Papers

Linking crimes by modus operandi has long been employed as an effective tool for crime investigation. The standard statistical method that underpins statistical crime linkage has been logistic regression. The simplicity and interpretability of this approach has been seen as an advantage for law enforcement agencies using statistical crime linkage. In 2023, the National Police Chiefs' Council published the Covenant for Using Artificial Intelligence in Policing designed to guide the development of novel methods for use within policing. In this article, we investigate more statistical and machine learning methods that could underpin crime linkage models. We investigate a range of methods including regression-, sampling-, and machine learning-based techniques and evaluate them against the principles of Explainability and Transparency from the Covenant. We investigate our methods on a new data set on romance fraud in the UK, where 361 victims of fraud reported the behaviours and characteristics of the suspects involved in their case. We propose a sensitive, Explainable, and Transparent machine learning model for crime linkage and demonstrate how this method could support crime linkage efforts by law enforcement agencies using a dataset of romance fraud with unknown linkage status.

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low sample size settings, such as genetic microarrays. Second, it improves interpretability as components are regularized to zero. However, over-regularization of sparse singular vectors can cause them to deviate greatly from the population singular vectors, potentially misrepresenting the data structure. Additionally, sparse singular vectors are often not orthogonal, resulting in shared information between components, which complicates the calculation of variance explained. To address these challenges, we propose a methodology for sparse PCA that reflects the inherent structure of the data matrix. Specifically, we identify uncorrelated submatrices of the data matrix, meaning that the covariance matrix exhibits a sparse block diagonal structure. Such sparse matrices commonly occur in high-dimensional settings. The singular vectors of such a data matrix are inherently sparse, which improves interpretability while capturing the underlying data structure. Furthermore, these singular vectors are orthogonal by construction, ensuring that they do not share information. We demonstrate the effectiveness of our method through simulations and provide real data applications. Supplementary materials for this article are available online.

Reinforcement learning (RL) has been widely applied to sequential decision making, where interpretability and performance are both critical for practical adoption. Current approaches typically focus on performance and rely on post hoc explanations to account for interpretability. Different from these approaches, we focus on designing an interpretability-oriented yet performance-enhanced RL approach. Specifically, we propose a spectral based linear RL method that extends the ridge regression-based approach through a spectral filter function. The proposed method clarifies the role of regularization in controlling estimation error and further enables the design of an adaptive regularization parameter selection strategy guided by the bias-variance trade-off principle. Theoretical analysis establishes near-optimal bounds for both parameter estimation and generalization error. Extensive experiments on simulated environments and real-world datasets from Kuaishou and Taobao demonstrate that our method either outperforms or matches existing baselines in decision quality. We also conduct interpretability analyses to illustrate how the learned policies make decisions, thereby enhancing user trust. These results highlight the potential of our approach to bridge the gap between RL theory and practical decision making, providing interpretability, accuracy, and adaptability in management contexts.

Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions. In this work, we propose a unified framework that explicitly models graph data as a mixture of probabilistic graph generative models represented by graphons. To characterize and estimate these graphons, we leverage graph moments (motif densities) to cluster graphs generated from the same underlying model. We establish a novel theoretical guarantee, deriving a tighter bound showing that graphs sampled from structurally similar graphons exhibit similar motif densities with high probability. This result enables principled estimation of graphon mixture components. We show how incorporating estimated graphon mixture components enhances two widely used downstream paradigms: graph data augmentation via mixup and graph contrastive learning. By conditioning these methods on the underlying generative models, we develop graphon-mixture-aware mixup (GMAM) and model-aware graph contrastive learning (MGCL). Extensive experiments on both simulated and real-world datasets demonstrate strong empirical performance. In supervised learning, GMAM outperforms existing augmentation strategies, achieving new state-of-the-art accuracy on 6 out of 7 datasets. In unsupervised learning, MGCL performs competitively across seven benchmark datasets and achieves the lowest average rank overall.

The introduction of machine learning methods has led to significant advances in automation, optimization, and discoveries in various fields of science and technology. However, their widespread application faces a fundamental limitation: the transfer of models between data domains generally lacks a rigorous mathematical justification. The key problem is the lack of formal criteria to guarantee that a model trained on one type of data will retain its properties on another.This paper proposes a solution to this problem by formalizing the concept of analogy between data sets and models using first-order logic and Hoare logic.We formulate and rigorously prove a theorem that sets out the necessary and sufficient conditions for analogy in the task of knowledge transfer between machine learning models. Practical verification of the analogy theorem on model data obtained using the Monte Carlo method, as well as on MNIST and USPS data, allows us to achieving F1 scores of 0.84 and 0.88 for convolutional neural networks and random forests, respectively.The proposed approach not only allows us to justify the correctness of transfer between domains but also provides tools for comparing the applicability of models to different types of data.The main contribution of the work is a rigorous formalization of analogy at the level of program logic, providing verifiable guarantees of the correctness of knowledge transfer, which opens new opportunities for both theoretical research and the practical use of machine learning models in previously inaccessible areas.

Per- and polyfluoroalkyl substances (PFAS) are persistent environmental pollutants of major public health concern due to their resistance to degradation, widespread presence, and potential health risks. Analyzing PFAS in groundwater is challenging due to left-censoring and strong spatial dependence. Although PFAS levels are influenced by sociodemographic, industrial, and environmental factors, the relative importance of these drivers remains unclear, highlighting the need for robust statistical tools to identify key predictors from a large candidate set. We present a Bayesian hierarchical framework that integrates censoring into a spatial process model via approximate Gaussian processes and employs a global-local shrinkage prior for high-dimensional variable selection. We evaluate three post-selection strategies, namely, credible interval rules, shrinkage weight thresholds, and clustering-based inclusion and compare their performance in terms of predictive accuracy, censoring robustness, and variable selection stability through cross-validation. Applied to PFOS concentrations in California groundwater, the model identifies a concise, interpretable set of predictors, including demographic composition, industrial facility counts, proximity to airports, traffic density, and environmental features such as herbaceous cover and elevation. These findings demonstrate that the proposed approach delivers stable, interpretable inference in censored, spatial, high-dimensional contexts, thereby offering actionable insights into the environmental and industrial factors affecting PFAS concentrations.

We introduce Group Policy Gradient (GPG), a family of critic-free policy-gradient estimators for general MDPs. Inspired by the success of GRPO's approach in Reinforcement Learning from Human Feedback (RLHF), GPG replaces a learned value function with a group-based Monte Carlo advantage estimator, removing the memory, compute, and hyperparameter costs of training a critic while preserving PPO's clipped-objective structure. We prove the consistency of the GPG estimator, analyze the bias-variance tradeoffs, and demonstrate empirically that GPG matches or outperforms PPO on standard benchmarks. GPG makes better use of parallel simulations, which, together with its critic-free design, results in more efficient use of computational resources than PPO.

This paper studies the computational challenges of large-scale attention-based models in artificial intelligence by utilizing importance sampling methods in the streaming setting. Inspired by the classical definition of the $\ell_2$ sampler and the recent progress of the attention scheme in Large Language Models (LLMs), we propose the definition of the attention sampler. Our approach significantly reduces the computational burden of traditional attention mechanisms. We analyze the effectiveness of the attention sampler from a theoretical perspective, including space and update time. Additionally, our framework exhibits scalability and broad applicability across various model architectures and domains.

Random survival forests are widely used for estimating covariate-conditional survival functions under right-censoring. Their standard log-rank splitting criterion is typically recomputed at each candidate split. This O(M) cost per split, with M the number of distinct event times in a node, creates a bottleneck for large cohort datasets with long follow-up. We revisit approximations proposed by LeBlanc and Crowley (1995) and develop simple constant-time updates for the log-rank criterion. The method is implemented in grf for R and reduces training time on large datasets while preserving predictive accuracy.

Sparse Autoencoders (SAEs) are widely used to steer large language models (LLMs), based on the assumption that their interpretable features naturally enable effective model behavior steering. Yet, a fundamental question remains unanswered: does higher interpretability indeed imply better steering utility? To answer this question, we train 90 SAEs across three LLMs (Gemma-2-2B, Qwen-2.5-3B, Gemma-2-9B), spanning five architectures and six sparsity levels, and evaluate their interpretability and steering utility based on SAEBench (arXiv:2501.12345) and AxBench (arXiv:2502.23456) respectively, and perform a rank-agreement analysis via Kendall's rank coefficients (tau b). Our analysis reveals only a relatively weak positive association (tau b approx 0.298), indicating that interpretability is an insufficient proxy for steering performance. We conjecture the interpretability utility gap may stem from the selection of SAE features, as not all of them are equally effective for steering. To further find features that truly steer the behavior of LLMs, we propose a novel selection criterion called Delta Token Confidence, which measures how much amplifying a feature changes the next token distribution. We show that our method improves the steering performance of three LLMs by 52.52 percent compared to the current best output score based criterion (arXiv:2503.34567). Strikingly, after selecting features with high Delta Token Confidence, the correlation between interpretability and utility vanishes (tau b approx 0), and can even become negative. This further highlights the divergence between interpretability and utility for the most effective steering features.

Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing memory needs for the same level of performance compared to explicit models. While it is empirically known that these compact models can often match or even exceed the accuracy of larger explicit networks by allocating more test-time compute, the underlying mechanism remains poorly understood. We study this gap through a nonparametric analysis of expressive power. We provide a strict mathematical characterization, showing that a simple and regular implicit operator can, through iteration, progressively express more complex mappings. We prove that for a broad class of implicit models, this process lets the model's expressive power scale with test-time compute, ultimately matching a much richer function class. The theory is validated across four domains: image reconstruction, scientific computing, operations research, and LLM reasoning, demonstrating that as test-time iterations increase, the complexity of the learned mapping rises, while the solution quality simultaneously improves and stabilizes.

PRTree is an R package for fitting Probabilistic Regression Trees (PRTrees), a class of regression trees that replaces deterministic splits with probabilistic associations to produce smooth prediction functions. The package implements both the original methodology and its recent extension for handling missing predictor values, allowing model fitting and prediction directly from incomplete datasets without prior imputation. It provides a unified framework for model fitting, prediction, visualization, smoothing-parameter selection, cross-validation, and model diagnostics through a standard R interface. Computationally intensive routines are implemented in FORTRAN, while the high-level interface follows the usual R workflow based on S3 classes and generic methods. This paper reviews the underlying methodology, describes the software architecture and main package components, and illustrates their use through reproducible examples.

Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations, such as nuclear norm and $\ell_1$ norm, to approximate the rank of a matrix and the $\ell_0$ functional (the number of non-zero elements) of another. In this work, we advocate a nonconvex regularization method, referred to as transformed $\ell_1$ (TL1), to improve both approximations. The rationale is that by varying the internal parameter of TL1, its behavior asymptotically approaches either $\ell_0$ or $\ell_1$. Since the rank is equal to the number of non-zero singular values and the nuclear norm is defined as their sum, applying TL1 to the singular values can approximate either the rank or the nuclear norm, depending on its internal parameter. We conduct a fine-grained theoretical analysis of statistical convergence rates, measured in the Frobenius norm, for both the low-rank and sparse components under general sampling schemes. These rates are comparable to those of the classical RPCA model based on the nuclear norm and $\ell_1$ norm. Moreover, we establish constant-order upper bounds on the estimated rank of the low-rank component and the cardinality of the sparse component in the regime where TL1 behaves like $\ell_0$, assuming that the respective matrices are exactly low-rank and exactly sparse. Extensive numerical experiments on synthetic data and real-world applications demonstrate that the proposed approach achieves higher accuracy than the classic convex model, especially under non-uniform sampling schemes.

Over the last four decades, the Arctic has warmed nearly four times faster than the rest of the planet, with anthropogenic aerosols among the major forcings. Greenland Summit Station has collected size-resolved particulate matter year-round since 2003, yet these records remain underutilized. Attributing multipollutant measurements to their sources (source apportionment) can be cast as a non-negative matrix factorization (NMF) problem. Because NMF is non-unique, source apportionment imposes often unverifiable constraints such as structural sparsity or rotations tuned using prior scientific knowledge, which is scarce for remote regions like the Arctic. Geometric NMF approaches offer a more data-driven route to identification, but many suffer from scaling ambiguity, assume exact separability, and lack a statistical framework for consistent estimation. We address these limitations by formally establishing statistical identifiability of the source attribution matrix under a stochastic framework that replaces hard separability with soft probabilistic relaxations. We then present a scalable geometric algorithm to estimate this matrix and prove its consistency, to our knowledge the first such result requiring no exact sparsity, no parametric distributional assumptions, and accommodating spatio-temporal dependence. Analyzing the 2003–2016 Summit record with our framework and HYSPLIT trajectories, we characterize long-range transport of anthropogenic and natural species into the Arctic.

Sequential estimation under partial observability requires tracking beliefs that may be high-dimensional, multimodal, and non-Gaussian. Classical Bayesian filters generalize zero-shot to any system whose dynamics can be evaluated, but their representations scale poorly: parametric filters struggle to capture multimodality, and particle filters require exponentially many particles in the state dimension. Generative Distribution Embeddings (GDEs) learn compact representations of complex distributions but have no sequential update. We present Neural Bayesian Filtering (NBF), which represents beliefs as embeddings and approximates their Bayesian update. At each step, NBF samples particles from a learned conditional generator, propagates them through the dynamics, and embeds the propagated set, weighted by the likelihood of the new observation. Regenerating the set from the embedding at each step, rather than resampling a surviving pool, mitigates the risk of impoverishment that degrades particle filters. The system dynamics and likelihood enter only through propagation and weighting, so NBF retains zero-shot adaptability to new dynamics as long as the beliefs they produce fall within the family the embedding was trained on. Training the GDE to represent that family requires only the states realized at training time. We validate NBF on Lorenz-96 and a pursuit–evasion domain, showing graceful scaling with state dimension, accurate tracking of multimodal posteriors, and zero-shot generalization to dynamics and likelihoods held out from training.

This paper introduces Hill-ADAM. Hill-ADAM is an optimizer with its focus towards escaping local minima in prescribed loss landscapes to find the global minimum. Hill-ADAM escapes minima by deterministically exploring the state space. This eliminates uncertainty from random gradient updates in stochastic algorithms while seldom converging at the first minimum that visits. In the paper we first derive an analytical approximation of the ADAM Optimizer step size at a particular model state. From there define the primary condition determining ADAM limitations in escaping local minima. The proposed optimizer algorithm Hill-ADAM alternates between error minimization and maximization. It maximizes to escape the local minimum and minimizes again afterward. This alternation provides an overall exploration throughout the loss space. This allows the deduction of the global minimum's state. Hill-ADAM was tested with 5 loss functions and 12 amber-saturated to cooler-shade image color correction instances.

Test-time scaling improves the reasoning capabilities of large language models (LLMs) by allocating extra compute to generate longer Chains-of-Thoughts (CoTs). This enables models to tackle more complex problem by breaking them down into additional steps, backtracking, and correcting mistakes. Despite its strong performance–demonstrated by OpenAI's o1 and DeepSeek R1, the conditions in the training data under which long CoTs emerge, and when such long CoTs improve the performance, remain unclear. In this paper, we study the performance of test-time scaling for transformers trained on an in-context weight prediction task for linear regression. Our analysis provides a theoretical explanation for several intriguing observations: First, at any fixed test error, increasing test-time compute allows us to reduce the number of in-context examples (context length) in training prompts. Second, if the skills required to solve a downstream task are not sufficiently present in the training data, increasing test-time compute can harm performance. Finally, we characterize task hardness via the smallest eigenvalue of its feature covariance matrix and show that training on a diverse, relevant, and hard set of tasks results in best performance for test-time scaling. We confirm our findings with experiments on large, nonlinear transformer architectures.

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of algorithms require either perfect samplers or sequential samplers for complex models, which are often either not available, or suffer from poor mixing, especially in high dimensions. We develop a method that does not require perfect or sequential sampling, and can be applied to both classes of methods: exact and approximate MCMC. The key to our approach is to utilize the tractable independence model underlying the intractable probabilistic graphical model for the purpose of constructing a finite sample unbiased Monte Carlo (and not MCMC) estimate of the Metropolis–Hastings ratio. This innovation turns out to be crucial for scalability in high dimensions. The method is demonstrated on the Ising model. Gradient-based alternatives to construct a proposal, such as Langevin and Hamiltonian Monte Carlo approaches, also arise as a natural corollary to our general procedure, and are demonstrated as well.

Learning dynamics is essential for model-based control and Reinforcement Learning in engineering systems, such as robotics and power systems. However, limited system measurements, such as those from low-resolution sensors, demand sample-efficient learning. Symmetry provides a powerful inductive bias by characterizing equivariant relations in system states to improve sample efficiency. While recent methods attempt to discover symmetries from data, they typically assume a single global symmetry group and treat symmetry discovery and dynamic learning as separate tasks, leading to limited expressiveness and error accumulation. In this paper, we propose the Latent Mixture of Symmetries (Latent MoS), an expressive model that captures a mixture of symmetry-governed latent factors from complex dynamical measurements. Latent MoS focuses on dynamic learning while locally and provably preserving the underlying symmetric transformations. To further capture long-term equivariance, we introduce a hierarchical architecture that stacks MoS blocks. Numerical experiments in diverse physical systems demonstrate that Latent MoS outperforms state-of-the-art baselines in interpolation and extrapolation tasks while offering interpretable latent representations suitable for future geometric and safety-critical analyses.

Measuring emotional states in transportation contexts is an emerging field. Methods based on self-reported emotions are limited by their low granularity and their susceptibility to memory bias. In contrast, methods based on physiological indicators provide continuous data, enabling researchers to measure changes in emotional states with high detail and accuracy. Not only are emotions important in the analysis, but understanding what triggers emotional changes is equally important. Uncontrolled variables such as traffic conditions, pedestrian interactions, and infrastructure remain a significant challenge, as they can have a great impact on emotional states. Explaining the reasons behind these emotional states requires gathering sufficient and proper contextual data, which can be extremely difficult in real-world environments. This paper addresses these challenges by applying an innovative approach, extracting contextual data (expert annotator level) from recorded multimedia using large language models (LLMs). In this paper, data are collected from an urban cycling case study of the City of Santiago, Chile. The applied models focus on understanding how different environments and traffic situations affect the emotional states and behaviors of the participants using physiological data. Sequences of images, extracted from the recorded videos, are processed by LLMs to obtain semantic descriptions of the environment. These discrete, although dense and detailed, contextual data are integrated into a hybrid model, where fatigue and arousal serve as latent variables influencing observed cycling behaviors (inferred from GPS data) like waiting, accelerating, braking, etc. The study confirms that cycling decisions are influenced by stress-related emotions and highlights the strong impact of urban characteristics and traffic conditions on cyclist behavior.

Detecting surface landmines and unexploded ordnances (UXOs) using deep learning has shown promise in humanitarian demining. However, deterministic neural networks can be vulnerable to noisy conditions and adversarial attacks, leading to missed detection or misclassification. This study introduces the idea of uncertainty quantification through Monte Carlo (MC) Dropout, integrated into a fine-tuned ResNet-50 architecture for surface landmine and UXO classification, which was tested on a simulated dataset. Integrating the MC Dropout approach helps quantify epistemic uncertainty, providing an additional metric for prediction reliability, which could be helpful to make more informed decisions in demining operations. Experimental results on clean, adversarially perturbed, and noisy test images demonstrate the model's ability to flag unreliable predictions under challenging conditions. This proof-of-concept study highlights the need for uncertainty quantification in demining, raises awareness about the vulnerability of existing neural networks in demining to adversarial threats, and emphasizes the importance of developing more robust and reliable models for practical applications.

Deep learning has gained attention for solving PDEs, but the black-box nature of neural networks hinders precise enforcement of boundary conditions. To address this, we propose a boundary condition-guaranteed evolutionary Kolmogorov-Arnold Network (KAN) with radial basis functions (BEKAN). In BEKAN, we propose three distinct and combinable approaches for incorporating Dirichlet, periodic, and Neumann boundary conditions into the network. For Dirichlet problem, we use smooth and global Gaussian RBFs to construct univariate basis functions for approximating the solution and to encode boundary information at the activation level of the network. To handle periodic problems, we employ a periodic layer constructed from a set of sinusoidal functions to enforce the boundary conditions exactly. For a Neumann problem, we devise a least-squares formulation to guide the parameter evolution toward satisfying the Neumann condition. By virtue of the boundary-embedded RBFs, the periodic layer, and the evolutionary framework, we can perform accurate PDE simulations while rigorously enforcing boundary conditions. For demonstration, we conducted extensive numerical experiments on Dirichlet, Neumann, periodic, and mixed boundary value problems. The results indicate that BEKAN outperforms both multilayer perceptron (MLP) and B-splines KAN in terms of accuracy. In conclusion, the proposed approach enhances the capability of KANs in solving PDE problems while satisfying boundary conditions, thereby facilitating advancements in scientific computing and engineering applications.

Generative models for sequential data often struggle with sparsely sampled and high-dimensional trajectories, typically reducing the learning of dynamics to pairwise transitions. We propose Interpolative Multi-Marginal Flow Matching (IMMFM), a framework that learns continuous stochastic dynamics jointly consistent with multiple observed time points. IMMFM employs a piecewise-quadratic interpolation path as a smooth target for flow matching and jointly optimizes drift and a data-driven diffusion coefficient, supported by a theoretical condition for stable learning. This design captures intrinsic stochasticity, handles irregular sparse sampling, and yields subject-specific trajectories. Experiments on synthetic benchmarks and real-world longitudinal neuroimaging datasets show that IMMFM outperforms existing methods in both forecasting accuracy and further downstream tasks.

Accurate numerical solutions of partial differential equations are essential in many scientific fields but often require computationally expensive solvers, motivating reduced-order models (ROMs). Latent Space Dynamics Identification (LaSDI) is a data-driven ROM framework that combines autoencoders with equation discovery to learn interpretable latent dynamics. However, enforcing latent dynamics during training can compromise reconstruction accuracy of the model for simulation data. We introduce multi-stage LaSDI (mLaSDI), a framework that improves reconstruction and prediction accuracy by sequentially learning additional decoders to correct residual errors from previous stages. Applied to the 1D-1V Vlasov equation, mLaSDI consistently outperforms standard LaSDI, achieving lower prediction errors and reduced training time across a wide range of architectures.

We study the problem of long-term (multiple days) mapping of a river plume using multiple autonomous underwater vehicles (AUVs), focusing on the Douro river representative use-case. We propose an energy - and communication - efficient multi-agent reinforcement learning approach in which a central coordinator intermittently communicates with the AUVs, collecting measurements and issuing commands. Our approach integrates spatiotemporal Gaussian process regression (GPR) with a multi-head Q-network controller that regulates direction and speed for each AUV. Simulations using the Delft3D ocean model demonstrate that our method consistently outperforms both single- and multi-agent benchmarks, with scaling the number of agents both improving mean squared error (MSE) and operational endurance. In some instances, our algorithm demonstrates that doubling the number of AUVs can more than double endurance while maintaining or improving accuracy, underscoring the benefits of multi-agent coordination. Our learned policies generalize across unseen seasonal regimes over different months and years, demonstrating promise for future developments of data-driven long-term monitoring of dynamic plume environments.

Confounding can lead to spurious associations. Typically, one must observe confounders in order to adjust for them, but in high-dimensional settings, recent research has shown that it becomes possible to adjust even for unobserved confounders. The methods for carrying out these adjustments, however, have not been thoroughly investigated. In this study, we derive a confounding framework in which the signal, bias, and variability can be cleanly partitioned and quantified, thereby enabling simulations in which one varies the bias-to-signal ratio while holding the signal-to-noise ratio fixed. Using this construction, we demonstrate the impact of the amount and complexity of unobserved confounding on the performance of competing methods, including the LASSO, principal components LASSO (PC-LASSO), and penalized linear mixed models (PLMMs). We identify scenarios in which each method outperforms the others and find that overall, PLMM is the most robust approach.

The pair-copula Bayesian Networks (PCBN) are graphical models composed of a directed acyclic graph (DAG) that represents (conditional) independence in a joint distribution. The nodes of the DAG are associated with marginal densities, and arcs are assigned with bivariate (conditional) copulas following a prescribed collection of parental orders. The choice of marginal densities and copulas is unconstrained. However, the simulation and inference of a PCBN model may necessitate possibly high-dimensional integration. We present the full characterization of DAGs that do not require any integration for density evaluation or simulations. Furthermore, we propose an algorithm that can find all possible parental orders that do not lead to (expensive) integration. Finally, we show the asymptotic normality of estimators of PCBN models using stepwise estimating equations. Such estimators can be computed effectively if the PCBN does not require integration. A simulation study shows the good finite-sample properties of our estimators.

The use of flexible machine-learning (ML) models to generate imputations of missing data within the framework of Multiple Imputation (MI) has recently gained traction, particularly in observational settings. For randomised controlled trials (RCTs), it is unclear whether ML approaches to MI provide valid inference, and whether they outperform parametric MI approaches under complex data generating mechanisms. We conducted two simulations in RCT settings that have incomplete continuous outcomes but fully observed covariates. We compared Complete Cases, standard MI (MI-norm), MI with predictive mean matching (MI-PMM) and ML-based approaches to MI, including classification and regression trees (MI-CART), Random Forests (MI-RF) and SuperLearner when outcomes are missing completely at random or missing at random conditional on treatment/covariate. The first simulation explored non-linear covariate-outcome relationships in the presence/absence of covariate-treatment interactions. The second simulation explored skewed repeated measures, motivated by a trial with digital outcomes. In the absence of interactions, we found that Complete Cases yields reliable inference; MI-norm performs similarly, except when missingness depends on the covariate. ML approaches can lead to smaller mean squared error than Complete Cases and MI-norm in specific non-linear settings, but provide unreliable inference for others. MI-PMM can lead to unreliable inference in several settings. In the presence of complex treatment-covariate interactions, performing MI separately by arm, either with MI-norm, MI-RF or MI-CART, provides inference that has comparable or with better properties compared to Complete Cases when the analysis model omits the interaction. For ML approaches, we observed unreliable inference in terms of bias in the estimated effect and/or its standard error when Rubin's Rules are implemented.

Communication efficiency is a central challenge in distributed machine learning training, and message compression is a widely used solution. However, standard Error Feedback (EF) methods (Seide et al., 2014), though effective for smooth unconstrained optimization with compression (Karimireddy et al., 2019), fail in the broader and practically important setting of composite optimization, which captures, e.g., objectives consisting of a smooth loss combined with a non-smooth regularizer or constraints. The theoretical foundation and behavior of EF in the context of the general composite setting remain largely unexplored. In this work, we consider composite optimization with EF. We point out that the basic EF mechanism and its analysis no longer stand when a composite part is involved. We argue that this is because of a fundamental limitation in the method and its analysis technique. We propose a novel method that combines Dual Averaging with EControl (Gao et al., 2024), a state-of-the-art variant of the EF mechanism, and achieves for the first time a strong convergence analysis for composite optimization with error feedback. Along with our new algorithm, we also provide a new and novel analysis template for inexact dual averaging method, which might be of independent interest. We also provide experimental results to complement our theoretical findings.

We study finite-horizon offline reinforcement learning (RL) with function approximation for both policy evaluation and policy optimization. Prior work established that statistically efficient learning is impossible for either of these problems when the only assumptions are that the data has good coverage (concentrability) and the state-action value function of every policy is linearly realizable ($q^\pi$-realizability) (Foster et al., 2021). Recently, Tkachuk et al. (2024) gave a statistically efficient learner for policy optimization, if in addition the data is assumed to be given as trajectories. In this work we present a statistically efficient learner for policy evaluation under the same assumptions. Further, we show that the sample complexity of the learner used by Tkachuk et al. (2024) for policy optimization can be improved by a tighter analysis.