Papers

We trace a conceptual genealogy from Abraham de Moivre's derivation of the normal curve (1733) to the modern distributional approach to statistics. De Moivre's Approximatio ad Summam Terminorum Binomii gave the first systematic derivation of the Gaussian density, its normalising constant (completed by Stirling's identification of $B = \sqrt{2\pi}$), and its tail probabilities computed to six decimal places – more than seventy years before Gauss. His method – extracting information from probability laws by evaluating sums against indicator probes – is recognisably an instance of the operational viewpoint that underlies distributional statistics. We identify a four-stage chain: coefficient extraction (De Moivre) $\to$ generating functions (Euler, Laplace) $\to$ characteristic functions (Fourier, Lévy) $\to$ distributional pairings $\langle T, \varphi \rangle$ (Schwartz). At each stage the probes become more flexible and the class of laws that can be studied grows wider. The distributional framework, in which a probability law is represented by a distribution–kernel pair $(T, \varphi) \in \mathcal{S}'(\mathbb{R}) \times \mathcal{S}(\mathbb{R})$, is the natural endpoint of this progression. We formulate and prove a distributional version of the De Moivre–Laplace theorem: the standardised binomial distribution converges to the Gaussian in $\mathcal{S}'(\mathbb{R})$, with De Moivre's original computation corresponding to the special case of indicator test functions. We also discuss the transversality framework, which provides a geometric explanation – via infinite codimension of degeneracy strata – for why pathologies such as moment indeterminacy, non-identifiability, and singular Fisher information are rarely encountered in parametric statistical models.

Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple environments in robotics with diffusion policies. This naturally leads to a multi-objective learning (MOL) problem. A key challenge is that achieving good Pareto trade-offs can require a generalist model class with substantially larger capacity than what suffices for solving any individual task, thereby increasing statistical cost since sample complexity typically scales with the model complexity. To reconcile this, we develop a principled MOL framework for diffusion models with limited data: a semi-supervised regime where paired (labeled) samples are scarce, but (unlabeled) condition data are abundant. We propose a two-stage training procedure that first fits lightweight specialist models from limited paired data, and then distills them into a generalist model by generating pseudo-samples. We establish generalization bounds showing that the required number of paired samples only depends on the complexity of the specialist model classes. We further extend the theory to diffusion policies for sequential decision making to account for distribution shift in on-policy rollouts. Extensive experiments on robotic control and image restoration tasks are conducted to verify our theoretical results.

Kernel Stein discrepancy (KSD) is among the most popular goodness-of-fit (GoF) measures on general domains with a large number of successful deployments. One of the main applications of KSD is in constructing powerful GoF tests. However, tests relying on the classical U-/V-statistic-based KSD estimators have two major drawbacks. (i) Their runtime scales quadratically in the number of samples. (ii) Their asymptotic null distribution is computationally intractable in most cases, typically handled by bootstrapping. While it is known that the Nyström method permits accelerating KSD estimation with no loss of statistical accuracy under mild conditions, to the best of our knowledge, the fundamental question of its impact on bootstrap-based GoF testing is open; resolving this question is the focus of the current paper. In particular, we prove that the key properties of the quadratic-time bootstrapped KSD-based GoF test (asymptotic level and local consistency) are preserved by its Nyström acceleration. We numerically demonstrate the efficiency of the accelerated KSD estimator and bootstrap in the context of GoF testing of spherical and functional data. Our numerical results show that the Nyström-accelerated method performs statistically on-par with the quadratic-time approach, while requiring substantially smaller runtime.

This article is the rejoinder to “The ICML 2023 Ranking Experiment: Examining Author Self-Assessment in ML/AI Peer Review,” to appear in the Journal of the American Statistical Association with discussion. To address the practical and theoretical points raised by the discussants, we organize our response around four core themes: (i) formulating peer review as a statistical estimation problem; (ii) mitigating equity and strategic concerns in the deployment of the Isotonic Mechanism; (iii) incorporating complementary signals such as reviewer rankings and structured metadata; and (iv) exploring a human-centered framework for peer review in the era of generative AI.

Public service programs often allocate limited resources under uncertainty about their benefits, creating a need for randomization to support credible evaluation. In practice, however, applicants commonly enter waitlists where resources are prioritized toward individuals judged to have higher need through tiered priority queues, making direct randomization difficult. Motivated by this, we develop an experimental design framework for learning treatment effects while treating those most in need where incoming applicants are randomized into priority queues based on their assessed risk scores. Treatments are then provided across queues in priority order and first-in-first-out within queue as budget becomes available. Our contributions are two-fold. First, we characterize what causal effects are identified under this priority-queue allocation. When arrivals are exogenous, treatments are conditionally randomized, and hence standard estimands are identified; when arrivals are endogenous, queue randomization instead provides an instrument for treatment, identifying local treatment effects induced by the queuing process. Second, we develop optimized queue-assignment designs that trade off statistical efficiency against prioritizing higher-need applicants. We show in the process that, despite dependence in treatment assignments induced by the design, usual iid efficiency bounds remain well-justified design objectives. We illustrate the proposed designs using data from a housing allocation program in a large U.S. county.

This paper introduces the Quantum Covariance Embedding, which embeds Positive Operator-Valued Measures into a tensor product of a Reproducing Kernel Hilbert Space and the quantum state space via a tensorized Bochner integral. This construction induces the Quantum Maximum Discrepancy that metrizes the space of quantum measurements. Applying this framework to Quantum State Tomography, we reformulate density estimation as a tensorized kernel regression, enabling optimal inference without the basis-dependent sparsity constraints that restrict existing methods. We develop a unified geometric design theory for quantum Gram superoperators, establishing that Unitary Designs are strictly E-optimal experimental designs and thus statistically superior to Pauli observables. For general structure-free estimation, we derive the exact minimax lower bound and prove that our tensorized estimators achieve this optimal rate. Furthermore, we introduce the QUAntum Regression with Kernels (QUARK) estimator to accommodate the spectral geometry of physical implementations, deriving central limit theorem and concentration inequalities. To facilitate practical estimation, we establish the exactness of trace-preserving projections and demonstrate efficient estimation under mutually unbiased bases via the fast Walsh-Hadamard transform.

We study inference-time alignment for diffusion-based generative models, aiming to steer a base model toward high-reward outputs without updating its weights. Recent Sequential Monte Carlo (SMC)-based steering methods approximate reward-tilted target distributions in a principled way, but their proposals remain largely tied to the base sampler. Since reward information is mainly used after propagation through particle reweighting and resampling, these methods can require large particle budgets and suffer from weight degeneracy and high-variance estimates. One way to reduce variance and improve particle efficiency is to iteratively learn twisting functions that provide look-ahead guidance, as in twisted SMC. However, existing learnable twisting methods are developed mainly for classical sequential inference and can be unstable when applied to diffusion-based alignment with high-dimensional state spaces and terminal, noisy, or black-box rewards. We propose Trust-Region Iterative Twisted Sequential Monte Carlo (TRI-TSMC), a trust-region framework for learning twisting functions in SMC-based inference-time alignment. Each iteration computes an exact KL-constrained update in path space, which admits a closed-form solution by tempered importance reweighting, and projects this target back to the parameterized twisted family by weighted maximum likelihood. Theoretically, we formalize the value-function interpretation of the optimal twisting function and show that it yields a zero-variance sampler. We prove that the trust-region update follows an escort path toward the target distribution, that the weighted maximum-likelihood update is a forward-KL projection, and that the path reduces residual importance-weight variance. Empirically, TRI-TSMC improves primary alignment objectives on discrete diffusion text generation and text-to-image generation under matched inference-time budgets.

Reinforcement learning algorithms are generally designed to maximize the expected return across a population. However, a policy that is optimal on average may be suboptimal for certain individuals, leading to potential safety concerns. To address this, we first formalize the notion of individual harm from a counterfactual perspective and define harm as the event in which a chosen action results in a strictly worse outcome than a baseline alternative. We then propose a general two-stage procedure for learning policies that maximize the expected return while accounting for individual harm. We further establish the finite-sample properties of the learned policy, derive an upper bound on its sub-optimality gap, and show that the harm rate remains well-controlled. Numerical experiments on both simulated and real-world datasets demonstrate the effectiveness of the proposed approach.

Accurate quantification of intracellular metabolic fluxes is central to systems biology and biotechnology. Flux estimation relies on biochemical network models, with $^{13}$C metabolic flux analysis (MFA) being the state-of-the-art approach. However, isotope labeling data are often insufficient to uniquely support a single network formulation. In such cases, flux estimates become model-dependent, highlighting the need for methods that explicitly account for structural uncertainty. Bayesian model averaging (BMA) provides a principled framework for this purpose, but its application to $^{13}$C-MFA has so far been restricted to uncertainty in reaction bidirectionality within fixed network topologies. We introduce a scalable Bayesian inference framework for $^{13}$C-MFA, Bayesian model set averaging, that applies BMA to encompass uncertainty in reactions and pathways. Our approach combines reversible jump Markov chain Monte Carlo for trans-dimensional exploration of model spaces with diffusive nested sampling for robust estimation of model evidences, enabling averaging over large families of metabolic network models. Using illustrative and application-scale synthetic case studies, we demonstrate that the method yields robust flux estimates, reveals when multiple network configurations are statistically indistinguishable, and recovers data-supported model structures. Importantly, rather than committing to a single model, the framework manages structural uncertainty: under limited data, competing models are retained, whereas increasing data informativeness improved model and flux recovery. The approach scales to billions of model variants, providing a practical foundation for uncertainty- and misspecification-aware quantitative flux inference in $^{13}$C-MFA.

Integrating multimodal datasets in clinical oncology is frequently hindered by high dimensionality and blockwise missingness, where entire data sources are unavailable for specific patient subsets. Standard survival models often struggle with these gaps, leading to biased results or patient exclusion. We introduce Multimodality Stacking with Blockwise missing values (MSB), a late-fusion framework for survival analysis that independently models modality-specific features before aggregating predictions via a cross-validated stacking meta-learner. MSB was validated on the PIONeeR study (n=443 patients, 378 biomarkers across eight heterogeneous sources) to predict progression-free survival in advanced non-small cell lung cancer patients receiving immunotherapy. MSB yielded higher predictive performance (C-index) than baseline algorithms. Improvements varied by baseline strength: linear models showed a 15.9% increase (p<0.001 for the Wilcoxon signed-rank test), random survival forests gained 5.4% (p=0.002), and gradient boosting methods improved by 2.1% (p=0.030). Beyond discrimination, MSB reduced the generalization gap (train-test difference in 5 folds cross-validation repeated 3 times: 0.055 vs 0.380 for linear models). Permutation importance analysis identified routine laboratory markers, clinical features, and PD-L1 expression as primary predictive drivers. Missing block indicators showed negligible importance, suggesting the model learned from biomarker values rather than data availability patterns. MSB provides a statistically validated framework for multimodal survival prediction with blockwise missingness. By enabling systematic biomarker evaluation without requiring complete data, MSB offers a practical tool for predictive modeling in biomedical research, pending external validation. Implementation is available at https://github.com/MohamedBoussena/MSB under Inria license.

Model-assisted interval designs such as the Keyboard design are transparent and easy to implement in phase I oncology trials. However, interim decisions based solely on data from the current dose may overlook informative signals from neighbouring doses, leading to unnecessary escalation or de-escalation. We propose the shared Keyboard design, a Bayesian model-assisted design that replaces the independent beta–binomial updating scheme at each dose with a posterior induced by a Beta kernel process using kernel-weighted pseudo-counts. The design preserves the decision structure of the Keyboard design while enabling controlled borrowing across nearby doses. To prioritise overdose control, we propose an asymmetric kernel that assigns greater weight to toxicities observed at higher doses during escalation. We further extend the proposed design to accommodate adaptive dose insertion when the initial dose grid is inadequate and time-to-event outcomes when late-onset toxicities are present. Extensive simulation studies demonstrate substantial improvements in both accuracy and safety for identifying the maximum tolerated dose. In settings involving dose insertion, the proposed design identifies inserted target doses more effectively than adaptive dose modification while maintaining a comparable modification rate.

Background. The reliability paradox describes the empirical observation that cognitive tasks producing robust group-level effects often yield poor between-individual reliability. Existing approaches rely predominantly on the intraclass correlation coefficient (ICC), which captures only linear, second-moment dependence between test and retest. Methods. We introduce a normalized, information-theoretic complement to ICC, NLR{\Delta}, defined as the difference between empirically estimated mutual information and the analytic Gaussian baseline implied by the test-retest correlation. We pair NLR{\Delta} with ICC(2,1), bias-corrected and accelerated (BCa) bootstrap intervals, Benjamini-Hochberg false discovery rate (FDR) control, and a 24-cell multiverse over the KSG nearest-neighbour parameter, correlation method, and minimum-sample threshold. The full pipeline is governed by pre-specified claim contracts, content-addressed provenance, and SHA-256-verified raw data ingestion, and is released as the MixMind Reliability Framework. Results. Across 50 estimable primary measures from the Flanker, Stroop, Stop-Signal, Go/No-Go, and Posner task families, the median NLR{\Delta} is -0.138 nats, with interquartile range [-0.257, -0.034]. Zero of 50 primary measures exceed the headline rule. The companion ICC(2,1) analysis recovers the classical reliability paradox pattern, and the 24-specification multiverse yields 0 of 1,200 estimable cells passing the headline rule. Conclusions. On these two public datasets, replacing or augmenting ICC with an information-theoretic reliability measure does not rescue cognitive tasks from the reliability paradox. The robust null is invariant to the analytic choices examined here. We release the full pipeline, raw-data hashes, and contracts to enable exact replication and extension to other datasets and tasks.

Random sampling is a fundamental tool in modern machine learning and numerical linear algebra for reducing the computational cost of large-scale matrix problems. Existing analyses, however, rely primarily on subspace embedding guarantees, which do not precisely characterize the statistical bias of nonlinear random oblique projections induced by sampling, which arises ubiquitously in subsampled least squares and fast low-rank approximation methods. Because (pseudo)inversion is nonlinear, these random oblique projections can be systematically biased even when the underlying sketch is unbiased, thereby introducing hidden bias into downstream least squares and low-rank approximation solutions. In this work, we develop a unified non-asymptotic theory for random oblique projections in high dimensions. We show that standard random sampling schemes generally induce a systematic statistical bias overlooked by classical subspace embedding-style analyses, and we propose a principled debiasing framework to correct it. We illustrate the power of the theory through two canonical applications. For subsampled least squares, we obtain sharp bias–variance characterizations, reveal previously unrecognized statistical suboptimality in widely used sampling schemes, and identify when debiasing yields provable improvements. For fast CUR decomposition, we develop a debiased approach with improved approximation accuracy. Numerical experiments further validate our theoretical findings.

In this paper, we study the numerical discretization of stochastic differential equations with locally Lipschitz, super-linearly growing drift, and the resulting implications for sampling from non-log-concave distributions satisfying a logarithmic Sobolev inequality. In this regime, the classical Euler–Maruyama scheme underlying the unadjusted Langevin algorithm (ULA) is known to be unstable. We analyze the KL-accelerated tamed unadjusted Langevin algorithm (kTULA) and introduce a new tamed randomized midpoint scheme, termed tRLMC. Building on the shifted-composition approach of \cite{chewi2024local}, we develop two new local-error frameworks that yield finite-time, non-asymptotic error estimates against the underlying SDE – in KL divergence for kTULA, and in total variation for tRLMC – valid for general locally Lipschitz drift. Specializing these frameworks to the sampling problem under a logarithmic Sobolev inequality, we obtain a near-optimal $\widetilde{O}(\varepsilon^{-1/2})$ iteration complexity for kTULA in KL divergence, with corresponding guarantees in total variation and Wasserstein distance. We further establish, for the first time, a non-asymptotic guarantee in total variation for a tamed randomized Langevin scheme under super-linear drift growth, together with the corresponding Wasserstein-distance bound, both with $\widetilde{O}(\varepsilon^{-1})$ complexity for tRLMC. As a consequence, both schemes yield non-asymptotic bounds for a non-convex excess-risk optimization problem.

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M $-component mixture distributions, we propose a family of estimators derived from the stochastic mirror descent (SMD) algorithm. This optimization-based approach provides a principled and flexible framework that generalizes traditional estimators and proposes a variety of novel estimators through the choice of Bregman divergences. A key advantage of our method is that it scales efficiently with the number of candidate components $ f_i $; that is, one can employ a large set of basis distributions in the mixture model without incurring significant computational overhead. This enables richer approximations and improved estimation accuracy. Moreover, in the case of categorical distribution (discrete outcomes) our estimators do not require a strict lower bound, in other words our framework does not require the precise knowledge of the support of the distribution. We demonstrate that, under mild conditions, the proposed $ \varphi $-SMD estimators achieve near-optimal convergence rates in both Kullback-Leibler (KL) divergence and $ \ell_2 $-norm and offer practical benefits when computation is expensive. Our numerical analysis highlights improved performance guaranties over classical estimators, particularly in terms of sample efficiency and scalability.

Quaternion neural networks are parameter-efficient and model multidimensional dependencies by representing four related features as a single entity. However, existing quaternion self-attention computes component-wise scores and applies independent softmax operations to each component, which increases the computational cost and allows attention distributions to diverge across components. We propose a shared-score quaternion self-attention mechanism that computes a single real-valued score using the quaternion inner product and applies a shared attention distribution across all components. This reduces score-computation multiplications by 75% and the number of softmax operations from four to one. We prove that, when queries and keys are produced by quaternion linear projections that induce component pre-mixing, the component-wise and shared scores lie in the same interaction subspace, indicating that independent component-wise attention primarily re-parameterizes the same interactions rather than expanding the feature interaction space. In speech enhancement, our method reduces inference time by up to 44.3% on a GPU and 58.1% on a CPU while maintaining quality, with consistent trends across vision and natural language processing.

Multiview latent-variable models provide a fundamental framework for discrete data analysis, with applications to latent structure models, topic models, and mixtures of product distributions. In the discrete setting, the joint distribution of the observed views can be represented as a nonnegative low-rank tensor, which we call a multiview density tensor. We study the problem of estimating this tensor from multinomial count data. A key challenge is that multinomial sampling induces heteroskedastic and dependent noise, so the difficulty of estimation depends not only on the ambient dimensions and rank, but also on how the probability mass is distributed across different locations of sample space. We propose a general scaling framework for density tensor estimation under multinomial sampling. This framework leads to a spectral estimator for which we prove a Frobenius-norm upper bound that directly handles heteroskedasticity and negative dependence. For the original multiview model, we obtain fiber-mass-dependent Frobenius upper bounds and minimax lower bounds showing that this dependence is unavoidable. Under $\ell_1$ loss, we develop both oracle and feasible data-driven estimators based on the same scaling principle, establish minimax lower bounds, and show near-optimality for the oracle rule at fixed rank and for slice normalization under bounded slice-to-fiber imbalance. Simulations support the theory and demonstrate the robustness of the proposed methods.

This paper studies nonparametric regression with repeated measurements when the response in the target domain is unobservable or costly to collect. We adopt a transfer learning framework that leverages a source domain with observable responses under covariate shift. The target regression function is estimated by correcting the distribution shift via the density ratio. We consider both known and unknown density ratio scenarios, which reflect different data available for nonparametric regression estimation. In both cases, we further address two settings: the uniformly bounded density ratio and the unbounded case with finite moment conditions. Under the unknown density ratio scenario, both the density ratio and the target regression function are estimated using rectified linear unit (ReLU) feedforward neural networks (FNNs), whereas under the known density ratio scenario, only the target regression function is estimated by ReLU FNNs. Theoretically, we establish non-asymptotic error bounds for the proposed estimators and prove that they achieve the minimax optimal convergence rate under the repeated measurements setting. Notably, we develop a novel approximation theory where the constants of the network parameters depend polynomially, rather than exponentially as in existing works, on the dimension, thereby mitigating the curse of dimensionality. Consequently, we derive sharper non-asymptotic bounds for the stochastic error. The finite sample performance of the proposed method is demonstrated through numerical simulations and a real data application.

Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide limited insight into the long-range statistical organization of generated text. We propose a complementary evaluation framework based on repeated subsequences. By analyzing their distribution across scales and relating it to higher-order Rényi entropies, we probe how texts reuse previously established structure under finite-length conditions. Experiments on human-written texts and length-matched GPT-generated texts show that, while power-law models can describe restricted ranges of block length, the observed entropy growth is often equally or better characterized by logarithmic–power forms. Across datasets, natural language exhibits stable entropy-growth patterns over accessible ranges, with consistent average behavior despite variability across individual texts. In contrast, GPT-generated texts show systematic and statistically significant shifts in estimated exponents with model size. These results demonstrate that repeated-subsequence entropy provides a quantitative structural diagnostic that reveals systematic differences in long-range organization, distinguishing natural language from state-of-the-art LLM outputs beyond surface-level fluency.

We analyze downstream courtroom governance in Philadelphia eviction cases using 755,004 Municipal Court landlord–tenant records filed from 1969 through 2022. Post-filing case processing is organized by repeated courtroom relationships, judge and tenant-attorney regimes, reusable agreement templates, and repeated team-property units. Among both-represented, both-attorney-named cases, 58.2% involve a plaintiff-side and tenant-side attorney pair that had appeared against one another in the prior year, and greater prior pair exposure predicts lower default, higher judgment-by-agreement, and higher served-writ rates. Judge-linked cases display statistically distinct baseline outcome, continuance, fee, and award regimes; tenant-attorney identity explains meaningful variance in both case outcomes and agreement terms. Settlement text is highly standardized: reusable templates explain strictness, waiver, lockout-trigger, payment-plan, deadline, and time-is-essence language far more strongly than raw attorney identity. Monetary burden concentrates in repeated plaintiff-attorney-property units. Assignment-cell support and balance audits indicate that judge-linked evidence reflects institutional heterogeneity rather than a clean judge lottery, and judge–triad interactions are not estimable in this docket. Eviction court emerges as a repeated institutional field that organizes bargaining, text, debt, and enforcement after cases enter the courtroom pipeline.

We introduce the Markov Distributional Conformal Prediction (MDCP) method that extends the distributional conformal prediction (previously developed for regression) to the setting of a strictly stationary Markov process. Instead of relying on a specific model structure to do prediction, the idea of distributional conformal prediction interval aligns with the Model-Free (MF) Prediction Principle. In analogy to MF prediction of Markov processes, our method exploits the probability integral transform based on estimated transition distribution functions to transform the Markov data to an i.i.d.~dataset. We show a non-asymptotic error bound of MDCPs unconditional coverage rate under a $\beta$-mixing condition and other standard assumptions on the kernel estimators. The asymptotic validity of the conditional prediction interval is also verified. In addition, we show that our conditional prediction interval is still asymptotically valid with Markov processes being $L^p$-$m$-approximable instead of satisfying the mixing property. Numerical simulations and real data experiments are deployed to empirically illustrate the finite-sample performance of MDCP, and compare it with the MF bootstrap prediction method.

Introduction: Logistic regression (LR)-type model limitations for causal inference are explained theoretically and empirically through the lens of the purported gateway effect from e-cigarette use to smoking. Previous studies have reported that baseline e-cigarette use quadruples odds of follow-up smoking (binarized) in LR-type models of adolescent longitudinal cohorts (LCs), such that increased e-cigarette use would counteract smoking declines. However, US population-level trends show accelerated smoking declines to record-lows when e-cigarette use increased, presenting an apparent paradox. Methods: Population Assessment of Tobacco and Health (USA) Youth Waves 3 to 4 were analyzed with Bayesian Additive Regression Trees (BART) to model baseline e-cigarette use (treatment) and change in number of days smoking from baseline to follow-up (numerical response) among never- and ever-smoking respondents (group effects), adjusting for confounding risk factors (socio-demographic, intra-individual, behavioural, peer influence, and family background). Unlike LR-type models, BART provides nonlinear, nonparametric modelling with counterfactuals and provides causal effect estimates with principled uncertainty estimation. Results: The average effect of e-cigarette use on smoking was both clinically and statistically significant among ever-smoking adolescents (-2 days smoking [diversionary effect; opposite to gateway]) and was not clinically significant among never-smoking adolescents (<1-day absolute change in days smoking [null effect]). Conclusions: When LC data are analyzed with causal inference techniques, the gateway effect disappears, consistent with population-level trends. This likely explains why gateway effects predicted in previous LR-type studies have not materialized in a population-level reversal/unexpected slowing of the US adolescent smoking decline, resolving the paradox.

We study the problem of detecting multiple change points in the mean vectors of an independent sequence of high-dimensional observations. Targeting at detecting dense alternatives in the regime where the dimension is comparable to the sample size, we propose a family of ridge-regularized CUSUM statistics built upon the adaptable ridge-regularized Hotelling's $T^2$ test of Li et al. (Ann. Statist. 48 (2020) 1815–1847). Ridge regularization provides stable covariance normalization while allowing the tests to adapt to the underlying population covariance structure. To accommodate multiple change points without prior knowledge of their number or locations, we scan over a multi-scale collection of adjacent segments. We further enhance adaptability by aggregating information across a collection of ridge regularization parameters through the maximum of the corresponding test statistics. Under mild conditions, we establish the limiting distributions of the proposed statistics under the null hypothesis and a class of local alternatives. Extensive simulation studies demonstrate their finite-sample performance.

The literature on test set contamination largely focuses on detection, but the correction of contaminated test scores is underexplored. Our core proposal is to spike the training data by intentionally contaminating some test examples at known rates. The spiked examples can then be used to calibrate predictors of model memorization which enable principled statistical correction of inflated test scores. To evaluate different correction estimators, we first present a simulation framework based on the Hubble models. Hubble models come in minimal pairs, where the perturbed model was deliberately contaminated with several test sets, while the standard model was not, serving as the counterfactual and correction target. We consider estimators that use information from a memorization predictor, correctness predictor, or both. In simulation, we establish basic statistical intuitions and show that estimators leveraging memorization and correctness information are better than naive estimation which makes no correction at all. We then instantiate several memorization and correctness predictors, and find that simple predictors such as Platt-scaled membership inference metrics provide good signal for correction. Finally, we examine the practical considerations of spiking. Simple memorization predictors need no more than 10 examples for calibration and often transfer from one dataset to another. Taken together, spiking is a promising solution for test set contamination.

Off-dynamics offline reinforcement learning seeks to learn a target-domain policy from a large source dataset and a limited target dataset under mismatched transition dynamics. Existing approaches such as reward augmentation and data filtering are constrained to the source dataset and cannot synthesize new target behavior to improve coverage beyond the collected source trajectories. While recent model-based methods attempt to address this by learning target-aware dynamics, the generated experience is constructed only at the transition level, which leads to accumulated errors over long horizons. These limitations necessitate a shift toward trajectory-level generation for off-dynamics offline RL. We propose CEDGE, a Cross-domain Energy-guided Diffusion GEneration framework. CEDGE trains a trajectory diffusion model on source-domain trajectories and adapts the generated samples to the target domain through energy guidance. This guidance is derived by minimizing the distribution mismatch between the source and desired target-domain trajectories and is decomposed into return, domain, and behavior energy components. The resulting energy-guided trajectories are useful both for direct planning and as synthetic data for policy learning. Since target adaptation is achieved via energy guidance rather than retraining the diffusion model, CEDGE can be efficiently adapted to new target dynamics compared to previous methods. Experiments on the ODRL benchmark demonstrate that trajectory-level energy-guided generation improves diffusion planning under dynamics shifts and produces synthetic data that improves downstream target policy learning.

Fragmentation is common in interdisciplinary fields with diverse methods and theoretical commitments. Predictive coding neuroscience is a clear example: its literature spans computational theory, electrophysiology, imaging, behavior, and modeling, creating a synthesis problem that conventional meta-analysis cannot easily resolve. Here, we describe a local multi-LLM pipeline for ontology-constrained literature synthesis. The pipeline reads papers, extracts evidence, incorporates figure descriptions, assembles constrained prompts, and validates outputs against an expert glossary. We manually defined a predictive-coding glossary of thirty-six concepts grouped into three hypotheses: predictive suppression, feedforward error propagation, and ubiquity. A council of ten local language models scored 31 studies according to their agreement or disagreement with each glossary factor across local and global oddball contexts. This enabled pairwise study-agreement analysis, cross-model comparison, and three-dimensional hypothesis-space mapping. Agreement was high for some hypotheses but weaker for others, revealing structured disagreement, particularly across local versus global oddball paradigms. We further define hypothesis-space temperature, a geometric dispersion metric measuring how compactly studies occupy the hypothesis space. Temperature was lower for local oddball contexts and higher for global oddball contexts, indicating greater dispersion in the latter. The scoring geometry also allowed us to estimate vectors of change between experimental contexts. These results demonstrate that local multi-LLM councils can produce auditable disagreement measurements that map heterogeneous literatures into quantitative evidence spaces. This framework may generalize to cross-study hypothesis mapping where conventional meta-analysis lacks a common comparison space.

Reward modeling is not only a prediction problem: in KL-regularized policy optimization, the learned reward is exponentiated to define the deployed policy, so downstream value depends on errors in reward-tilted regions. We study this feedback in a Gaussian single-index model with $r^*(x) = \sigma^*(\langle \theta^*, x\rangle)$ and $x \sim N(0, I_d)$. We analyze a two-stage neural reward model that first learns the hidden direction $\theta^*$ from reward-weighted samples and then fits the readout layer by weighted ridge regression. Exponential reward weighting changes the Hermite signal available to the first layer; for any feature-learning temperature $\beta_1$ above a dimension-free $O(1)$ threshold, a constant fraction of neurons recover the hidden direction, with weak-recovery complexity governed by the generative exponent. After feature recovery, we derive tilted-policy value-gap bounds for an idealized label-weighted fit with weights $e^{y/\beta_2}$ and a more practical surrogate-weighted fit with weights $e^{r_{a_0}(x)/\beta_2}$. Keeping the $\beta_2$-dependence explicit yields an admissible set of deployment temperatures, balancing the gain from lowering $\beta_2$ against the learning cost amplified by exponential weighting; in the surrogate-weighted case, proxy-dependent factors shrink this admissible set.

We study the sample complexity of robust binary hypothesis testing under three standard contamination models: $\varepsilon$-additive (Huber), $\varepsilon$-subtractive, and $\varepsilon$-total variation (TV), denoted by $n^*_{\mathrm{Hub}}(\varepsilon)$, $n^*_{\mathrm{Sub}}(\varepsilon)$, and $n^*_{\mathrm{TV}}(\varepsilon)$, respectively. For subtractive contamination, we show that least favourable distributions exist and provide explicit formulas for the same, bringing this model in line with the classical Huber and TV models. Next we show that in all three models, sample complexity may be highly unstable in the contamination parameter $\varepsilon$, increasing by polynomial factors even for $o(\varepsilon)$ perturbations. Similarly, there may be polynomial factor gaps between the sample complexities when $\varepsilon$ is known exactly versus when it is known up to $o(\varepsilon)$ error. Despite the instability of the sample complexity in all models, we show that the sample complexities across models are comparable up to constant-factor rescaling of $\varepsilon$. Specifically, for any fixed $\delta_0>0$, the following hold for all distributions $p$ and $q$: (i) $n^*_{\mathrm{Hub}}(\varepsilon) \lesssim n^*_{\mathrm{TV}}(\varepsilon) \lesssim n^*_{\mathrm{Hub}}(2\varepsilon)$, (ii) $n^*_{\mathrm{Sub}}(\varepsilon) \lesssim n^*_{\mathrm{TV}}(\varepsilon) \lesssim n^*_{\mathrm{Sub}}((2+\delta_0)\varepsilon)$, and (iii) $n^*_{\mathrm{Sub}}(\varepsilon) \lesssim n^*_{\mathrm{Hub}}(\varepsilon) \lesssim n^*_{\mathrm{Sub}}((1+\delta_0)\varepsilon)$, and the scaling constants are tight. Finally, we extend our results to adaptive versions of the contamination models.

Identifying the most influential nodes in a network, typically using centrality measures, is a central task in applied network analysis. However, real-world networks are often constructed from noisy or incomplete data, which can distort rankings and lead to errors in identifying the true top-$k$ nodes. In this paper, we study how network noise affects the recovery of the true top-$k$ node set based on degree centrality. Specifically, we consider a noisy network observation in which edges are randomly added or removed according to a probabilistic noise model, and analyze the resulting empirical top-$k$ set. We show that top-$k$ recovery under network noise is governed by the relationship between the degree gap and the noise magnitude, which separates recoverable and unrecoverable regimes. To quantify ranking stability, we derive upper and lower bounds on the expected discrepancy between the empirical and true top-$k$ sets in a general framework and for specific network models. We also extend the analysis to eigenvector centrality, showing that similar noise-gap tradeoffs arise in spectral rankings. Simulation studies support our theoretical findings and illustrate the practical impact of network noise across a range of settings.

We establish four structural results for feature learning in wide two-layer neural networks under the Maximal Update Parametrization ($\mu$P). First, we prove global existence and uniqueness of the mean-field limit of noisy gradient descent under $\mu$P, identifying the maximal admissible weight $w^*$ on the moment sequence of the initialization as the reciprocal parameter-moment-growth boundary, and hence the largest weighted moment class propagated by the flow. The finite-particle approximation has uniform-in-time squared-Wasserstein rate $O(N^{-1})$. Second, we characterize identifiability of the mean-field limit: two admissible parameter measures induce the same network function in $L^2$ exactly when their active components agree modulo the finite-rank realization symmetry of the architecture. The orbit depth $D^*_{\mathrm{orb}}$ is separated from the moment-variety depth $D^*_{\mathrm{var}}$. Third, under the Barron-Hermite target condition the active support of the long-time limit measure admits a sparse-dictionary decomposition: it is supported on at most $S^*$ atoms modulo finite-rank realization symmetry, with $S^*$ bounded by an explicit coefficient-threshold number. Fourth, we derive the total feature-learning-error decomposition into statistical, optimization, propagation-of-chaos, and sparse-residual components, with a target-dependent Hermite/Barron tail replacing any initialization-only residual. The four results are tied together by an architectural identity: the triple $(w^*, D^*_{\mathrm{orb}}, S^*)$ – the maximal admissible weight, the orbit identifiability depth, and the sparse-dictionary depth at which the target is realizable – is the natural learning cell of the architecture-data pair $(\sigma, \rho)$. The proofs are self-contained except for standard results from $\mu$P and mean-field Langevin theory.