Papers

The Gutenberg-Richter power-law relationship essentially governs the frequency-magnitude distribution (FMD) of seismic activity. The b-value, as the slope of this distribution, is widely recognized not only as a quantifier of the relative proportion of small to large events but also as a diagnostic precursor of crustal differential stress and potential big to huge earthquakes. This study investigates the spatiotemporal evolution of b-values across major tectonic regions in mainland China, for instance, the Sichuan-Yunnan, North China, and Northwest regions. Our analysis of over 50 years of seismic records systematically examines b-value variations across major seismogenic zones in mainland China to evaluate their utility as precursors for moderate-to-strong earthquakes. Moreover, our comparison suggests that the b-positive estimator is less affected by changes in detection capability and short-term aftershock incompleteness than the classical b-value estimator in the cases examined. While the Sichuan-Yunnan region displays a complex "mosaic" of high and low b-values reflecting fluid-driven processes and localized locking, the North China Plain and Northwest regions exhibit consistently lower b-values, suggesting high background stress and rigid crustal integrity. We also find that several of the rupture areas of moderate-to-large earthquakes in our catalog coincide with localized low-b patches identified in earlier long-term windows. This study provides a foundation for systematic, prospective evaluation of b-value-based precursor monitoring in mainland China.

Let $\boldsymbol{X} = (X_1,\ldots,X_n)$ be a centered Gaussian vector, not necessarily nondegenerate. It is proved that, for every $\alpha_1,\ldots,\alpha_n > 0$, \[ \mathsf{E}\left[\prod_{i=1}^n |X_i|^{\alpha_i}\right] \geq \prod_{i=1}^n \mathsf{E}\left[|X_i|^{\alpha_i}\right]. \] When all marginal variances are positive, equality holds if and only if the coordinates are independent. This settles Frenkel's 18-year-old Gaussian product inequality (GPI) conjecture and, in fact, its later strengthening to arbitrary positive exponents. Through Frenkel's hafnian formulation, this result also provides a short proof of the 28-year-old real linear polarization constant conjecture, which was settled this year as a consequence of the strong polarization inequality. The main result leads to the exact real linear polarization constant, a sharp weighted product inequality for real linear functionals, spherical moment bounds, hafnian inequalities for positive-semidefinite matrices together with complete characterizations of their equality cases, logarithmic variance and covariance inequalities, a Rényi total-correlation certificate, and unconditional versions of mixed-sign Gaussian moment bounds previously conditional on the positive-exponent GPI.

Simple and complex contagions differ mechanistically; multiple exposures act synergistically in the latter but independently in the former. Yet correlated mixtures of simple contagions may appear complex when inferring global contagion rules, a phenomenon we call "emergent complexity." We present a measure of contagion complexity and an inferential framework for estimating mixtures of nonparametric contagion rules from time-series data. Our work reframes past studies on complex contagion by offering heterogeneous mixtures of simple contagions as an alternative explanation.

In network meta-analysis (NMA) of oncology time-to-event outcomes, there is growing recognition that progression-free survival (PFS) and overall survival (OS) are better synthesized jointly than in separate analyses. The multistate NMA of Jansen et al. addresses this with a tri-state (stable, progressed, dead) Markov model fitted to aggregate survival curves, but it cannot adjust for imbalance in effect-modifying covariates across trials, so its relative effects may be biased or not relevant for the target population of interest. Multilevel network meta-regression (ML-NMR) resolves covariate imbalance by integrating an individual-level model over the aggregate covariate distribution, coherently combining individual participant data (IPD) and aggregate data (AgD); however, it has been developed only for single-endpoint outcomes. This paper introduces multilevel network meta-regression for multistate models (ML-NMR-MS), which embeds the ML-NMR integrated IPD-plus-AgD likelihood inside an illness–death multistate model. For IPD studies the full multistate likelihood over linked transitions is used; for AgD studies covariate-marginal state-occupancy probabilities are computed by quasi-Monte-Carlo integration of the occupancies implied by the transition intensities over the reconstructed covariate distribution, and entered through a conditional-survival likelihood. This yields population-adjusted joint PFS/OS treatment effects and can directly parameterize a state-transition economic model. On an illustrative oncology network, ML-NMR-MS resolves a treatment's joint effect into its component transitions, separating an effect on progression from an effect on post-progression survival, and produces conditional and marginal effects. A simulation study with fully known truth confirms unbiased recovery and near-nominal coverage under correct specification.

We prove that harmonic functions with Dirichlet boundary data in Barron space, a function class tailored to wide ReLU networks with a single hidden layer and suitably bounded weights, are generally neither Lipschitz continuous nor in the Sobolev class $H^2$. A fortiori, they are not in any function class in which the norm controls the Lipschitz constant, which rules out not only Barron space regularity, but also regularity in function classes for deeper ReLU networks with bounded coefficients. They can, however, be approximated to accuracy $\sim \varepsilon$ by Barron functions of low norm $\sim |\log\varepsilon|$ in various Lebesgue and Sobolev norms (with at most two derivatives). The positive result holds on very simple domains: Half-spaces in arbitrary dimension and rectangular domains in two dimensions. As an application of this regularity theory, we obtain a priori error estimates for Deep Ritz neural PDE solvers.

The alignment of Small Language Models (SLMs) in the 70–500M parameter range using reinforcement learning is often considered unstable, though the underlying failure mechanisms have not been systematically investigated. In the State-of-the-Art (SOTA) research, fifteen (model, corpus) configurations were trained using Proximal Policy Optimization (PPO). The experiments included Pythia-70M, 160M, 410M and SmolLM2-135M, 360M on the TinyStories, CNN/DailyMail, and Wikitext-103 corpora. Three reproducible failure modes were identified in small-scale language models: silent LoRA parameter freezing in standard PEFT/TRL pipelines, numerical overflow in importance ratios when using bfloat16, and catastrophic policy collapse due to reward-model error. These issues were addressed using a merge-and-reinitialize adapter technique, float32 precision during PPO updates, and a three-layer safety mechanism comprising reward whitening, importance-ratio guarding, and weight rollback. In this paper, a capacity-headroom hypothesis is proposed, which states that PPO performance at the SLM scale depends on both a fluent supervised model ($\text{PPL}<20$) and a discriminative reward signal, rather than on the number of model parameters. The proposed system converged stably in all experiments and improved preference win rate over the SFT baseline in configurations with a fluent prior and an informative reward signal. Furthermore, it outperformed instruction-tuned baselines while requiring significantly less training data. All checkpoints, preference datasets, and training scripts are publicly released$^{\S}$.

Synthetic control (SC) matches a treated unit's pre-treatment trajectory to a weighted combination of donor units. We study Spectral SC, which instead matches the treated unit in coordinates defined by the leading temporal singular vectors of the donor panel, and a hybrid estimator that places separately tunable weight on retained and discarded directions, nesting raw-path SC and truncated Spectral SC as endpoints. We prove that the family reduces exactly to raw-path SC at full rank, that exact balance on $K$ retained dimensions with $N_0$ donors is underdetermined whenever $N_0>K+1$, with an affine solution set of dimension $N_0-K-1$, and that spectral imbalance maps to treatment-effect bias through a finite-sample best-linear-predictor decomposition. We evaluate the estimators across eleven data-generating regimes, using $400$ replications per regime and donor-only placebo validation to select regularization and the mixing weight. Truncated Spectral SC has significantly higher RMSE than tuned raw-path SC in every regime, with paired differences equal to $4$ to $11$ Monte Carlo standard errors. The hybrid estimator selects raw-path matching in most replications and is statistically indistinguishable from tuned SC in most regimes. The result is highly sensitive to preprocessing. With raw inputs, the performance gap is large; after removing unit and time fixed effects before spectral decomposition, as suggested by the assumptions behind our bound, the gap nearly disappears and placebo validation begins to favor truncation. We interpret these findings diagnostically rather than as evidence that Spectral SC should replace raw-path SC. Basis-estimation noise, balancing underdetermination, and fixed-effects contamination determine when spectral matching can help.

Causal mediation analyses are increasingly used in psychological sciences. Among the required assumptions, positivity is unfortunately seldom mentioned, likely due to the lack of tools for checking it. Mediational positivity is more complex than positivity in standard, non-mediated exposure effect analysis, because it requires positivity for both the exposure and the mediator, and because the specific form of the positivity assumption depends on the mediation estimand of interest. We propose an extension of the Positivity Regression Trees (PoRT) algorithm – which was recently designed to check positivity in non-mediated settings without requiring assumptions about the modeling or the data-generating process – to controlled, natural and interventional mediational effects. We illustrate its use through an application in mental health and have made it accessible through the port R package and a related notebook available at github.com/ArthurChatton/dePoRT-notebook. Finally, we discuss consequences and provide recommendations for when positivity violations are identified.

Likelihood-based inference for compositional data generally requires fully observed compositions, hindering the direct treatment of missing or censored components on the simplex. In this paper, we develop an expectation-maximisation (EM)-type algorithm for maximum likelihood estimation of the Dirichlet parameters in the presence of missing and censored components under a unified coarsening framework. The Dirichlet distribution—the canonical probability model for compositional data, which plays a role analogous to that of the multivariate normal distribution for unconstrained multivariate data—provides the foundation for our methodology. Our methodology preserves the compositional structure of the data while simultaneously performing parameter estimation and model-based imputation. We evaluate the performance of our estimators and imputations through a simulation study under increasingly complex coarsening mechanisms, including both missing and censored data. We compare our method with an existing model-based approach and a nonparametric alternative. Finally, we illustrate the practical utility of our methodology using mercury speciation data, in which compositions are only partially observed because of detection limits and incomplete speciation. Our results indicate that the Dirichlet distribution provides a suitable model for these data and that our method yields imputations that better preserve the observed compositional structure than competing approaches.

Clustering is a fundamental problem in statistics, with applications across many scientific disciplines. In many modern applications involving clustering, the primary dataset (the target data) is accompanied by related datasets (the source data). Transferring information from such sources may improve clustering accuracy in the target, making transfer learning for clustering practically important. Despite recent progress, the conditions under which source data improve target clustering remain unclear in high-dimensional settings, even for the canonical Gaussian mixture model. In this paper, we study the clustering problem in a two-community Gaussian mixture model where relatedness is captured by the geometric alignment of the target and source cluster means. We develop a minimax-optimal transfer-assisted clustering procedure and characterize, up to logarithmic factors, the phase transition for consistent target clustering in terms of the signal-to-noise ratios, sample sizes, ambient dimension, and degree of alignment between the datasets. The technique is also extended to adaptively choose between the target-only or the source assisted clustering depending on the target signal strength. Furthermore, we also extend our techniques to accommodate multiple communities and and multiple source datasets. Extensive simulations and an analysis of a human lung single-cell RNA-sequencing atlas demonstrate the practical effectiveness of our methods.

In this work, we present a simulation-based parameter estimation framework for a model defined by a computational simulation of a physical system. We specifically outline an estimation framework consisting of two closely-integrated steps that facilitate an overall end-to-end parameter estimation scheme. The first step involves utilizing an embedded normalizing flow which is used to transform the unknown complex distribution of the residual information into a simple base distribution corresponding to the transformed residual information. In the second step, an empirical-likelihood estimator, under moment restrictions, is utilized for imposing an indirect constrain on the base distribution, where such an instantiated task reasonably allows us to treat the transformed residual information as random variables arising from discretely distribution population with each transformed data point as a single-cell from a set of finite-cell contingencies. Moreover, we use first-order gradient methods for updating the estimated parameter values of the model defined by the computational simulation and the corresponding parametrized embedded normalizing flow, that call for all gradient-related information by leveraging implicitly differentiations of the empirical-likelihood function, which is constructed from the implied empirical probabilities under moment restrictions. Here, it is worth mentioning that the problem formulation presented in this work, which highlights an information-theoretic interpretation, allows to present a computational framework for algorithmic implementations. Finally, as a-by-product, the inverse of the parametrized embedded normalizing flow, w.r.t. the estimated parameter values, serves as a surrogate model for the computational simulation model, which provides useful information for quantifying model discrepancies and sensitivity analysis.

In practical settings, medical image segmentation models are often developed with limited annotated data rather than fully labeled datasets. Training frequently begins in ultra-low labeled regimes where only a small number of volumes are annotated. In such scenarios, practitioners must simultaneously decide which cases to annotate and how to best use the remaining unlabeled data. Although active learning (AL) and semi-supervised learning (SSL) both target annotation scarcity, they are typically designed and optimized independently, resulting in objective mismatch and unstable training during early-stage "cold start" conditions. We propose RegAL, a unified active semi-supervised framework governed by a shared topology-aware Pareto optimization that couples sample acquisition with unlabeled data utilization. RegAL evaluates images along three complementary axes, voxel-wise uncertainty, feature diversity, and a novel topological consistency metric, to select anatomically informative edge cases for annotation. On the other hand, the same criteria are used to identify geometrically stable atlas candidates for diffeomorphic registration-guided augmentation to train a self-supervised Mean Teacher segmentation network. Across BraTS 2021, dHCP, and ProstateX, RegAL remains stable with few labeled volumes and consistently outperforms state-of-the-art AL, SSL, and active semi-supervised baselines across Dice and boundary-distance (ASD, HD95) metrics under extreme annotation scarcity.

It is a surprising, modestly known fact that when given a single observation from a normal distribution with unknown mean and unknown variance, valid and non-trivial confidence intervals for the mean can be constructed. These intervals are presented in papers fully formed, providing limited intuition for how they arise or how to generalize them. We show that these intervals can be constructed in a principled way using two separate Bayesian reasonings. In the first, for any continuous symmetric location-scale family (under mild regularity conditions) with $n=1$ observation, we derive priors which produce $(1 - \alpha)100\%$ credible intervals that are, asymptotically in the confidence level $\alpha \rightarrow 0$, valid $(1 - \alpha)100\%$ confidence intervals. In the second, we show that the $n=1$ frequentist intervals can be seen as $t$-intervals augmented with a prior value, and that these augmented $t$-intervals are equivalent to inverted frequentist tests using a Bayes factor (using appropriate priors) as a test statistic. For $n \geq 2$, our credible interval approach does not maintain the confidence level. However, for $n \geq 2$, our augmented $t$-intervals produce valid confidence intervals with lower expected squared width in parts of the parameter space than the Student $t$-intervals, indicating improvements when prior knowledge is available. We demonstrate these methods on an $n = 3$ dataset of hyperbolic excess velocities of interstellar objects.

The accuracy of inference from a regression model depends largely on how well the model represents the relationship between the mean and variance of the outcomes. As this relationship is rarely of direct interest, it is natural to treat it as a nuisance parameter, rather than attempt to estimate it. We take this approach in the context of a monotonically transformed linear regression model using a pseudo-likelihood based on an extended notion of ranks. This approach can accommodate a wide range of mean-variance relationships and any ordinal data type, including continuous and discrete ordered data, and requires no estimation or prior specification of the transformation, or decision to treat an outcome as continuous or discrete. We show that the extended rank likelihood incurs no asymptotic information loss at the two extremes of continuous and binary data, and that rank-based prediction intervals can obtain approximate coverage control conditional on the features. Bayesian parameter estimates and prediction intervals are available via a simple Gibbs sampling algorithm. For settings where the model is in doubt, conformal calibration of the Bayesian predictive distribution provides intervals with guaranteed marginal frequentist coverage.

Generative models are increasingly adopted in distributionally robust optimization (DRO), but existing approaches trade off model compatibility and adversarial structure: methods that accept arbitrary samplers do not restrict worst-case laws to a generator family, while generator-parameterized adversaries rely on model-specific access such as likelihoods, scores, or training data. We propose Generative Distributionally Robust Optimization (GDRO), a principled framework that accepts any sampleable conditional generator as the nominal model and restricts worst-case laws to a chosen conditional generator family. The key is the sampler-Sinkhorn pairing: samplers represent the conditional laws exactly, while Sinkhorn divergence compares their induced distributions without likelihood access and can be estimated from samples alone. The resulting population problem admits a direct finite-sample approximation and differentiable primal-dual implementation at the active decision context. For Lipschitz losses, the population Sinkhorn radius bounds downstream degradation. Across explicit and implicit generators, our method reduces rare-context inventory regret by 60% and SocialGAN navigation collisions by 50% relative to nominal decisions.

In many classification problems, reliable instance-level labels are unavailable. However, it is often possible to construct weakly enriched unlabeled samples: datasets selected by different cuts, sources, populations, or experimental conditions that change latent class proportions without revealing them. Classification without Labels (CWoLa) shows that, in the binary case ($K=2$), a classifier trained to distinguish two impure mixtures with different class proportions can recover an optimal class discriminator without knowing the mixture proportions. We extend this principle to multiclass learning from several unlabeled mixtures ($K>2$), where the learner observes only mixture identity and neither latent class labels nor class-prior matrices. We prove that, for a multiclass mixture model, the Bayes-optimal mixture classifier $g^\star$ maps data points into a $(K-1)$-simplex embedded in mixture-posterior space. The $K$ vertices of this simplex are induced by the latent classes through the unknown mixing matrix. Leveraging this geometry, we propose prior-free procedures that train a standard classifier to distinguish mixture identities and then extract latent class structure using either post-hoc simplex fitting or a bottleneck architecture. Experiments on MNIST, CIFAR-10, and Galaxy10 DECaLS show that mixture identity alone can recover latent classes and their fractions in the mixture. By narrowing the gap between weakly supervised and fully supervised performance, we provide a mathematically grounded, scalable tool for multiclass discovery in label-scarce domains.

Bahadur's Lectures on the Theory of Estimation develop the classical theory of point estimation inside the geometry of Hilbert space, and they record with unusual honesty where the theory strains: the locally best unbiased estimate depends on the parameter, a two-point parameter space yields an estimate Bahadur calls absurd, the odds ratio in binomial sampling has no unbiased estimate, and the virtues of maximum likelihood enter as heuristics and remain heuristics. We present a subset of the lectures, in Bahadur's notation and development, and at each strain make one small modification: for each value in the sample space, an estimate $\tau$ becomes a function on the parameter space rather than a point in it, the continuum of null hypotheses that Fisher described in 1955. Bahadur's own definition of an estimate, square-integrable at every distribution in the family, already supplies the domain. The payoffs are tracked lecture by lecture: estimators that exist at boundary samples where point estimates do not; an elementary lemma showing that no pointwise criterion admits a uniformly optimal estimator, which explains why admissibility, minimaxity, Bayes averaging, and unbiasedness arose as responses; assessment by information, $\Lambda(\tau)$, with the score attaining the Fisher information bound uniformly by a three-line argument; Cramér–Rao attainment and sufficiency recovered as equality cases of that bound under two maps from point estimators to generalized estimators; and the maximum likelihood heuristics converted into exact statements about the score. Nothing classical is overturned; the classical apparatus is explained using Fisher's characterization of estimation as a continuum of significance tests.

Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples. The goal is to learn an unknown distribution $p$ on a finite domain $[n]$. The learner is given a fixed family of queryable sets $\mathscr{S} \subseteq 2^{[n]}$, and each query to $S \in \mathscr{S}$ returns an independent sample from the conditional distribution $p(\cdot \mid S)$. Learnability is governed by the co-occurrence graph associated with $\mathscr{S}$: two domain elements are adjacent if they appear together in some queryable set. Pointwise consistency is achievable when this graph is connected on the target support. PAC learning requires more: it is possible when the co-occurrence graph is complete. The optimal sample complexity of PAC learning ranges from nearly linear to quadratic. Every query family with complete co-occurrence graph admits sample complexity $\widetilde O(n^2/\epsilon^2)$, and this bound is tight in the worst case. On the other hand, if $[n]$ is queryable then ordinary sampling improves the bound to $\Theta(n/\epsilon^2)$, and this cannot be improved further even if every set is queryable. More generally, we identify hierarchical comparabilityas a sufficient structural condition on $\mathscr S$ under which the optimal complexity is nearly linear, $\widetilde \Theta(n/\epsilon^2)$, with pairwise query families as a canonical example. Finally, the full range of polynomial rates between linear and quadratic is attainable: for every $\alpha \in (1,2)$, there exists a query family with optimal PAC rate $\widetilde \Theta(n^\alpha/\epsilon^2)$.

A derangetropy operator reweighs a probability density by a fixed profile of its own cumulative distribution function, acting through ranks alone. We prove that these operators are precisely the transformations of absolutely continuous laws equivariant under monotone changes of variable, and that they compose through interval maps, making their dynamics exactly solvable: iteration condenses every law onto its median with a universal Koenigs limit law, the continuous flow is solvable in closed form with the Cauchy family as invariant hyperbolic manifold, and balanced against diffusion the distribution function obeys an overdamped sine-Gordon equation whose unique steady law, the hyperbolic secant, is a globally stable kink. A variational principle selects the canonical kernel, the squared ground state of the Dirichlet Laplacian on the unit interval, whose update is a Bayesian posterior costing exactly one bit for every law, and a unitary lift equips each law with an isospectral Sturm-Liouville system and a quantum carpet: a strong law of large numbers for the critical Sobolev mass, with sharp constant given by Wiener's jump statistic, proves the fractality of the Schrödinger density for arbitrary real bounded-variation data with a jump, previously known only for rational step data. A lift to the dual of the Virasoro algebra, at central charge one, a normalization, identifies laws with disconjugate Hill potentials, tails with conformal weights, and the Cauchy family with the exceptional orbit. Randomized phases yield an exact sampler and a multiplicative chaos, log-correlated in the weakly tempered regime; in several dimensions, dependence stratifies into a conserved interaction, a torsion driven by maximal correlation, and a flat Sinkhorn transport.

Recent advances in spatial transcriptomics have enabled researchers to profile gene expression at the single-cell spatial resolution, often for multiple tissue samples in a single study. This high-dimensional molecular profile for each cell can be used to sort cells into cell types with distinct functions, or segment the tissue into biologically relevant spatial domains. Although many non-spatial and spatial clustering methods have been developed to cluster these cells into cell types or spatial domains, most have two main limitations: first, they perform dimension reduction and clustering separately; second, they cluster cells at a single scale, rather than treating cell type and spatial domain clustering as distinct tasks at two different scales. To overcome these limitations, we propose BayesClint, a Bayesian method that simultaneously performs factor analysis and spatial clustering on multiple samples, where the clustering is done jointly at the single-cell and tissue regional scale. To increase interpretability, we employ a feature selection mechanism within the estimation of the sparse factor loadings matrix, which detects active genes and differentially expressed genes that discriminate between cell type clusters. We illustrate the advantages of the method over alternative state-of-the-art approaches through simulation studies and two real data applications.

We describe Causal-TS, an open-source Python library for causal discovery in high-dimensional and nonstationary multivariate time series. Causal-TS provides four specialized algorithms-CDNOTS, CDNOTS+, CEDAR, and GRACE-along with wrappers for GES, Granger, LASSO-VAR, and LGES, all sharing a unified conditional independence (CI) test layer with GPU acceleration via PyTorch. A regime discovery pipeline detects structural breaks via pluggable changepoint detectors and runs discovery per regime with regime-specific parameters. A command-line interface, synthetic data generators, and optional DoWhy integration provide an end-to-end pipeline from raw time series to causal effect estimates. The library is pip-installable, tested on Python 3.10–3.12, and available at https://github.com/bloomberg/causal-ts.

Early inquiries into the statistical properties of natural language found that words tend to occur with power-law frequencies. This observation, closely associated with Zipf's law, has spurred many investigations into why this power-law pattern emerges with such regularity. Rarely, however, has this property of text been leveraged in statistical inference. In this paper, we demonstrate that the Latent Dirichlet Allocation (LDA) model can accommodate power-law word frequencies. In particular, when the document length distribution is regularly varying, the word frequency distribution admits a hierarchy of power laws across documents and topics. We further leverage this finding to develop an efficient tensor decomposition algorithm for estimating the topic matrix via the moments of normalized extreme word frequencies. Applying our algorithm to the twenty newsgroups corpus reveals that the extreme-value methodology exhibits robustness to certain choices made in the pre-processing of the data. This work furthers the recent interest in adapting machine learning methods to the study of multivariate extremes.

We study imbalanced crowdsourcing with a focus on class-dependent annotator accuracy, a setting that, to the best of our knowledge, remains relatively underexplored despite its importance in real-world inspection systems where the labels of greatest operational importance are also the rarest ones. In this setting, annotators may be reliable on both classes, unreliable on both classes, majority-class specialists, or minority-class specialists. Existing models only partially address this problem: they either capture class-dependent errors but ignore item difficulty, or they model item difficulty without capturing class-dependent errors. To fill this gap for imbalanced datasets in crowdsourcing, we introduce a generative aggregation model combining item difficulty with class-dependent annotator competence. The model allows both annotator abilities and item difficulties to vary across classes. We then revisit Condorcet's Jury Theorem in the class-imbalanced setting. We also show that majority voting asymptotically preserves the underlying class proportion. We evaluate our model on $33$ real-world crowdsourcing datasets, covering multiclass tasks such as images and text, as well as two large-scale regimes: large-scale annotation datasets, with many annotations per item, and large-scale item datasets, with a large number of annotated instances. Across these diverse settings, our model consistently achieves the highest minority recall while remaining competitive in balanced accuracy, making it particularly relevant when rare-label recovery is the primary objective.

This paper proposes a stage independent multiple sampling plan (SIMSP) to improve inspection efficiency by reducing the number of samples required at each sampling stage. Unlike conventional multiple sampling plans (MSP), the proposed SIMSP eliminates the dependence of each sampling stage on the outcome of the preceding inspection. The proposed approach is developed for non-repairable products sold under a pro-rata warranty policy based on the generalized process capability index $C_{py}$. The SIMSP is designed under a Type-II hybrid censoring scheme (Type-II HCS), which provides greater flexibility in controlling test time and failure information in life testing experiments. The asymptotic distribution of the process capability index estimate is used to compute the operating characteristic (OC) function, and the exact Fisher information matrix (FIM) is obtained for further statistical analysis. A constraint optimization problem is formulated to determine the optimal design by minimizing the total cost subject to the manufacturer's and consumer's risk. Numerical investigations are conducted to examine the effects of model parameters, warranty policy characteristics, and cost factors on the optimal solution. The results demonstrate that the proposed approach provides an economically efficient and feasible method for lot acceptance while satisfying the tolerable risks requirements.

In linear mixed effects models (LMM), inference on fixed effects typically relies on either the generalized least squares (GLS) variance estimator obtained by assuming that the variance parameters are known, or on the Kenward-Roger method with a small-sample bias adjustment. A simulation study shows that both approaches can underestimate the variance of the treatment effect and inflate the type I error rate in large clinical trials under missing at random (MAR) mechanisms, with greater type I error inflation as the differences in the missingness mechanisms between treatment groups increase. Counterintuitively, the estimated fixed effects and variance parameters exhibit asymptotic dependence. Ignoring this dependence may lead to invalid inference. To account for this additional source of variability, we propose a new asymptotic variance estimator and a small-sample bias-corrected estimator to quantify uncertainty in estimation and prediction in LMM under MAR. The proposed methods are theoretically justified, and their performance is demonstrated by numerical examples.

Transportation network partitioning is essential for applications such as traffic analysis, simulation, and mobility pattern identification. However, transportation networks combine structural information with heterogeneous operational attributes, ranging from scalar indicators to temporal profiles. Existing approaches generally rely on predefined formulations to integrate these sources of information, limiting the ability to control their relative influence. This paper proposes a flexible framework for partitioning heterogeneous transportation networks represented as attributed graphs. The proposed methodology relies on a distance-based graph representation and an optimal transport formulation based on the semi-relaxed Fused Gromov-Wasserstein discrepancy, enabling joint consideration of network structure and attributes with explicit control over their trade-off. The proposed methodology is evaluated on two transportation systems with distinct characteristics: an urban road network for traffic-oriented partitioning and a bicycle-sharing system for identifying usage-based communities. Results demonstrate the ability of the framework to adapt the resulting partitions according to different structural and attribute preferences.

We study the task of estimating a $d-$dimensional quantum state $\rho$ under the constraint that the measurement is $\alpha-$gentle. Such measurements $M$ do not collapse the state; they issue both a random variable $R^M = \omega$ containing statistical information and a post-measurement state $\rho_{M \to \omega}$ such that $\|\rho_{M\to \omega} - \rho\|_{Tr} \leq \alpha$. We describe gentle measurements and their connection to quantum differential privacy. Our results show that the optimal minimax estimation rate in Frobenius norm is of order $d^3/(n \alpha^2)$, instead of $d^2/n$ for general measurements. Moreover, for rank $r$ states with $r\leq d$ we prove that the optimal minimax rate is $rd^2/(n \alpha^2)$, instead of $rd/n$. Very surprisingly, the loss for gentleness $d/\alpha^2$ scales with the ambient dimension of the Hilbert space, rather than the number of parameters $rd$, typically seen in classical differential privacy. We propose optimal gentle measurements and indicate how they can be physically implemented using an ancillary state and a CNOT gate to entangle it with the initial state. We notice that the resulting random variable has a likelihood that satisfies local differential privacy. Lower bounds are proven through a new quantum information-theoretic inequality applied to well chosen families of states in the manifold of (small-rank) quantum states.

We develop a general framework of identification and estimation for automatic debiased machine learning (DML) where the parameter of interest $\theta_0$ is identified by a moment condition involving a nuisance $\gamma_0$ that may be high dimensional. We establish conditions under which the Riesz representer $\alpha_0$, which is at the core of DML, is identified, and show that the identification occurs precisely when $\alpha_0$ uniquely optimizes a quadratic functional. This characterization enables us to develop a general estimation procedure for $\alpha_0$ that allows for generic $\gamma_0$ including those defined by models with endogeneity and encompasses both classical sieves and modern architectures such as deep neural networks. To improve estimation precision and mitigate the curse of dimensionality, we incorporate shape constraints on $\gamma_0$ by embedding them into a possibly nonlinear parameter space. We illustrate our estimation procedure through simulations and empirical applications.

Reservoir computing has emerged as an efficient machine learning framework for predicting time series generated by dynamical systems. In contrast to other machine and deep learning approaches, a reservoir computing trains only the output layer via linear regression, leaving the reservoir (recurrent layer) untrained. This simplification makes reservoir computers easier to train and more amenable to experimentation. However, because current reservoirs consist of networks of randomly connected nodes and require the optimization of numerous hyperparameters, a framework that precisely explains how reservoir computing operates and how it can be optimized remains missing. Here, we propose a frequency-based reservoir inspired by the brain's oscillatory dynamics and its hierarchy of timescales. The frequency-based reservoir can be interpreted as an ensemble of independent oscillatory units, each processing a portion of the input's frequency content. This allows us to understand the reservoir's internal behavior by modeling it as a single unit driven by an external input. Borrowing from the theory of a nonlinear oscillator forced by complex periodic inputs, we found that units of the frequency-based reservoir selectively amplify and store specific input frequencies, which are then used for prediction. The frequency-based reservoir performs as well as or better than equivalent random reservoirs. Furthermore, the frequency-based approach can be optimized to improve short-term prediction, a property that random reservoirs lack. Finally, we show that the frequency-based reservoir can also predict complex spatiotemporal dynamics. Our results show that reservoir computing can be designed using brain properties and theoretical insights borrowed from the physics of forced nonlinear oscillators.

Proxy outcomes (such as short-term behavioral signals, model predictions, or surrogate endpoints) are frequently used in place of primary outcomes that are too slow to mature, rare, or challenging to measure directly. But valid inference on a proxy does not guarantee valid inference on the primary estimate as proxy-based estimates can be systematically biased in ways that are difficult to predict, leading to improperly calibrated confidence intervals. We present proxymate, a framework and open-source Python package for proxy validation and adjustment. proxymate organizes into four levels: The Representativity Level (population validity), the Unit Level (measurement quality), the Estimate Level (decision validity), and the Domain Level (cross-domain transportability). Within each level, proxymate provides diagnostic checks, and targeted adjustment strategies that map specific failures to appropriate corrections. At Meta, proxymate has been adopted by many different use cases, spanning experimentation, prevalence estimation, and monitoring use cases, all facing different proxy challenges (limited human review time, long maturation window of outcomes, low detectability) and showcasing the modularity of the framework. Across all products, proxymate assessed and corrected millions of proxy, primary unit comparisons. It has facilitated launches across multiple work streams including enabling quick decision making on thousands of experiments.