for some $p \in (1,2)$, with possibly infinite variance. An epoch-based algorithm with truncated means achieves regret $\widetilde{O}(T^{(2-p)/p})$ in the parametric model and $\widetilde{O}(T^{1-2\beta(p-1)/(\beta p + d(p-1))})$ when the market value function is $\beta$-Hölder, with matching $\Omega(\cdot)$ lower bounds – under a mild nondegeneracy condition – via Assouad's method and a fixed-support mixture construction – characterizing the minimax rate in $T$ up to logarithmic factors over the effective smoothness range $\beta \in (0,1]$, interpolating between the classical nonparametric rate at $p{=}2$ and the trivial linear rate as $p \to 1^+$. The enabling structural step extends the self-bounding property of Bachoc et al. (ICML 2025) from bounded to real-valued valuations: within our conditionally independent, conditionally centered noise model, bounded conditional densities and finite first moments suffice for the expected regret of any price $\pi$ to satisfy $\mathbb{E}[g(m,V,W) - g(\pi,V,W)] \le L|m-\pi|^2$ – no second moment is needed.

Conformal prediction delivers prediction intervals with distribution-free coverage, but its intervals can look overconfident in regions where the model is extrapolating, because standard conformal scores do not explicitly represent epistemic uncertainty. Credal methods, by contrast, make epistemic effects visible by working with sets of plausible predictive distributions, but they are typically model-based and lack calibration guarantees. We introduce CREDO, a simple "credal-then-conformalize" recipe that combines both strengths. CREDO first builds an interpretable credal envelope that widens when local evidence is weak, then applies split conformal calibration on top of this envelope to guarantee marginal coverage without further assumptions. This separation of roles yields prediction intervals that are interpretable: their width can be decomposed into aleatoric noise, epistemic inflation, and a distribution-free calibration slack. We provide a fast implementation based on trimming extreme posterior predictive endpoints, prove validity, and show on benchmark regressions that CREDO maintains target coverage while improving sparsity adaptivity at competitive efficiency.

A utility function has been proposed that values more lives that are lost than those that are saved. I do not dispute the ethical motivation behind this kind of asymmetry. However, I show with a simple example that the scope of applicability of such a decision criterion is considerably more limited than it may first appear.

The growing scale of deep learning demands distributed training frameworks that jointly reason about parallelism, memory, and network topology. Prior works often rely on heuristic or topology-agnostic search, handling communication and memory separately. Without per-device memory awareness, these methods typically ensure feasibility post hoc by sharding parameters and activations across many devices, increasing synchronization, inflating communication, and underutilizing compute-limiting scalability and efficiency on real datacenter networks. We present NEST, a network-, compute-, and memory-aware device placement framework that unifies model parallelism, topology modeling, and memory feasibility via structured dynamic programming. NEST's DP operates on operator graphs with tensor and expert parallel configurations, explicit allreduce latencies across hierarchical or arbitrary networks, and memory/compute profiles. By factoring parallelism across tensor, pipeline, data, and expert dimensions, NEST defines a principled search space for hybrid strategies while jointly optimizing co-location, network latency, and memory feasibility. Evaluations across diverse hardware and networks show NEST achieves up to 2.43 times higher throughput, better memory efficiency, and improved scalability over state-of-the-art baselines, providing a foundation for co-designing parallelization strategies and datacenter interconnects for next-generation AI infrastructure. The source code of NEST is available at: https://github.com/scai-tech/Nest

We examine the estimation of the Kullback-Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate continuous distributions. Our starting point is the maximum entropy principle for Shannon entropy: among all distributions with a fixed mean vector and covariance matrix, the multivariate Gaussian distributions uniquely maximize entropy. As a result, the KL divergence from a moment-matched Gaussian distribution to an unknown density can then be written as the entropy difference, which is a suitable information-theoretic measure of divergence from the Gaussian distribution. To estimate, we use $k$-nearest neighbor (kNN) estimators based on Shannon entropy and KL divergence derived from the Kozachenko-Leonenko approach and subsequent improvements, along with the consistency and $L^{2}$-convergence results established for these estimators. Motivated by previous entropy-based goodness-of-fit ideas developed for Rényi-type functionals under generalized Gaussian and Student-type models, we describe a KL-based test statistic as being the difference between (i) the entropy of a Gaussian model fitted to the sample mean and covariance and (ii) the KL divergence between the unknown entropy and the kNN estimate. The statistic converges to zero under multivariate normality and converges to a strictly positive bound under non-Gaussian alternatives. Results from Monte Carlo simulations on various dimensions and sample sizes indicate that the proposed procedure achieves accurate Type I error control and accurate, generally superior power compared to conventional multivariate tests of normality, particularly at medium and high dimensions.

The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the underlying system behavior. In this work, we propose a latent autoencoder ensemble Kalman filter (LAE-EnKF) that addresses this limitation by reformulating the assimilation problem in a learned latent space with linear and stable dynamics. The proposed method learns a nonlinear encoder–decoder together with a stable linear latent evolution operator and a consistent latent observation mapping, yielding a closed linear state-space model in the latent coordinates. This construction restores compatibility with the Kalman filtering framework and allows both forecast and analysis steps to be carried out entirely in the latent space. Compared with existing autoencoder-based and latent assimilation approaches that rely on unconstrained nonlinear latent dynamics, the proposed formulation emphasizes structural consistency, stability, and interpretability. We provide a theoretical analysis of learning linear dynamics on low-dimensional manifolds and establish generalization error bounds for the proposed latent model. Numerical experiments on representative nonlinear and chaotic systems demonstrate that the LAE-EnKF yields more accurate and stable assimilation than the standard EnKF and related latent-space methods, while maintaining comparable computational cost and data-driven.

Concept learning is a form of supervised machine learning that operates on knowledge bases in description logics. State-of-the-art concept learners often rely on an iterative search through a countably infinite concept space. In each iteration, they retrieve instances of candidate solutions to select the best concept for the next iteration. While simple learning problems might require a few dozen instance retrieval calls to find a fitting solution, complex learning problems might necessitate thousands of calls. We alleviate the resulting runtime challenge by presenting a semantics-aware caching approach. Our cache is essentially a subsumption-aware map that links concepts to a set of instances via crisp set operations. Our experiments on 5 datasets with 4 symbolic reasoners, a neuro-symbolic reasoner, and 5 popular pagination policies demonstrate that our cache can reduce the runtime of concept retrieval and concept learning by an order of magnitude while being effective for both symbolic and neuro-symbolic reasoners.

Existing models of political violence often emphasize discrete transitions, when conflicts emerge, escalate, or subside, without considering the longer trajectories of violence that accumulate across time and space. This paper introduces a spatially explicit longitudinal sequence analysis to address this gap. Using event-level data from the Armed Conflict Location and Event Dataset covering Africa from 1997 to 2024, we classify locations according to the intensity and spatial concentration of violence, tracing how these states evolve into distinct conflict trajectories. Applying optimal matching and clustering techniques, we identify six recurrent patterns ranging from short-lived, localized outbreaks to protracted high-intensity conflicts. We further assess how these trajectories align across neighboring areas, revealing evidence of spatial interdependence, particularly in border regions. By highlighting the temporal rhythms and geographic linkages of political violence, the study advances conflict research beyond isolated transitions and provides a framework for understanding the life cycles of violence.

This paper investigates the role of the augmentation parameter in the Finite Selection Model (FSM) and its impact on estimator performance. Through a comprehensive Monte Carlo simulation study, we analyze the sensitivity of bias, variance, and mean squared error to different values of the augmentation parameter. The results demonstrate that moderate augmentation improves covariate balance while maintaining estimation efficiency. However, excessive augmentation may increase variance and reduce estimator stability. The findings provide practical guidelines for selecting the augmentation parameter in applied experimental design settings.

Background: We aim to develop enriched radiomics features that integrate classical structural radiomics with novel functional radiomics derived from liver MRI for diagnosis and risk stratification in liver cancer. The proposed framework leverages enhancement pattern mapping (EPM) images to provide an automated and robust radiomics representation that captures intratumoral heterogeneity through pixel-level functional information. Methods: Pixel-wise EPM data reflecting blood perfusion were extracted from T1-weighted MRI scans. Classical structural radiomics features were extracted via existing software such as PyRadiomics. In addition, empirical quantiles of EPM values over all pixels within the image, and then smoothed using suitable basis. The smoothed quantiles, along with the classical structural quantiles, are used as functional radiomics features for diagnostic classification and tumor grade stratification, using L1-penalized logistic model that automatically downweights the contribution of the irrelevant features. Further, we conducted longitudinal analyses using Bayesian tensor response regression, which enables spatial smoothing and parsimonious modeling of temporally evolving imaging patterns. Results: The enriched radiomics features illustrate higher diagnostic classification performance (AUC=0.96, sensitivity> 0.8) and superior tumor grade stratification accuracy (AUC=0.87, sensitivity=0.8) compared to alternate radiomics features. Moreover, we find that the proportion of lesion pixels with significant reduction in EPM values over time is considerably higher (median = 0.12) in aggressive lesions versus stable or mildly aggressive lesions (median = 0.025). Conclusion: The enriched novel radiomics features can potentially replace classical radiomics analysis and be used for imaging biomarkers in cross-sectional and in longitudinal cancer imaging studies.

Distribution regression, where the goal is to predict a scalar response from a distribution-valued predictor, arises naturally in settings where observations are grouped and outcomes depend on group-level characteristics rather than on individual measurements. We introduce DistBART, a Bayesian nonparametric approach to distribution regression that models the regression function as a linear functional with the Riesz representer assigned a Bayesian additive regression trees (BART) prior. We argue that shallow decision tree ensembles encode reasonable inductive biases for tabular data, making them appropriate in settings where the functional depends primarily on low-dimensional marginals of the distributions. We show this both empirically on synthetic and real data and theoretically through an adaptive posterior concentration result. We also establish connections to kernel methods, and use this connection to motivate variants of DistBART that can learn nonlinear functionals. To enable scalability to large datasets, we develop a random-feature approximation that samples trees from the BART prior and reduces inference to sparse Bayesian linear regression, achieving computational efficiency while retaining uncertainty quantification.

Housing instability is a persistent challenge faced by households in cities across the United States. In worst-case scenarios, households are displaced from their residences and forced to start anew. In an effort to mitigate the harms of residential displacement, local policymakers have an interest in monitoring residential displacement within their communities. In this work, we propose a new strategy to estimate sub-county residential displacement within the Central Puget Sound Region using data from three household survey programs. We first estimate residential displacement between 2016-2023 from a local household travel survey using a Bayesian spatiotemporal model, and poststratify with data from the American Community Survey. We then benchmark these estimates to the American Housing Survey to ensure consistency across sources. The results reveal east-west and north-south differences in residential displacement rates within the region as well as a temporary moderation of displacement in the 2020-2021 cohort of movers. Our estimates are publicly available for interested stakeholders to further study trends in residential displacement in the Central Puget Sound Region, and our methodology is transportable to other jurisdictions with similar data contexts.

Neural network methods for PDEs require reliable error control in function space norms. However, trained neural networks can typically only be probed at a finite number of point values. Without strong assumptions, point evaluations alone do not provide enough information to derive tight deterministic and guaranteed bounds on function space norms. In this work, we move beyond a purely black-box setting and exploit the neural network structure directly. We present a framework for the certified and accurate computation of integral quantities of neural networks, including Lebesgue and Sobolev norms, by combining interval arithmetic enclosures on axis-aligned boxes with adaptive marking/refinement and quadrature-based aggregation. On each box, we compute guaranteed lower and upper bounds for function values and derivatives, and propagate these local certificates to global lower and upper bounds for the target integrals. Our analysis provides a general convergence theorem for such certified adaptive quadrature procedures and instantiates it for function values, Jacobians, and Hessians, yielding certified computation of $L^p$, $W^{1,p}$, and $W^{2,p}$ norms. We further show how these ingredients lead to practical certified bounds for PINN interior residuals. Numerical experiments illustrate the accuracy and practical behavior of the proposed methods.

Detecting interaction effects (IEs) in meta-regression is challenging, especially when few studies are available and many plausible interactions are considered. In many meta-analyses, interpretability is essential, which limits the use of complex machine learning methods. Tree-based approaches offer a potentially useful compromise, but their role in meta-regression with random effects is not yet well understood. This paper examines how traditional linear and tree-based methods can support variable selection for IEs in random effects meta-regression. We compare test-based and information-criterion-based linear selection procedures with meta-CART approaches. These include single trees and tree ensembles, which combine single meta-CARTs into a stability selection ensemble based on bootstrapped data. All methods are evaluated using a real-world meta-analytic dataset and a simulation study. The data-generating process assumes linear IEs, complemented by settings with simple non-linear interactions. Our results show that under strictly linear interactions, linear selection methods perform as expected and achieve superior performance for IE detection. Tree-based methods are more conservative when the number of studies is small, but become competitive as sample size increases, particularly the stability-selected variants. When IEs deviate from strict linearity, Wald-type approaches can deteriorate, whereas criterion-based methods maintain a relatively stable performance. Tree-based methods, particularly stabilized versions of random-effects meta-CART, provide a robust alternative when a sufficient number of observations is available. They could thus be used for pre-selection and sensitivity analyses, guarding against more complex data structures. Additionally, selection frequency patterns from meta-CART tree ensembles can help to reveal structural patterns in the data in an exploratory way.

Statistical modeling of dependent directional data remains relatively underexplored, particularly in high-dimensional spatial settings. Existing approaches for spatial angular data primarily rely on wrapped Gaussian process (WGP) models, which provide a coherent framework for capturing spatial dependence on the circle. However, WGP-based methods become computationally challenging when the spatial domain is large, and observations are available at high resolution. This limitation is especially relevant in the analysis of large-scale geological and climate phenomena, such as tsunamis and hurricanes, where directional measurements (e.g., wave or wind directions) may be available over an entire ocean basin. To address these challenges, we propose a wrapped Gaussian Markov random field (WGMRF) model for large spatial directional datasets. By exploiting the sparse precision structure inherent in Gaussian Markov random fields, the proposed approach achieves substantial computational gains while preserving flexible spatial dependence on the circular scale. We discuss key properties of the model, including its identifiability and dependence characteristics. The model fitting involves standard Markov chain Monte Carlo techniques. Through extensive simulation studies and an application to the wave direction data across the Indian Ocean during the 2004 Indian Ocean Tsunami, we compare the proposed method with both a non-spatial wrapped Gaussian model and a low-rank WGP alternative. The results demonstrate that the WGMRF offers improved predictive performance and scalability in large-domain applications.

In the face of vast numbers of preventable deaths worldwide and gaping disparities in their distribution, we cannot afford to conduct null and inconclusive effectiveness and implementation trials of evidence-based interventions. The gold standard in biomedical research, the individually randomized clinical trial, is ill-suited as the primary tool for knowledge generation for contextually relevant, scalable, complex public health interventions of multi-component strategies. In this paper, we discuss the new Learn-As-you-GO (LAGO) design. In LAGO trials, the components of a complex intervention package are repeatedly optimized in pre-planned stages, until the package achieves its outcome and power goals with minimized cost and/or other optimization criteria, such as maximizing patient satisfaction. In this paper, the inputs to, and outputs of, LAGO are described, along with its general methodology. The methods are illustrated in the BetterBirth study, a large trial that aimed to reduce maternal and neonatal mortality in Uttar Pradesh, India, using the WHO essential birth practices checklist. Despite its scale, the BetterBirth study failed to demonstrate a significant effect of the intervention package on the primary health endpoint that included maternal mortality. We show how this unfortunate outcome could have been remedied had LAGO been used. LAGO is further illustrated through the discussion of several ongoing LAGO-informed implementation trials of HIV and non-communicable diseases in the United States and Sub-Saharan Africa. The Learn-As-you-GO (LAGO) design optimizes a complex, multi-level intervention for minimum cost, pre-specified power, and a pre-specified effectiveness goal, by adapting the intervention as the study is conducted, reducing risk of trial failure.

In this paper, we propose a novel bounded asymmetric elastic net ($L_{baen}$) loss function and combine it with the support vector machine (SVM), resulting in the BAEN-SVM. The $L_{baen}$ is bounded and asymmetric and can degrade to the asymmetric elastic net hinge loss, pinball loss, and asymmetric least squares loss. BAEN-SVM not only effectively handles noise-contaminated data but also addresses the geometric irrationalities in the traditional SVM. By proving the violation tolerance upper bound (VTUB) of BAEN-SVM, we show that the model is geometrically well-defined. Furthermore, we derive that the influence function of BAEN-SVM is bounded, providing a theoretical guarantee of its robustness to noise. The Fisher consistency of the model further ensures its generalization capability. Since the \( L_{\text{baen}} \) loss is non-convex, we designed a clipping dual coordinate descent-based half-quadratic algorithm to solve the non-convex optimization problem efficiently. Experimental results on artificial and benchmark datasets indicate that the proposed method outperforms classical and advanced SVMs, particularly in noisy environments.