Papers

We explore and utilize the algorithmic relationship between the closed testing principle for multiple tests with family-wise error rate (FWER) control and the partitioning principle for the construction of simultaneous confidence intervals. Starting with the simple observation that a multiple test with FWER control is formally equivalent to a one-sided simultaneous confidence interval for the vector of binary parameter indicating whether the null or alternative hypothesis is true, we show that the closed testing and partitioning principles follow the same computational approach. We will then utilise this relationship to extend concepts of consonance for closed tests to the partitioning principle, with the aim of deriving computationally feasible and efficient algorithms for the calculation of simultaneous confidence intervals. We will also utilize the relationship between closed testing and partitioning principle to extend common closed testing procedures to simultaneous confidence intervals, referencing the existing literature on informative simultaneous confidence intervals. The relationships and extensions will be illustrated by simple, instructive examples.

Multimorbidity poses a growing challenge for individual health, reducing quality of life and increasing treatment burden, resulting in a multiplicative impact on healthcare system management and fragmented care trajectories. Comorbidity networks could provide crucial insight into characterising multimorbidity and disease relationships. However, existing approaches to comorbidity network construction face critical limitations: they overlook temporal information by relying on cross-sectional statistics, produce biased association estimates by ignoring confounding due to shared risk factors, and fail to distinguish between direct and indirect disease associations, thereby yielding fully connected networks. To address these limitations, we develop a methodological framework for population-level disease network inference that uses individual health trajectories to learn disease associations, capturing semantic similarity and temporal co-occurrence. Sparse network estimation is achieved via Gaussian Graphical Models with Lasso regularisation, informed by prior clinical knowledge on shared risk factors derived from a dedicated confounding evaluation step. Applied to UK Biobank data comprising 24 cardiometabolic diseases and 76 risk factors, the resulting network revealed clinically meaningful disease patterns. Topological analysis identifies key pathological hubs, reveals potential actionable targets for multimorbidity management, and identifies four distinct disease communities that align with the established cardiometabolic taxonomy. Building on this community structure, we derive community-based patient representations that capture disease progression dynamics. Clustering these representations reveals four progression phenotypes with significantly different long-term survival trajectories, highlighting the potential of the framework for risk stratification and personalised care.

Uncertain data often arises in complex environments because of frequency instability and subjective judgment. This paper establishes two types of uncertain single-index models to capture the inherent properties of such data. Based on the semiparametric least-squares principle, the Nadaraya-Watson kernel and B-spline methods are used to estimate the unknown coefficients in various scenarios with both crisp and imprecise explanatory variables. Residual analysis and hypothesis testing under uncertainty assess the fit of the proposed models. Furthermore, simulation studies verify the models' validity, and a real-data application demonstrates their effectiveness in practical settings.

Quantifying how much of the variation in a response is explained by its conditional mean is central to many statistical problems. In this paper, we develop a unified framework for this problem, centered on a normalized conditional mean discrepancy that coincides with the classical Sobol' index for univariate responses and its natural trace-based extension for multivariate responses. We propose a simple estimator of this measure based on nearest-neighbor graphs that can be computed in near-linear time. We establish its consistency and derive its rate of convergence. Further, under the null hypothesis of conditional mean independence, a studentized version of the statistic is asymptotically standard normal. This leads to a computationally efficient test for conditional mean independence that attains the correct asymptotic level and is universally consistent, without requiring bootstrap calibration or sample splitting. Building on the same estimator, we develop a model-free sequential variable-screening procedure that selects a sufficient set with high probability and an exponential error bound. We also discuss extensions of the framework to quantifying interaction effects through higher-order Sobol' indices. Simulations and real-data experiments demonstrate strong power, effective variable screening, and substantial computational gains over existing methods.

Probabilistic inference in high-dimensional Bayesian networks is difficult because exact manipulation of the joint distribution scales exponentially with network size. We propose a decomposition framework based on directed convex subgraphs and introduce a minimal d-decomposition tree. Together, they provide a principled alternative to classical junction-tree constructions. The proposed framework represents the joint distribution by lower-dimensional sub-models that can be learned and stored separately. This decomposition reduces computational cost and naturally enables parallel computation. Based on a minimal d-decomposition tree, we further develop two parallel algorithms for parameter estimation and probabilistic inference. Experiments show that the proposed method substantially improves computational efficiency over junction-tree methods while maintaining inference accuracy, especially for low-dimensional queries.

Scalable Bayesian inference for generalized linear mixed models (GLMMs) provides uncertainty-aware analysis of correlated longitudinal data, but existing scalable approaches largely assume low-dimensional tabular predictors and do not directly accommodate high-dimensional modalities such as images and text. We address this limitation by learning one or more modality-specific neural encoders jointly with a GLMM objective, then performing variance-corrected stochasticgradient MCMC for the GLMM parameters conditional on the learned representation. This conditional-Bayes design combines supervised representation learning with posterior uncertainty quantification for population-level effects, subjectspecific heterogeneity, and modality-level random slopes. The resulting model preserves interpretable fixed and random effects for structured covariates and learned modalities while scaling gracefully to large longitudinal datasets. In simulation studies, our method recovers posterior means and variance estimates from full-data MCMC benchmarks after covariance correction. We further evaluate uncertainty through parameter-level interval coverage in simulations and predictive calibration on held-out data. Applications to glaucoma progression and adolescent mental health demonstrate that the framework allows nuanced assessment of the relative importance of each modality on both individual and population levels without sacrificing predictive performance.

We develop a general framework for design-based causal inference under interference in cluster experiments conducted via two-stage randomization on a network of interconnected units, without relying on exposure mapping assumptions, exclusion of cross-cluster interference, or Bernoulli treatment assignments. Within this framework, we establish a complete characterization of linear weighted estimators (LW) as defined by Godambe (1955) that achieve identification of various network causal effects under interference. This general class includes several new estimators with improved theoretical guarantees and superior finite-sample performance relative to existing approaches such as standard inverse-probability-of-treatment weighting. For most estimators in this class, we establish central limit theorems and conservative variance estimators, which allows us to describe the distinct asymptotic behavior exhibited by different weighting schemes potentially of interest. In particular, we study how randomization at the cluster-level affects the asymptotic behavior of various estimators, and we identify a subclass of cluster-agnostic LW estimators whose convergence rates are independent of the number of clusters and attain the optimal root-N rate, where N denotes the total number of units. Notably, for complete randomization we develop new techniques that may be of independent interest, both to establish a central limit theorem for sums of general dependent statistics and to construct conservative and bias-corrected variance estimators. We complement our theoretical results with extensive simulation studies that offer practical guidance on the choice of weighting method and experimental design under a wide range of interference structures.

Understanding the complex relationships between atmospheric pollutant emissions and their multifaceted determinants presents a dual challenge: driving factors operate at fundamentally different temporal resolutions, from continuously monitored meteorological variables to annually reported socio-economic indicators, and their interconnections evolve dynamically over time. To address these challenges, we propose a Partially Functional Dynamic Structural Equation Model (PFDSEM) that coherently integrates functional covariates (e.g., high-frequency meteorological data) and scalar predictors (e.g., economic and demographic indicators) within a unified dynamic structural framework. The model captures non-stationary temporal dependencies and inter-variable correlations via a Conditional Autoregressive (CAR) structure combined with a Linear Model of Coregionalization (LMC), while functional covariates are incorporated through basis expansion with Bayesian P-spline smoothing. Bayesian inference via Markov Chain Monte Carlo provides full uncertainty quantification. Comprehensive simulation studies confirm accurate parameter recovery and robustness to prior specifications under diverse conditions. Applying the PFDSEM to pollutant emissions data from 30 Chinese provinces (2015–2020), we identify temporally dynamic and province-specific associations between ten categories of socio-environmental factors and ten major air pollutants, including CO$_2$. The results reveal substantial cross-province heterogeneity in the strength and direction of these associations and pronounced seasonal patterns in meteorological effects, offering a quantitative evidence base for designing temporally adaptive and regionally tailored environmental policies.

In this paper, we study the universal approximation property of residual neural networks. For input and output dimensions $d_x$ and $d_y$, and LeakyReLU, ReLU, ReLU-like activation functions, the upper and lower bounds of the minimum block width are established. To achieve $L^p$ approximation $(1\leq p <+\infty)$ on any compact set, we show that the exact minimum block width is $\max\{d_x,d_y\}$ when each residual branch has inner width 1. Furthermore, we show that residual neural networks with block width $\min\{d_x+d_y, \max\{2d_x+1,d_y\}\}$ can achieve uniform approximation on any compact set under the constraint that each residual branch has inner width 1. Besides, for any activation function family, we prove that there exist functions that cannot be approximated by residual neural networks with block width less than $\max\{d_x, d_y\}$, both in the $L^p$ sense and the uniform sense, regardless of inner width. Consequently, for LeakyReLU, ReLU, ReLU-like activation functions and $d_y\geq 2d_x+1$, the exact minimum block width for uniform approximation is $d_y$ when each residual branch has inner width 1.

Most classification problems assume the classes are roughly separable, so that an individual sample can usually be assigned to one class. Single-cell perturbation data violates this assumption: two perturbations can produce different populations of cells while overlapping so much that an individual cell could belong to either. Per-cell accuracy then measures this overlap rather than model quality. We see this on Tahoe-100M and the Virtual Cell Challenge, where a linear classifier, an MLP, and a Transformer all plateau near macro-F1 0.2-0.3 even though almost every pair of perturbations is statistically distinguishable. The fix is to score perturbations across the whole population rather than cell by cell. We average a classifier's per-cell probability vectors over all cells of a perturbation to form a population profile, then rank candidate perturbations by this profile; we call the resulting score the Classifier Discrimination Score (CDS). Taking the top-ranked class recovers the winning perturbation. It needs no retraining, costs linear time in the number of cells, and recovers near-perfect identification from the same weak models. CDS differs from the pseudobulk-based Perturbation Discrimination Score (PDS) used in recent benchmarks only in where the average is taken, raw gene expression for PDS versus a learned discriminative space for CDS, and identifies the true perturbation more reliably on both datasets, with the gap widening as cells grow scarce. Because a metric that misranks the ground truth will misrank the models scored against it, per-cell accuracy and raw-pseudobulk scores should be used with caution when comparing perturbation models.

Early-phase oncology trials often require protocol-ready interim rules for deciding whether an experimental regimen shows sufficient activity relative to prespecified clinical benchmarks. Existing Bayesian optimal phase II designs provide calibrated count boundaries for such decisions, but evidence is quantified through posterior probabilities and sample-size-dependent cutoff functions. We propose calibrated e-value monitoring (CEVAM), a likelihood-ratio evidence framework that defines monitoring evidence directly relative to prespecified clinical benchmarks, without requiring a Bayesian analysis prior or sample-size-dependent posterior-probability cutoff functions. For a binary efficacy endpoint, CEVAM constructs efficacy and reverse-futility e-processes targeted to clinically meaningful benchmark rates and converts them into monotone response-count boundaries. We distinguish a fixed-threshold e-process version, which has an anytime-valid interpretation under optional monitoring, from planned-look calibrated versions designed for conventional finite-look phase II trials. In simulations based on binary benchmark settings used in existing posterior-cutoff phase II designs, the proposed tuned planned-look rule controlled the nominal type I error and achieved the smallest expected sample size across all evaluated settings while retaining similar rejection probabilities. In an application to an actual phase II breast cancer trial, CEVAM classified the reported pathological complete response result as sufficient evidence for early success stopping. Extensions to categorical and multicomponent endpoints are provided in the Supplementary Material. CEVAM offers an analysis-prior-free, protocol-ready likelihood-ratio evidence scale for binary benchmark monitoring in early-phase oncology trials.

Benchmark contamination, the leakage of test items into training data, is widely described as a threat to the reliability of large language model (LLM) leaderboards. We argue that this concern conflates two distinct questions: whether contamination inflates absolute scores, and whether it reorders the ranking of models. We recast contamination as a violation of anchor-item invariance and measure it through the differential functioning of original versus semantically equivalent paraphrased items, a within-item contrast that holds the measured skill fixed and isolates memorization from capability. Using per-instance responses from 47 publicly released models and 74 models finetuned with a known dose of contamination, across four benchmarks (ARC, GSM8K, HellaSwag, MMLU), we first calibrate the measure against ground truth: it recovers injected contamination dose-responsively (a corrected effect of +0.187 accuracy points for test-set leakage) and never flags a negative-control model trained only on the legitimate training split (-0.012). We then quantify leaderboard impact: the rank correlation between a standard leaderboard and a paraphrase-controlled leaderboard is 0.997, and a sensitivity analysis shows that the observed differential contamination is far below the level needed to move rankings, with only 3 of 188 model-by-benchmark cases showing differential contamination corroborated across two references. Contamination among these public models is therefore largely uniform: it inflates absolute scores without reordering the leaderboard, and ranking distortion requires the rare case of differential contamination. We provide a calibrated invariance audit, released as a reference implementation, and recommend that leaderboards report paraphrase-controlled rankings alongside confidence intervals.

This paper explores the "Granularity Paradox" in time-series forecasting, wherein finer temporal disaggregation (e.g., Monthly to Weekly/Daily) improves in-sample diagnostics and dataset size (N), but degrades out-of-sample accuracy due to recursive error compounding over longer horizons (H). Conversely, coarse aggregation (Annual) eliminates recursive error propagation but reduces data available to estimators. We formalize this trade-off and benchmark 10 models - spanning naïve, statistical, machine learning, and deep learning architectures - across six granularities using a 13-year public procurement dataset. The empirical results reveal a non-monotonic threshold structure: recursive autoregressive and seasonal models degrade substantially under high-frequency forecasting (e.g., Holt-Winters reaches a Test R-squared of -151 and TPFE of 425.85% at the Daily grain), while the LSTM traces a U-shaped error curve, worsening from Monthly (19.66%) through Bi-Weekly (35.94%) before overcoming the error propagation penalty at Daily (TPFE of 4.35%, R-squared of 0.66). Linear Regression remains stable across all granularities (16.3-17.0% TPFE), confirming that the paradox is driven by recursive feedback topology, not model complexity. The results demonstrate that standard pointwise metrics (RMSE, MAE) systematically mask cumulative error propagation, and that evaluating forecasts without goal-dependent cumulative metrics produces misleading assessments of model adequacy. We introduce a consensus-dissensus diagnostic comparing the directional behaviour of pointwise metrics against cumulative TPFE across granularities, enabling the identification of models whose standard diagnostics mask systematic error propagation.

Orthogonal and Stiefel constraints are widely used in neural network optimization to control weight geometry, improve conditioning, and stabilize signal propagation. Yet standard Stiefel optimization imposes a hidden restriction: while learning the directions of a linear map, it fixes every singular value to one, preventing the model from learning how strongly different directions should be amplified or suppressed. We introduce ManifoldFlow, a spectrum-learnable extension of Stiefel optimization that separates directional geometry from spectral scaling through $W=QS^{1/2}$, where $Q^\top Q=I$ and $S\succ0$. Beyond simply making the spectrum trainable, ManifoldFlow uses the gradient component rejected by the Stiefel constraint as a signal for how the spectrum should change, accumulates this signal across aligned tangent spaces, and jointly updates the orthonormal basis and a bounded SPD spectrum. This construction preserves exact spectral interpretability because $W^\top W=S$, while recovering standard Stiefel optimization when $S=I$. We establish the geometry of the rejected gradient, characterize optimization over the resulting Stiefel–SPD product space, and derive how the learned spectrum affects conditioning, signal propagation, and spectral complexity. Across diverse tasks, ManifoldFlow consistently outperforms matched fixed-spectrum Stiefel baselines, with particularly strong gains in recurrent language modeling. Our code is available at https://github.com/Hik289/manifold_flow.git.

Biological systems exhibit a hierarchical structure, characterised by directed flow from upstream regulators to downstream effects. Although this ordering provides a natural scaffold for causal inference, most causal discovery and GRN methods either ignore the tiered organisation or condition on all upstream variables, which becomes infeasible for high-dimensional omics data. We present ASCEND (Ancestral Scalable Causal discovEry via iNherited Descent), a constraint-based framework that leverages known two-tiered structure to enable genome-scale causal discovery. ASCEND introduces a divide-and-conquer strategy that maintains dynamically updated ancestral conditioning sets for each downstream variable, dramatically reducing the number of conditional independence tests required, and achieves polynomial-time complexity where traditional approaches face exponential blow-up. Through extensive simulations and real biological data, we demonstrate that ASCEND accurately recovers ancestral relationships, scales properly and much faster, and outperforms existing gene regulatory network inference methods in both causal precision and computational efficiency. The algorithm's ability to resolve directionality makes it particularly suited for integrating multi-omic data where upstream regulators (e.g., SNPs, methylation sites) and downstream responses (e.g., gene expression) are measured jointly.

We study the small-noise asymptotics of Euclidean heat regularizations of probability measures supported on manifolds with corners. Near a boundary or corner stratum, the relevant regime is a conical boundary layer in which the observation point approaches the stratum at the same scale as the Gaussian smoothing parameter. After rescaling this layer, the support is replaced to leading order by its inward tangent cone. We prove a two-term expansion for the heat-regularized density in this regime. The leading coefficient is the Gaussian mass of the linearized cone, weighted by the density on the support and by the adapted corner Jacobian; the first correction records the variation of the density, the Jacobian, and the quadratic geometry of the embedding. A localization argument then yields the corresponding expansion for the full heat regularization, with the nonlocal contribution exponentially small. From this density expansion we derive logarithmic asymptotics and uniform expansions for the score, the log-Hessian, and the scale derivative of the score. These formulas show how lower-dimensional support, boundary faces, corners, and curvature are encoded in the singular differential structure of small-noise Gaussian regularizations.

We study two recently discovered "dimension-free" Monte Carlo sampling algorithms, the multiproposal and multiple-try preconditioned Crank-Nicolson methods (mpCN and MTpCN). These methods were designed to address certain non-parametric (i.e. infinite-dimensional) sampling problems, defined relative to a Gaussian reference measure, by combining proposal and acceptance mechanisms that take non-trivial advantage of parallel computing architectures. We provide the first rigorous analysis of both algorithms, establishing exponential convergence to the target measure through the weak Harris framework, both for a finite number of proposals and in the infinite-proposal limit. The resulting mixing rates are independent of the dimension and uniform in the number of proposals, and apply to targets with bounded, Lipschitz log-likelihoods, without requiring convexity. At the center of the analysis are two new coupling constructions, together with analytical tools of independent interest, yielding Wasserstein contraction estimates, $L^2$ spectral gaps, and associated statistical guarantees (laws of large numbers, central limit theorems, and non-asymptotic concentration bounds) for the corresponding Monte Carlo estimators. These theoretical results are complemented by a numerical study on benchmark problems with complex posterior geometries and high-dimensional structure, comparing mpCN and MTpCN against standard pCN and independent parallel-chain implementations. The experiments indicate that the multiproposal methods can offer a shorter warm-up phase and greater robustness to the choice of tuning parameters as the number of proposals grows.

Local causal discovery is a scalable alternative to global structure learning. However, it can struggle to identify valid adjustment sets in data-scarce settings because of finite-sample uncertainty, incomplete local neighborhoods, and unresolved Markov equivalence. Although many application domains provide structured background knowledge, its integration into local causal discovery remains limited. We propose b-LOAD, a knowledge-informed extension of the LOAD algorithm for local discovery of optimal adjustment sets. b-LOAD incorporates prior edge constraints directly into the local structure-learning procedure and uses Meek's rules to expand the discovery frontier dynamically, yielding a knowledge-constrained partially directed graph over the relevant local subgraph. This strategy helps prevent structurally relevant nodes introduced by prior knowledge from being excluded by local search. We prove that, under sound background knowledge, the procedure monotonically refines the admissible equivalence class and can enlarge the set of identifiable causal queries, enabling recovery of optimal adjustment sets that are not identifiable from observational conditional-independence information alone. Empirically, b-LOAD improves downstream causal effect estimation relative to purely data-driven and standard knowledge-augmented baselines, particularly in data-scarce and structurally complex regimes. Results on real-world biological networks show that locally targeted prior knowledge provides the largest gains and remains beneficial under moderate structural noise. These findings position b-LOAD as a scalable approach for converting fragmented domain knowledge into more reliable causal-effect estimation.

Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution. Their training and evaluation primarily rely on an Evidence Lower Bound (ELBO), which relates the Kullback-Leibler (KL) divergence of model samples to the score matching loss along the path, which serves as a tractable surrogate. The difference between sample quality and the score matching loss produced by this bound leads to the score matching gap, which is known to be tight in the worst-case but not descriptive of sample quality in general. In this work, we provide a theoretical analysis of this gap, developing tighter bounds for three metrics: KL divergence, reverse KL divergence, and Wasserstein distance, effectively exploiting the regularity of the class of score estimators. Our results suggest that the quality of the score approximation has more impact on closing the score matching gap for low noise scales. To obtain these bounds, our key technical insight is to exploit the contraction properties of the backward processes. In particular, we rely on entropy flows, logarithmic Sobolev inequalities and reflection couplings, rigorously linking the ergodicity of the Langevin diffusion to the score matching gap problem.

Quantile regression provides a powerful tool for summarizing the conditional distribution of a real-valued random variable (r.v.) of interest $Y$ as a function of covariates $Z$ in cases where it shows a large dispersion with high probability, going beyond the situation where standard least square regression is informative/predictive. This article aims to extend this methodology to the pairwise setting, where the variable to be explained is a similarity score between two independent observations (e.g., pixelated ID photos used as input to biometric systems), and the explanatory variables consist of the pair of covariates attached to these observations, such as age or hair color. We establish theoretical guarantees for solutions of this statistical learning problem, considered here as empirical minimizers of a pairwise version of the pinball loss. Leveraging sharp concentration results for $U$-processes, we prove generalization bounds and identify mild conditions under which fast learning rates can be achieved. Confirming the probabilistic analysis, experiments based on simulation data also provide solid empirical evidence of the validity of the methodology promoted here for pairwise quantile regression. Finally, its usefulness from an application perspective is demonstrated by a detailed study aimed at analyzing errors in similarity scoring for facial recognition.

The Dvoretzky–Kiefer–Wolfowitz–Massart inequality gives an upper bound on the probability that the empirical distribution function of a finite sequence of independent random variables deviates from its theoretical value. It is widely used in statistics in tests and in the production of confidence intervals. The original proof by Massart, later reformulated by Dudley, is very long and technical. Recently, Reeve slightly extends Dvoretzky–Kiefer–Wolfowitz–Massart inequality and presents an alternative, much shorter proof, that uses a continuous time martingale. We present a simpler and less technical proof of the original Dvoretzky–Kiefer–Wolfowitz–Massart inequality, based on a discrete-time martingale and Sion's minimax theorem.

We solve two open problems about spatial (or geometric) quantiles and depth. First we show that in infinite dimension, the spatial distribution function and the associated spatial quantiles characterize the underlying distribution, which has been established in Koltchinski (1997) in finite dimension but remained unknown in infinite dimension. Second, and more surprisingly, we show that the spatial depth also fully characterizes probability measures, which has been an open problem even in finite dimension since the introduction of these concepts in Chaudhuri (1996) and Vardi & Zhang (2000). Our results provide theoretical foundations for nonparametric depth-based statistical inference and introduce novel proof techniques to investigate these questions for other depth and quantile concepts.

Conditional generative models have emerged as powerful tools for sampling from target conditional distributions, driving substantial advances across a wide range of scientific and applied domains. As these models proliferate, practitioners often face multiple plausible generators whose performance can vary with the task, data, or input condition. We propose an optimal model averaging framework for conditional generative models, allowing candidate generators to be combined even when they are accessible only through conditional samples without tractable densities. Specifically, we use a sample-based maximum mean discrepancy between conditional distributions, which first leads to a static model averaging method, StaticMA, assigning fixed weights to different candidates. In addition, we develop MoEMA (mixture-of-experts model averaging), an input-adaptive method that parameterizes covariate-dependent weights through a softmax neural-network gate. We establish in-sample and out-of-sample asymptotic optimality for the proposed methods, together with consistency of the estimated adaptive weight function under regularity conditions. The framework applies directly to Euclidean responses and extends to unstructured data by combining our formulation with fixed representation maps. Across a broad set of simulations and real-data studies spanning tabular, image, and text modalities, MoEMA generally improves over competing baselines, demonstrating the effectiveness of our proposed methods.

Balancing the efficiency of an estimator under ideal conditions against its robustness under contamination remains a central challenge in robust statistics. While minimum divergence methods offer a flexible alternative to traditional M-estimation, choosing the appropriate discrepancy measure has historically relied on heuristic or empirical justifications. This manuscript introduces a rigorous optimality criterion for this selection process. By investigating the comprehensive Generalized Alpha-Beta Divergence (GABD) family, we explicitly characterize the Pareto frontier dictating the lowest possible asymptotic variance for any strictly enforced asymptotic breakdown point. Our main theoretical results establish that the estimator achieving this mathematical optimum invariably falls within the extended $(\phi, \gamma)$-divergence class. Crucially, the derived optimal tuning parameter, $\phi^*$, given other parameters, depends solely on the desired breakdown threshold and is entirely invariant to both the assumed parametric model and the exact nature of the data contamination. Supported by comprehensive derivations of asymptotic normality, influence functions, and breakdown thresholds for both continuous and discrete settings, this work offers a unified, theoretical resolution to the long-standing problem of optimal divergence selection in robust inference.

Meta-analyses guide clinical and policy decisions, but they estimate the effect among published trials, not the effect in the population a decision concerns. We introduce reference-anchored meta-analysis, which uses an external untreated-outcome distribution for two purposes: to define the target population, and, through each trial's control-arm mean as an externally anchored instrument, to correct publication selection. In an antidepressant literature with recovered unpublished trials, a strict holdout – removing the hidden trials from both fitting and anchoring – recovers a held-out all-trials benchmark. Applied to insomnia total sleep time and the placebo-controlled HbA1c literature in type-2 diabetes, it returns target-population effects materially smaller than the published averages, while a first-stage diagnostic flags, in advance, where the correction should not be attempted. Evidence synthesis becomes a target-explicit estimate with auditable selection assumptions.

This paper studies the problem of identifying the treatment that maximizes the expected natural direct potential outcome (NDPO), which captures the potential outcome of an intervention while excluding the pathway transmitted through a mediator that researchers may wish to remove from evaluation. We first establish population-level identification of the expected NDPO in a causal bandit setting using observable interventional distributions. We then develop a fixed-confidence best-arm identification (BAI) algorithm based on the Track-and-Stop (TaS) framework, employing a cutting-set method to solve the resulting semi-infinite optimization problem. The proposed algorithm achieves sample-efficient identification with a high-probability correctness guarantee. We prove that it satisfies $\delta$-correctness and asymptotic optimality. Finally, we validate the approach through empirical evaluations on a large-scale real-world advertising dataset (IPinYou).

International migrants face well-documented barriers to healthcare access, yet the extent to which these barriers shape patterns of disease co-occurrence remains poorly understood. Drawing on a nationwide dataset of approximately 13 million hospital admissions from around 4 million individuals in Austria (2015-2019), we constructed and compared comorbidity networks between Austrian nationals and non-Austrian migrants, matched 1:1 by age, sex, and time of first hospital admission (272,779 per group). Following matching, metabolic and cardiovascular diagnoses, including type 2 diabetes and myocardial infarction, were more common among non-Austrians, while depression was more common among Austrians. Comorbidity network analysis showed that among all disease pairs that differed significantly between groups, 70% showed stronger co-occurrence in Austrian patients and 30% in non-Austrian patients. Distinct sex-specific patterns appeared: Austrian males showed stronger associations between alcohol use disorder and mental health diagnoses, whereas non-Austrian males more frequently presented with acute somatic conditions. Among non-Austrian women, a pronounced cluster of recurrent depression, somatoform disorders, and dorsalgia was observed. We interpret the disproportionately fewer comorbidity links observed in non-Austrians not as evidence of lower disease burden, but as a likely reflection of structural access barriers, including language differences, cultural factors, and crisis-oriented admission patterns, that prevent comprehensive diagnostic assessment, though a contribution from the healthy migrant effect cannot be excluded. These findings stress the need for culturally aware care strategies and earlier identification of high-risk multimorbidity profiles in migrant populations.

Building AI Scientist agents with Large Language Models (LLMs) has recently attracted growing attention. Since scientific discovery fundamentally relies on uncovering causal relationships from observations, the capability of causal thinking, i.e., distinguishing causation from correlation and recognizing hidden biases, is essential to LLM agents. Although a number of benchmarks exist for AI Scientists, none explicitly incorporate challenges from selection bias, measurement error, and hidden confounders that widely exist in real-world scientific discovery. To this end, we present CausalGame, a benchmark that evaluates the causal thinking capabilities of LLM agents through interactive games. CausalGame asks LLM agents to actively design experimental protocols, collect observation data, and derive a final solution with an explanation report. To emulate realistic scientific discovery challenges, we design 14 scenarios that incorporate selection bias, measurement error, and hidden confounders. Across 30 LLM agents, none demonstrates reliable causal thinking: the best model reaches only 68.0% survival against analytical optima of 78-85%, and merely 5-7% of sessions receive credits on the causal-reasoning rubrics. CausalGame provides a scalable and controlled testbed for evaluating the causal thinking of AI Scientist agents.

We propose the first deep learning algorithm, the Certainty Equivalent Learning (CEL) algorithm, for solving high-dimensional discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is numerically challenging because the recursive utility does not have an explicit representation and the Bellman equation contains a certainty equivalent that is difficult to evaluate. The CEL algorithm learns this certainty-equivalent value directly with neural networks and jointly approximates value functions, policy functions, and certainty-equivalent functions. The CEL algorithm is mesh-free and simulation-based, allowing high-dimensional state and control spaces, and does not rely on Euler equations, first-order conditions, or differentiability of the state transition function. The CEL algorithm also works for dynamic programming problems with expected utility as expected utility is a special case of recursive utility. We apply the CEL to discounted linear exponential quadratic Gaussian control, small-noise robust control, Epstein-Zin DSGE, and multivariate strategic asset allocation problems. Compared with closed-form and VFI-based benchmarks, the CEL delivers accurate value and policy approximations, remains effective in high-dimensional problems, achieves accuracy comparable to VFI in the small-noise robust-control case, and produces out-of-sample Bellman errors and Euler or first-order residuals that are in the range from 1.0e-4 to 1.0e-3 for most problems.

Tensor probabilistic independent component analysis (TPICA) is a popular approach to analyzing functional magnetic resonance imaging (fMRI) data, which draws its popularity from its ability to enrich the advantages of the statistics-based ICA with the awareness of the multi-way nature of these data, brought about and exploited via a deterministic 3-way (time $\times$ space $\times$ subjects) tensor decomposition (Canonical Polyadic Decomposition (CPD)) model. It has, however, received critique concerning its robustness in realistic fMRI unmixing scenarios, notably those involving sources that are strongly overlapped in space. Such cases may not meet the assumption of statistical independence required in ICA. They can instead be better described as independent vectors (or subspaces) of dependent components, pointing to the adoption of alternative statistical approaches, notably independent vector analysis (IVA). On the other hand, on the deterministic side, CPD is often restrictive and is outperformed by the more flexible block-term decomposition (BTD) model, also in the fMRI source unmixing context. Given the above, plus strong evidence of links between IVA and BTD, it is deemed worthwhile to consider the possibilities of generalizing TPICA to a BTD-based “TPIVA" extension, which would more successfully combine the power of statistics and tensor decomposition. This could also entail a generalization of the BTD model, where (non)collinearity would be replaced by statistical (in)dependence. This note aims to outline the state-of-the-art and the above ideas in more detail, serving as a preliminary, motivating step in this research direction.