Papers

Real-world problems, for example in climate applications, often require causal reasoning on spatially gridded time series data or data with comparable structure. While the underlying system is often believed to behave similarly at different Points in space and time, those variations that do exist are relevant twofold: They often encode important information in and of themselves. And they may negatively affect the stability and validity of results if not accounted for. We study the information encoded in changes of the causal graph, with stability in mind. Two core challenges arise, related to the complexity of encoding system-states and to statistical convergence properties in the presence of imperfectly recoverable non-stationary structure. We provide a framework realizing principles conceptually suitable to overcome these challenges - an interpretation supported by numerical experiments. Primarily, we modify constraint-based causal discovery approaches on the level of independence testing. This leads to a framework which is additionally highly modular, easily extensible and widely applicable. For example, it allows to leverage existing constraint-based causal discovery methods (demonstrated on PC, PC-stable, FCI, PCMCI, PCMCI+ and LPCMCI), and to systematically divide the problem into simpler subproblems that are easier to analyze and understand and relate more clearly to well-studied problems like change-point-detection, clustering, independence-testing and more. Code is available at https://github.com/martin-rabel/Causal_GLDF.

In many applications of causal inference, the treatment received by one unit may influence the outcome of another, a phenomenon referred to as interference. Although there are several frameworks for conducting causal inference in the presence of interference, practitioners often lack the data necessary to adjust for its effects. In this paper, we propose a weighting-based sensitivity analysis framework that can be used to assess the systematic bias arising from ignoring interference. Unlike most of the existing literature, we allow for the presence of unmeasured confounding, and show that the combination of interference and unmeasured confounding is a notable challenge to causal inference. We also study a third factor contributing to systematic bias: lack of transportability. Our framework enables practitioners to assess the impact of these three issues simultaneously through several easily interpretable sensitivity parameters that can reflect a wide range of intuitions about the data.

A fundamental theoretical question in network analysis is to determine under which conditions community recovery is possible in polynomial time in the Stochastic Block Model (SBM). When the number $K$ of communities remains smaller than $\sqrt{n}$ –where $n$ denotes the number of nodes–, non-trivial community recovery is possible in polynomial time above, and only above, the Kesten–Stigum (KS) threshold, originally postulated using arguments from statistical physics. When $K \geq \sqrt{n}$, Chin, Mossel, Sohn, and Wein recently proved that, in the sparse regime, community recovery in polynomial time is achievable below the KS threshold by counting non-backtracking paths. This finding led them to postulate a new threshold for the many-communities regime $K \geq \sqrt{n}$. Subsequently, Carpentier, Giraud, and Verzelen established the failure of low-degree polynomials below this new threshold across all density regimes, and demonstrated successful recovery above the threshold in certain moderately sparse settings. While these results provide strong evidence that, in the many community setting, the computational barrier lies at the threshold proposed in~Chin et al., the question of achieving recovery above this threshold still remains open in most density regimes. The present work is a follow-up to~Carpentier et al., in which we prove Conjecture~1.4 stated therein by: \\ 1- Constructing a family of motifs satisfying specific structural properties; and\\ 2- Proving that community recovery is possible above the proposed threshold by counting such motifs.\\ Our results complete the picture of the computational barrier for community recovery in the SBM with $K \geq \sqrt{n}$ communities. They also indicate that, in moderately sparse regimes, the optimal algorithms appear to be fundamentally different from spectral methods.

Causal inference is a central goal across many scientific disciplines. Over the past several decades, three major frameworks have emerged to formalize causal questions and guide their analysis: the potential outcomes framework, structural equation models, and directed acyclic graphs. Although these frameworks differ in language, assumptions, and philosophical orientation, they often lead to compatible or complementary insights. This paper provides a comparative introduction to the three frameworks, clarifying their connections, highlighting their distinct strengths and limitations, and illustrating how they can be used together in practice. The discussion is aimed at researchers and graduate students with some background in statistics or causal inference who are seeking a conceptual foundation for applying causal methods across a range of substantive domains.

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e. particle filters), the EnKF leverages either the linear Gaussian structure of the SSM or an approximation thereof, to maintain diversity of the sampled latent states (the so-called ensemble members) via shifting-based updates. Joint parameter and state inference using an EnKF is typically achieved by augmenting the state vector with the static parameter. In this case, it is assumed that both parameters and states follow a linear Gaussian state-space model, which may be unreasonable in practice. In this paper, we combine the reweighting and shifting methods by replacing the particle filter used in the SMC^2 algorithm of Chopin et al. (2013), with the ensemble Kalman filter. Hence, parameter particles are weighted according to the estimated observed-data likelihood from the latest observation computed by the EnKF, and particle diversity is maintained via a resample-move step that targets the marginal parameter posterior under the EnKF. Extensions to the resulting algorithm are proposed, such as the use of a delayed acceptance kernel in the rejuvenation step and incorporation of nonlinear observation models. We illustrate the resulting methodology via several applications.

We study nonparametric Bayesian binary classification, in the case where the unknown probability response function is possibly spatially inhomogeneous, for example, being generally flat across the domain but presenting localized sharp variations. We consider a hierarchical procedure based on the Besov-Laplace priors from the inverse problems and imaging literature, with a carefully tuned hyper-prior on the regularity parameter. We show that the resulting posterior distribution concentrates towards the ground truth at optimal rate, automatically adapting to the unknown regularity. To implement posterior inference in practice, we devise an efficient Markov chain Monte Carlo (MCMC) algorithm based on recent ad-hoc dimension-robust methods for Besov-Laplace priors. We then test the considered approach in extensive numerical simulations, where we obtain a solid corroboration of the theoretical results.

Response-Adaptive Randomization (RAR) is recognized for its potential to deliver improvements in patient benefit. However, the utility of RAR is contingent on regularization methods to mitigate early instability and preserve statistical integrity. A standard regularization approach is the ”burn-in” period, an initial phase of equal randomization before treatment allocation adapts based on accrued data. The length of this burn-in is a critical design parameter, yet its selection remains unsystematic and improvised, as no established guideline exists. A poorly chosen length poses significant risks: one that is too short leads to high estimation bias and type-I error rate inflation, while one that is too long impedes the intended patient and power benefits of using adaptation. The challenge of selecting the burn-in generalizes to a fundamental question: what is the statistically appropriate timing for the first adaptation? We introduce the first systematic framework for determining burn-in length. This framework synthesizes core factors - total sample size, problem difficulty, and two novel metrics (reactivity and expected final allocation error) - into a single, principled formula. Simulation studies, grounded in real-world designs, demonstrate that lengths derived from our formula successfully stabilize the trial. The formula identifies a ”sweet spot” that mitigates type-I error rate inflation and mean-squared error, preserving the advantages of higher power and patient benefit. This framework moves researchers from conjecture toward a systematic, reliable approach.

A/B testing plays a central role in data-driven product development, guiding launch decisions for new features and designs. However, treatment effect estimates are often noisy due to short horizons, early stopping, and slowly accumulating long-tail metrics, making early conclusions unreliable. A natural remedy is to pool information across related experiments, but naive pooling potentially fails: within experiments, treatment effects may evolve over time, so mixing early and late outcomes without accounting for nonstationarity induces bias; across experiments, heterogeneity in product, user population, or season dilutes the signal with unrelated noise. These issues highlight the need for pooling strategies that adapt to both temporal evolution and cross-experiment variability. To address these challenges, we propose a local empirical Bayes framework that adapts to both temporal and cross-experiment heterogeneity. Throughout an experiment's timeline, our method builds a tailored comparison set: time-aware within the experiment to respect nonstationarity, and context-aware across experiments to draw only from comparable counterparts. The estimator then borrows strength selectively from this set, producing stabilized treatment effect estimates that remain sensitive to both time dynamics and experimental context. Through theoretical analysis and empirical evaluation, we show that the proposed local pooling strategy consistently outperforms global pooling by reducing variance while avoiding bias. Our proposed framework enhances the reliability of A/B testing under practical constraints, thereby enabling more timely and informed decision-making.

The recent proof of quasi-Gaussianity for the 2D stochastic Navier–Stokes (SNS) equations by Coe, Hairer, and Tolomeo establishes that the system's unique invariant measure is equivalent (mutually absolutely continuous) to the Gaussian measure of its corresponding linear Ornstein–Uhlenbeck (OU) process. While Gaussian process (GP) frameworks are increasingly used for fluid dynamics, their priors are often chosen for convenience rather than being rigorously justified by the system's long-term dynamics. In this work, we bridge this gap by introducing a probabilistic framework for 2D SNS built directly upon this theoretical foundation. We construct our GP prior precisely from the stationary covariance of the linear OU model, which is explicitly defined by the forcing spectrum and dissipation. This provides a principled, GP prior with rigorous long-time dynamical justification for turbulent flows, bridging SPDE theory and practical data assimilation.

Small and medium-sized enterprises (SMEs) play a crucial role in driving economic growth. Monitoring their financial performance and discovering relevant covariates are essential for risk assessment, business planning, and policy formulation. This paper focuses on predicting profits for SMEs. Two major challenges are faced in this study: 1) SMEs data are stored across different institutions, and centralized analysis is restricted due to data security concerns; 2) data from various institutions contain different levels of missing values, resulting in a complex missingness issue. To tackle these issues, we introduce an innovative approach named Vertical Federated Expectation Maximization (VFEM), designed for federated learning under a missing data scenario. We embed a new EM algorithm into VFEM to address complex missing patterns when full dataset access is unfeasible. Furthermore, we establish the linear convergence rate for the VFEM and establish a statistical inference framework, enabling covariates to influence assessment and enhancing model interpretability. Extensive simulation studies are conducted to validate its finite sample performance. Finally, we thoroughly investigate a real-life profit prediction problem for SMEs using VFEM. Our findings demonstrate that VFEM provides a promising solution for addressing data isolation and missing values, ultimately improving the understanding of SMEs' financial performance.

Prediction models developed before the introduction of a new treatment may be used to estimate treatment effects of newly introduced treatments. One approach, known as model-based clinical evaluation in radiotherapy, does this by comparing observed outcomes under a new treatment with predicted outcomes had these patients received the standard treatment. This article clarifies the relevant conditions needed for valid average treatment effect estimation using this approach, using the potential outcomes framework and a practical case study.

Post-Double-Lasso is becoming the most popular method for estimating linear regression models with many covariates when the purpose is to obtain an accurate estimate of a parameter of interest, such as an average treatment effect. However, this method can suffer from substantial omitted variable bias in finite sample. We propose a new method called Post-Double-Autometrics, which is based on Autometrics, and show that this method outperforms Post-Double-Lasso. Its use in a standard application of economic growth sheds new light on the hypothesis of convergence from poor to rich economies.

Variational inference (VI) is a cornerstone of modern Bayesian learning, enabling approximate inference in complex models. However, its formulation depends on expectations and divergences defined through high-dimensional integrals, often rendering analytical treatment impossible and necessitating heavy reliance on approximations. Possibility theory, an imprecise probability framework, allows us to directly model epistemic uncertainty instead of relying on a subjective interpretation of probabilities. While this framework provides robustness and interpretability under sparse or imprecise information, adapting VI to the possibilistic setting requires rethinking core concepts such as divergences, which presuppose additivity. In this work, we develop a principled formulation for performing possibilistic VI by establishing a maxitive analogue of the classical Donsker-Varadhan formulation. The resulting framework enables us to derive a learning rule for possibilistic VI with exponential-family candidates and practical update rules for neural-network training, giving rise to a family of optimizers termed CBOpt. Finally, we demonstrate that CBOpt achieves competitive performance on both in-domain and out-of-domain image classification tasks.

Recognizing that asset markets generally exhibit shared informational characteristics, we develop a portfolio strategy based on transfer learning that leverages cross-market information to enhance the investment performance in the market of interest by forward validation. Our strategy asymptotically identifies and utilizes the informative datasets, selectively incorporating valid information while discarding the misleading information. This enables our strategy to achieve the maximum Sharpe ratio asymptotically. The promising performance is demonstrated by numerical studies and case studies of two portfolios: one consisting of stocks dual-listed in A-shares and H-shares, and another comprising equities from various industries of the United States.

Large language models (LLMs) are widely used as scalable evaluators of model responses in lieu of human annotators. However, imperfect sensitivity and specificity of the LLM judges induce bias in naive evaluation scores. We propose a simple plug-in framework that corrects this bias and enables statistically principled uncertainty quantification. Our framework constructs confidence intervals that account for uncertainty from both the test dataset and a human-labeled calibration dataset. Additionally, it uses an adaptive strategy to allocate calibration samples for tighter intervals. Importantly, we characterize parameter regimes defined by the true evaluation score and the LLM judge's sensitivity and specificity in which our LLM-based evaluation yields more reliable estimates than human-only evaluation. Moreover, we show that our framework remains unbiased under distribution shift between the test and calibration datasets, in contrast to existing approaches.

We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a maximum likelihood estimator with a group l0-regularization that penalizes the number of edges in the graph. The resulting estimator is formulated through a convex mixed-integer program, enabling the use of branch-and-bound methods to obtain a solution that is guaranteed to be accurate up to a pre-specified optimality gap. Our formulation can naturally encode background knowledge, such as the presence or absence of edges and partial order constraints among the variables. We establish consistency guarantees for our estimator in terms of graph recovery, even when the number of variables grows with the sample size. Additionally, by connecting the optimality guarantees with our statistical error bounds, we derive an early stopping criterion that allows terminating the branch-and-bound procedure while preserving consistency. Compared with existing approaches that either assume equal error variances, restrict to linear structural equation models, or rely on heuristic procedures, our method enjoys both optimization and statistical guarantees. Extensive simulations and real-data analysis show that the proposed method achieves markedly better graph recovery performance.

This paper investigates the partial linear model by Least Absolute Deviation (LAD) regression. We parameterize the nonparametric term using Deep Neural Networks (DNNs) and formulate a penalized LAD problem for estimation. Specifically, our model exhibits the following challenges. First, the regularization term can be nonconvex and nonsmooth, necessitating the introduction of infinite dimensional variational analysis and nonsmooth analysis into the asymptotic normality discussion. Second, our network must expand (in width, sparsity level and depth) as more samples are observed, thereby introducing additional difficulties for theoretical analysis. Third, the oracle of the proposed estimator is itself defined through a ultra high-dimensional, nonconvex, and discontinuous optimization problem, which already entails substantial computational and theoretical challenges. Under such the challenges, we establish the consistency, convergence rate, and asymptotic normality of the estimator. Furthermore, we analyze the oracle problem itself and its continuous relaxation. We study the convergence of a proximal subgradient method for both formulations, highlighting their structural differences lead to distinct computational subproblems along the iterations. In particular, the relaxed formulation admits significantly cheaper proximal updates, reflecting an inherent trade-off between statistical accuracy and computational tractability.

The rapid growth of high-dimensional datasets across a wide range of scientific domains has created an urgent need for new statistical methods to compare distributions with underlying low-dimensional structure. Assessing similarity between high-dimensional datasets whose observations concentrate near low-dimensional manifolds is particularly challenging due to the nontrivial effects of noise in high dimensions. We propose a principled framework for statistical inference on the similarity and alignability of high-dimensional datasets with low-dimensional smooth signals under heterogeneous noise. The key idea is to link the spectral properties of the observed data matrices to the geometry of their underlying signal distributions. Under a manifold signal-plus-noise model, we build on the principal variances associated to the underlying signals and develop a scale- and rotation-invariant dissimilarity measure between two datasets that may differ in sample size and noise structure. We further construct an estimator of the dissimilarity and a statistical test of dataset alignability, namely, whether the dissimilarity vanishes. The proposed methodology and its theoretical guarantees under high-dimensional asymptotic settings draw on recent advances in random matrix theory (RMT). The proposed framework accommodates heterogeneous noise across datasets and provides a fast, theoretically grounded approach to comparing high-dimensional datasets with low-dimensional structures. Through extensive simulations and analyses of multiple single-cell datasets, we demonstrate that the proposed method substantially outperforms existing approaches.

We propose a novel randomized algorithm for constructing binary neural networks with tunable accuracy. This approach is motivated by hyperdimensional computing (HDC), which is a brain-inspired paradigm that leverages high-dimensional vector representations, offering efficient hardware implementation and robustness to model corruptions. Unlike traditional low-precision methods that use quantization, we consider binary embeddings of data as points in the hypercube equipped with the Hamming distance. We propose a novel family of floating-point neural networks, G-Nets, which are general enough to mimic standard network layers. Each floating-point G-Net has a randomized binary embedding, an embedded hyperdimensional (EHD) G-Net, that retains the accuracy of its floating-point counterparts, with theoretical guarantees, due to the concentration of measure. Empirically, our binary models match convolutional neural network accuracies and outperform prior HDC models by large margins, for example, we achieve almost 30% higher accuracy on CIFAR-10 compared to prior HDC models. G-Nets are a theoretically justified bridge between neural networks and randomized binary neural networks, opening a new direction for constructing robust binary/quantized deep learning models. Our implementation is available at https://github.com/GNet2025/GNet.

Zipf's law in language lacks a definitive origin, debated across fields. This study explains Zipf-like behavior using geometric mechanisms without linguistic elements. The Full Combinatorial Word Model (FCWM) forms words from a finite alphabet, generating a geometric distribution of word lengths. Interacting exponential forces yield a power-law rank-frequency curve, determined by alphabet size and blank symbol probability. Simulations support predictions, matching English, Russian, and mixed-genre data. The symbolic model suggests Zipf-type laws arise from geometric constraints, not communicative efficiency.

Fine-tuning large language models (LLMs) for downstream tasks typically exhibit a fundamental safety-capability tradeoff, where improving task performance degrades safety alignment even on benign datasets. This degradation persists across standard approaches including supervised finetuning (SFT) and reinforcement learning from human feedback (RLHF). While reinforcement learning with verifiable rewards (RLVR) has emerged as a promising alternative that optimizes models on objectively measurable tasks, its safety implications remain unexplored. We present the first comprehensive theoretical and empirical analysis of safety properties in RLVR. Theoretically, we derive upper bounds on safety drift under KL-constrained optimization and prove conditions under which safety degradation is eliminated. Empirically, we conduct extensive experiments across five adversarial safety benchmarks, demonstrating that RLVR can simultaneously enhance reasoning capabilities while maintaining or improving safety guardrails. Our comprehensive ablation studies examine the effects of optimization algorithms, model scale, and task domains. Our findings challenge the prevailing assumption of an inevitable safety capability trade-off, and establish that a specific training methodology can achieve both objectives simultaneously, providing insights for the safe deployment of reasoning-capable LLMs.

We consider the problem of estimating Ising models over $n$ variables in Total Variation (TV) distance, given $l$ independent samples from the model. While the statistical complexity of the problem is well-understood [DMR20], identifying computationally and statistically efficient algorithms has been challenging. In particular, remarkable progress has occurred in several settings, such as when the underlying graph is a tree [DP21, BGPV21], when the entries of the interaction matrix follow a Gaussian distribution [GM24, CK24], or when the bulk of its eigenvalues lie in a small interval [AJK+24, KLV24], but no unified framework for polynomial-time estimation in TV exists so far. Our main contribution is a unified analysis of the Maximum Pseudo-Likelihood Estimator (MPLE) for two general classes of Ising models. The first class includes models that have bounded operator norm and satisfy the Modified Log-Sobolev Inequality (MLSI), a functional inequality that was introduced to study the convergence of the associated Glauber dynamics to stationarity. In the second class of models, the interaction matrix has bounded infinity norm (or bounded width), which is the most common assumption in the literature for structure learning of Ising models. We show how our general results for these classes yield polynomial-time algorithms and optimal or near-optimal sample complexity guarantees in a variety of settings. Our proofs employ a variety of tools from tensorization inequalities to measure decompositions and concentration bounds.

Background: True cognitive longitudinal decline can be obscured by repeated testing, which is called practice effects (PEs). We developed a modeling framework that aligns participants by baseline and estimates visit-specific PEs independently of age-related change. Method: Using real data ($N=175$), we estimated within-subject correlations via linear mixed-effects modeling and applied these parameters to simulate longitudinal trajectories for healthy controls (HC) and individuals with schizophrenia (SZ). Simulations incorporated aging, diagnostic differences, and cumulative PE indicators. Generalized estimating equations (GEEs) were fit with and without PEs to compare model performance. Results: Models that ignored PEs inflated estimates of cognitive stability and attenuated HC–SZ group differences. Including visit-specific PEs improved recovery of true trajectories and more accurately distinguished aging effects from learning-related gains. Interaction models further identified that PEs may differ by diagnosis or by age at baseline. Conclusion: Practice effects meaningfully bias longitudinal estimates if left unmodeled. The proposed alignment-based GEE framework provides a principled method to estimate PEs and improves accuracy in both simulated and real-world settings. Keywords: practice effects; repeat testing; serial testing; longitudinal testing; mild cognitive impairment; cognitive change.

Methods for causal inference are well developed for binary and continuous exposures, but in many settings, the exposure has a substantial mass at zero-such exposures are called semi-continuous. We propose a general causal framework for such semi-continuous exposures, together with a novel two-stage estimation strategy. A two-part propensity structure is introduced for the semi-continuous exposure, with one component for exposure status (exposed vs unexposed) and another for the exposure level among those exposed, and incorporates both into a marginal structural model that disentangles the effects of exposure status and dose. The two-stage procedure sequentially targets the causal dose-response among exposed individuals and the causal effect of exposure status at a reference dose, allowing flexibility in the choice of propensity score methods in the second stage. We establish consistency and asymptotic normality for the resulting estimators, and characterise their limiting values under misspecification of the propensity score models. Simulation studies evaluate finite sample performance and robustness, and an application to a study of prenatal alcohol exposure and child cognition demonstrates how the proposed methods can be used to address a range of scientific questions about both exposure status and exposure intensity.

Analysis of competing risks data is often complicated by the incomplete or selectively missing information on the cause of failure. Standard approaches typically assume that the cause of failure is missing at random (MAR), an assumption that is generally untestable and frequently implausible in observational studies. We propose a novel sensitivity analysis framework for the proportional cause-specific hazards model that accommodates missing-not-at-random (MNAR) scenarios. A sensitivity parameter is used to quantify the association between missingness and the unobserved cause of failure. Regression coefficients are estimated as functions of this parameter, and a simultaneous confidence band is constructed via a wild bootstrap procedure. This allows identification of a range of MNAR scenarios for which effects remain statistically significant; we refer to this range as a robustness interval. The validity of the proposed approach is justified both theoretically, via empirical process theory, and empirically, through simulation studies. We apply the method to the analysis of data from an HIV cohort study in sub-Saharan Africa, where a substantial proportion of causes of failure are missing and the MAR assumption is implausible. The analysis shows that key findings regarding risk factors for care interruption and mortality are robust across a broad spectrum of MNAR scenarios, underscoring the method's utility in situations with MNAR causes of failure.

SVEMnet is an R package for fitting Self-Validated Ensemble Models (SVEM) with elastic-net base learners and performing multi-response optimization in small-sample mixture-process design-of-experiments (DOE) studies with numeric, categorical, and mixture factors. SVEMnet wraps elastic-net and relaxed elastic-net models for Gaussian and binomial responses from glmnet in a fractional random-weight (FRW) resampling scheme with anti-correlated train/validation weights; penalties are selected by validation-weighted AIC- and BIC-type criteria, and predictions are averaged across replicates to stabilize fits near the interpolation boundary. In addition to the core SVEM engine, the package provides deterministic high-order formula expansion, a permutation-based whole-model test heuristic, and a mixture-constrained random-search optimizer that combines Derringer-Suich desirability functions, bootstrap-based uncertainty summaries, and optional mean-level specification-limit probabilities to generate scored candidate tables and diverse exploitation and exploration medoids for sequential fit-score-run-refit workflows. A simulated lipid nanoparticle (LNP) formulation study illustrates these tools in a small-sample mixture-process DOE setting, and simulation experiments based on sparse quadratic response surfaces benchmark SVEMnet against repeated cross-validated elastic-net baselines.

Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain – even well-calibrated models provide no mechanism to identify which specific predictions are unreliable. We develop a geometric framework addressing both calibration and instance-level uncertainty quantification for neural network probability outputs. Treating probability vectors as points on the $(c-1)$-dimensional probability simplex equipped with the Fisher–Rao metric, we construct: (i) Additive Log-Ratio (ALR) calibration maps that reduce exactly to Platt scaling for binary problems while extending naturally to multi-class settings, and (ii) geometric reliability scores that translate calibrated probabilities into actionable uncertainty measures, enabling principled deferral of ambiguous predictions to human review. Theoretical contributions include: consistency of the calibration estimator at rate $O_p(n^{-1/2})$ via M-estimation theory (Theorem~1), and tight concentration bounds for reliability scores with explicit sub-Gaussian parameters enabling sample size calculations for validation set design (Theorem~2). We conjecture Neyman–Pearson optimality of our neutral zone construction based on connections to Bhattacharyya coefficients. Empirical validation on Adeno-Associated Virus classification demonstrates that the two-stage framework captures 72.5% of errors while deferring 34.5% of samples, reducing automated decision error rates from 16.8% to 6.9%. Notably, calibration alone yields marginal accuracy gains; the operational benefit arises primarily from the reliability scoring mechanism, which applies to any well-calibrated probability output. This work bridges information geometry and statistical learning, offering formal guarantees for uncertainty-aware classification in applications requiring rigorous validation.

Two-sample tests have been extensively employed in various scientific fields and machine learning to discriminate whether two sets of samples come from the same distribution or not. Kernel-based procedures for hypothetical testing have been proposed to efficiently disentangle high-dimensional complex structures in data to obtain accurate results in a model-free way by embedding the data into the reproducing kernel Hilbert space (RKHS). While the choice of kernels plays a crucial role for their performance, little is understood about how to choose kernel especially for small datasets. Here we construct a hypothetical test which can be effective even for small datasets, based on the theoretical foundation of kernel-based tests using maximum mean discrepancy, which is called MMD-FUSE. We enhance the MMD-FUSE framework by incorporating quantum kernels and propose a novel hybrid testing strategy that fuses classical and quantum kernels. This approach creates a powerful and adaptive test by combining the domain-specific inductive biases of classical kernels with the unique expressive power of quantum kernels. We evaluate our method on various synthetic and real-world clinical datasets, and our experiments reveal two key findings: 1) With appropriate hyperparameter tuning, MMD-FUSE with quantum kernels consistently improves test power over classical counterparts, especially for small and high-dimensional data. 2) The proposed hybrid framework demonstrates remarkable robustness, adapting to different data characteristics and achieving high test power across diverse scenarios. These results highlight the potential of quantum-inspired and hybrid kernel strategies to build more effective statistical tests, offering versatile tools for data analysis where sample sizes are limited.

Real-time water-level monitoring across many locations is vital for flood response, infrastructure management, and environmental forecasting. Yet many sensing methods rely on fixed instruments - acoustic, radar, camera, or pressure probes - that are costly to install and maintain and are vulnerable during extreme events. We propose a passive, low-cost water-level tracking scheme that uses only LTE downlink power metrics reported by commodity receivers. The method extracts per-antenna RSRP, RSSI, and RSRQ, applies a continuous wavelet transform (CWT) to the RSRP to isolate the semidiurnal tide component, and forms a summed-coefficient signature that simultaneously marks high/low tide (tide-turn times) and tracks the tide-rate (flow speed) over time. These wavelet features guide a lightweight neural network that learns water-level changes over time from a short training segment. Beyond a single serving base station, we also show a multi-base-station cooperative mode: independent CWTs are computed per carrier and fused by a robust median to produce one tide-band feature that improves stability and resilience to local disturbances. Experiments over a 420 m river path under line-of-sight conditions achieve root-mean-square and mean-absolute errors of 0.8 cm and 0.5 cm, respectively. Under a non-line-of-sight setting with vegetation and vessel traffic, the same model transfers successfully after brief fine-tuning, reaching 1.7 cm RMSE and 0.8 cm MAE. Unlike CSI-based methods, the approach needs no array calibration and runs on standard hardware, making wide deployment practical. When signals from multiple base stations are available, fusion further improves robustness.

Heterogeneous Treatment Effect (HTE) and Conditional Average Treatment Effect (CATE) models relax the assumption that treatment effects are the same for every user. We present a large scale industrial framework for estimating HTE using experimental data from hundreds of millions of Snapchat users. By combining results across many experiments, the framework uncovers latent user characteristics that were previously unmeasurable and produces stable treatment effect estimates at scale. We describe the core components that enabled this system, including experiment selection, base learner design, and incremental training. We also highlight two applications: user influenceability to ads and user sensitivity to ads. An online A/B test using influenceability scores for targeting showed an improvement on key business metrics that is more than six times larger than what is typically considered significant.