Papers

We propose a novel regularity-informed filtering framework for data assimilation in the context of hyperbolic conservation laws and other time-dependent partial differential equations. We focus on systems whose states exhibit steep gradients and jump discontinuities. While filtering is widely used to improve numerical simulations by incorporating observational data, traditional filtering methods lack awareness of the spatial regularity of states produced in these systems. As a result, data assimilation often produces unphysical state estimates, introducing spurious oscillations in smooth regions and smearing sharp features. To address this limitation, we introduce a filtering framework that incorporates edge-preserving regularization into the filter's analysis step; this framework balances simulation forecasts, observational data, and structural prior knowledge. We formalize this approach using the ensemble Kalman filter (EnKF) and a class of hierarchical generalized sparse Bayesian learning (GSBL) priors, which adaptively infer spatially varying hyperparameters to promote non-oscillatory behavior in smooth regions while preserving discontinuities. We demonstrate the effectiveness of the resulting GSBL-EnKF method on challenging benchmark problems governed by hyperbolic conservation laws. Our results show that enforcing regularity in the analysis step yields sharper, less oscillatory state estimates and lower errors of the ensemble mean. This sometimes comes at the cost of ensemble spread, which we quantify and discuss.

Synthetic tabular data are often judged by realism, privacy, or downstream-task scores. Those scores do not answer whether a proposed release is supported for a named use, population, and threat model. We introduce SynthGuard-ReleaseBench, an audit framework that locks the use, candidate panel, tolerances, and audit schedule before evaluation. It compares real-trained and synthetic-trained workflows on protected data, gives simultaneous finite-sample bounds for bounded loss gaps, requires controls, and keeps utility, empirical privacy risk, mechanism claims, and human release authority separate. Across four American Community Survey studies, five non-ACS records, two chronological diagnostics, and a sealed prototype, the benchmark retains favorable, unfavorable, and excluded outcomes. Transparent baselines pass some locked audits; compact learned models fail under the declared budgets; a health-table case is excluded because its negative control passes. A post-audit scaling arm, repeated across three generation seeds, shows the same locked criterion admitting those learned models once they are fit on enough data while still rejecting a dependence-destroying control at every size, so the criterion discriminates rather than merely rejects; the same repetition withdraws a finer single-seed ordering. The theory adds a pre-audit sample-size rule, variance-adaptive and anytime-valid certificates that tighten the bound two to ten times on the same locked evidence, a temporal certificate for time-ordered audits, and two lower bounds: ordinary bounded queries reconstruct a protected audit once the query budget reaches its size, and the panel-size correction is necessary rather than conservative. The contribution is a reproducible workflow for use-specific release evidence, not a claim that any generator is private, safe, or deployment-ready.

Modern generative models increasingly produce distribution-valued outputs, such as predicted cellular responses to genetic perturbations in single-cell genomics. While these models provide valuable auxiliary information, they are inherently imperfect, creating a need for statistical methods that leverage their predictions without relying on their correctness. We propose generation-powered inference (GPI), a general framework for improving inference on distribution-valued parameters using auxiliary generative models. Focusing on Wasserstein barycenters and related distributional functionals, we introduce a function-valued bridge representation that transforms inference in the nonlinear Wasserstein space into estimation of a mean function in a Hilbert space, enabling an augmented estimation framework analogous to prediction-powered inference. We develop a family of GPI estimators with optimal information borrowing, establish consistency, asymptotic normality, and simultaneous confidence bands, and derive valid inference for linear functionals and Wasserstein distances. Simulation studies demonstrate efficiency gains over labeled-data-only methods and robust performance under generative model misspecification. We illustrate the proposed framework using a Perturb-seq study of K562 cells, where synthetic perturbation responses generated by the State foundation model are used to improve inference for pathway-level consensus gene expression distributions associated with perturbations of the 40S ribosome module.

Network datasets in modern applications often involve multiple types of interactions occurring over a shared set of individuals. Characterizing the generating mechanisms of these interactions can be enhanced by joint modelling, as shared vertices allow layers to help explain the structure of other layers. We model multiplex observations using graph limits, called a scaled set of graphons, and develop a nonparametric joint estimator based on blockmodel approximations, termed the multi-network histogram. This nonparametric framework captures each layer's varying sparsity and connection structure, accounting for heterogeneity via shared latent variables across all layers. We establish the theoretical properties of the multi-network histogram, providing an upper bound for the weighted mean integrated squared error and deriving the optimal bandwidth that minimizes this error. By leveraging information across layers, this joint modelling achieves a reduction in error and a smaller optimal bandwidth, which enables high-resolution estimation even in sparser layers. Its usefulness is demonstrated through simulation studies and an application to socioeconomic networks in an Indian village.

This study investigates the methodological and theoretical properties of session handover in applications that use large language models. A task may continue in a new session when the context reaches the model's input limit, when the application restarts, or when another agent is asked to finish the task. The application must then decide which information from the earlier session to pass on. We formulate handover as the transfer of a task-relative in-context learning (ICL) state and distinguish exact recovery of earlier material from preservation of the target distribution. Under an exogeneity condition, predictive equivalence characterizes the coarsest deterministic sufficient handover and gives a fixed-length bit requirement. The analysis isolates the effects of the memory constraint, the writer, and the continuation procedure, and quantifies the cost of writing before the realized downstream query is known. We propose a three-part record that stores decisions and constraints exactly, uses task-justified statistics for repeated evidence, and retains original observations whose effect is not preserved by those statistics. Gaussian linear regression gives an exact finite-dimensional handover and finite-bit perturbation bounds, while nonparametric regression gives upper and lower bounds that relate memory to squared prediction error. These results provide a theory and method for deciding what a handover must retain and how its memory requirement depends on the continuation task.

We propose a measure of lottery complexity that combines probabilistic dispersion with dissimilarity between outcomes. Taking degenerate lotteries, which yield a single outcome with certainty, as the simplest alternatives, we measure complexity by proximity to this class. Specifically, for each degenerate lottery, we compute the expected distance between its certain outcome and the lottery's outcomes, and take the minimum across all degenerate lotteries. We provide an axiomatic characterization establishing uniqueness up to positive rescaling, study how complexity changes under outcome compression, and characterize maximally complex lotteries. Finally, we introduce Complexity-Adjusted Expected Utility preferences and characterize adherence to stochastic dominance and strong risk aversion.

The paper focuses on information theoretic converse bounds for the alignment of $m$ correlated graphs and for the detection of correlation among $m$ graphs. A simple idea for $m\geq 3$ is that if the alignment of $m-1$ of the graphs is revealed as extra information (by a genie for example) then it is still necessary to produce the alignment between the one remaining graph and the others, i.e. the last matching must be accomplished. For both Gaussian and Erdos-Renyi models, the last-matching problem is equivalent to one with two observed graphs, providing a path to extend converse bounds for $m=2$ to larger $m$. While the method is rather obvious for alignment, we show that the method can also be used to derive converse bounds for weak detection of correlation.

Reinforcement learning (RL) post-training provides a direct way to align diffusion models with human preferences and task-specific rewards. However, current RL algorithms for diffusion models remain fragmented: reverse-trajectory methods rely on discretized likelihood ratios, whereas forward-matching methods train on reward-labeled noising versions of the rollout samples. This paper shows that these seemingly different losses arise from a single path-space principle. Starting from the regularized diffusion-RL objective, we use importance sampling between sampling SDEs to obtain an explicit policy-gradient estimator on trajectory space. The estimator contains the stochastic Itô integral underlying Flow-GRPO-type updates; we derive an equivalent variance-reduced value-gradient form that recovers the forward-matching structure of AWM and DiffusionNFT. This identifies the empirical gap between these method families as a variance-reduction effect rather than a difference in RL principle. The derivation yields a unified design space organized by value-gradient estimation, weight functions, and sampling choices. Within this space, we propose a multi-sample KDE value-gradient estimator that reuses rollout groups, together with scale-bounded weight families that retain stable existing recipes while excluding singular ones. Experiments on SD3.5-M and Qwen-Image models validate the variance-reduction explanation and show that the resulting recipe improves over prior diffusion-RL baselines.

We study online statistical inference for functionals of the return distribution under a fixed policy. The return distribution is estimated by nonparametric distributional temporal-difference learning from a single Markov trajectory. For the Polyak–Ruppert averaged estimator, we prove that its root-$T$ error converges weakly to a centered Gaussian random element in Cramér space. We also prove that, conditionally on the observed trajectory, the root-$T$ difference between the bootstrap and original averages converges weakly to the same Gaussian limit. These results justify bootstrap inference for smooth statistical functionals, including variance, CVaR, expected shortfall, and expectiles. For nonsmooth statistical functionals, we develop a local asymptotic theory for the estimated return CDF over $T^{-1/2}$-neighborhoods of finitely many thresholds, together with its bootstrap analogue. This theory allows us to conduct inference for nonsmooth statistical functionals characterized by CDF equations, including return quantiles.

Whittle-Matérn (WM) Gaussian random fields (GRFs) are defined as solutions of stochastic partial differential equations (SPDEs) and provide a natural analog of Matérn GRFs on non-Euclidean geometry where the Matérn covariance function is not valid. In particular, WM GRFs on metric graphs have been an active area of research motivated by road and river networks where spatial dependence is more naturally described by intrinsic distances in the network than by Euclidean distances. This family of GRFs is controlled by three parameters relating to marginal variance, spatial range, and smoothness, but can be extended to so-called generalized WM GRFs through spatially varying coefficients in the SPDE. Recent work has considered the use of spatially varying covariates, but the full possibilities of flexibility have not been considered. In this work, we introduce latent GRFs that describe the spatially varying coefficients of the SPDE. This flexible model is compared to less flexible models in a simulation study evaluating both the ability to estimate the covariance structure and predictive ability. An important focus is the number of observations and replications necessary to reliably recover the covariance structure. We find that the flexible model improves over less flexible models in the presence of sufficient data. We also demonstrate practical applicability on traffic counts in a part of Madrid, and observe major differences between in-sample and out-of-sample predictive abilities of the models compared.

This paper studies two mechanistic explanations for human mortality by examining reliability theory and vitality modelling through a unified actuarial perspective. While the two approaches arise from different ageing mechanisms, we show that both can naturally generate the Gompertz law under suitable assumptions and can be extended to produce the Makeham law and late-life mortality plateaus. Using Canadian mortality data, we investigate the empirical behaviour of each approach and highlight the roles of heterogeneity, extrinsic risk, and stochastic randomness. Furthermore, we develop parallel definitions of biological age under both approaches and analyse how subjective survival beliefs emerge from misspecified parameters. Our comparison of these two approaches provides actuarial insights into the natural foundations of Gompertz mortality and the interpretation of ageing, frailty and death.

In offline RL, estimating the optimal action-value function $Q^*$ can be formulated as solving the optimal Bellman equation based solely on offline observations. A fundamental challenge is that the reward function and transition kernel are unknown, so the optimal Bellman operator is not directly observable from data. To address this issue, we propose a novel framework that decouples operator estimation from value function learning. In this approach, we first formulate conditional diffusion models to estimate the reward law and transition kernel, which induces a data-driven approximation of the optimal Bellman operator. We then plug these estimators into the Bellman equation and obtain a deep estimator of $Q^*$ by minimizing the empirical Bellman residual over a neural network function class. Theoretically, we first establish sharp nonasymptotic convergence rates for learning the optimal Bellman operator through an end-to-end analysis of conditional diffusion estimation in total variation distance. We then establish the oracle value-stage rate $\widetilde{\mathcal O}\bigl(n^{-\frac{2\beta}{d_x+d_a+2\beta}}\bigr)$ for the excess Bellman residual risk. Finally, under a concentrability condition, we translate this residual bound into an $L^2$ convergence rate of $\widetilde{\mathcal O}\bigl(n^{-\frac{\beta}{d_x+d_a+2\beta}}\bigr)$ for the resulting deep estimator of $Q^*$, where $d_x$ and $d_a$ denote the dimensions of the state and action spaces, respectively, and $\beta$ denotes the Hölder smoothness index of $Q^*$. Importantly, our theoretical analysis does not rely on completeness assumptions commonly used in deep RL theory. Extensive numerical experiments demonstrate the effectiveness of the proposed method and its strong empirical performance.

We present new inference tools for change point detection in high-dimensional time series. We discuss two distinct statistical applications: First, sequential change point testing in an incoming data-stream. Second, retrospective localization of multiple changes, with confidence intervals at a globally controlled error level. Test statistics are built on the maximum norm to generate power against sparse and asynchronous changes. Both problems are tackled by related multiscale statistics that search for changes in the data at many different levels of resolution. For fixed dimension, our statistical approaches can be validated using traditional Hölderian invariance principles. In this paper, we present the high-dimensional analogue: Hölder-Gauss-approximations, which can be (roughly) interpreted as the Gaussian approximation for a Hölder-norm of the high-dimensional partial sum process. Such approximations are of interest beyond change point detection and can be used for other problems such as for stationarity testing in high dimensions. We evaluate finite-sample performance in a simulation study and give an application to air contamination due to wildfires in California, which occurs asynchronously across a panel of measuring stations.

Ensuring food security across all regions of a country requires continuous monitoring, yet household surveys often leave significant spatio-temporal gaps due to resource constraints and operational priorities. In this paper, we propose a spatio-temporal additive Gaussian process model to estimate sub-national food security time series by regions. To address the computational cost of Gaussian process models, we exploit Kronecker structure of the spatio-temporal covariance matrix for scalable inference. We evaluate the proposed approach on food security survey data from Nigeria and Chad comparing it against other statistical and machine learning models and show how our proposal achieves better accuracy while retaining reliable uncertainty, especially when covariates are informative. We further apply the model to generate estimates for Nigerian states not covered by the survey, demonstrating its operational value for filling geographic gaps in food security monitoring.

Regional wet-bulb temperature means omit the spatial distribution of humid heat. We compare upper-quartile and middle-half days of the monthly regional mean at 121 sites in a specified eastern-China domain. A prespecified multiscale architecture combines Gaussian-weighted semivariances at five bandwidths with equal-month, equal-scale and equal-summer aggregation. The specification was developed on the 2015 and 2022 summers and applied unchanged to 33 other summers in 1991-2025. On high-mean days, the weighted mean squared pairwise WBT contrast was 7.28% lower. This corresponds to a 3.71% reduction after square-root transformation and a 3.97% mean reduction in record-level root-mean-square pairwise differences. Contraction strengthened as the Gaussian graph bandwidth increased, from 2.86% at h = 126 km to 13.27% at h = 2,013 km. Exact Laplacian decompositions localised the broad-scale contrast to daily anomalies opposing the monthly north-south climatological pattern, while anomaly energy changed little. The pattern persisted in 1950-1990. A sparse external station comparison showed concordant broad-scale direction. High regional humid heat was associated with a flatter broad geographic field, a feature that a regional mean cannot identify.

Occam's inversion is a robust algorithm to perform nonlinear geophysical inversion. It provides the smoothest model within observation noise, thereby discouraging geological overinterpretation. While Occam originally penalised l2 model roughness, l1 can be used to provide models that are visually sharp. However, l1 regularised geophysical inversion has diverged from the larger body of statistics and imaging literature. For example, l1 regularisation with a difference operator (i.e., total variation) in multiple dimensions has two distinct forms, only one of which is invariant to edge orientation – a distinction often overlooked in geophysics. In one dimension this reduces to the fused lasso problem in statistics. Within the Occam framework, for l2 data norm and l1 model regularisation, we show that lasso fusion through either synthesis or analysis leads to the same 1D problem. We extend the framework to multiple dimensions and to operators such as wavelet transforms in a dictionary, unravelling the mathematics behind three commonly used solvers for l1 regularised problems. These are coordinate descent, iteratively reweighted least squares (IRLS), and split Bregman. We use them to solve a sequence of problems that are linear (1D regression, 2D deblurring) and nonlinear (1D airborne transient electromagnetics) including a field data example. We recommend coordinate descent for 1D problems, and IRLS over split Bregman for 2D problems, with IRLS requiring up to an order of magnitude fewer least squares solves. We hope this work will further encourage geophysicists to adopt l1 regularised inversion, by presenting its various forms as a familiar Occam's inversion.

Tabular anomaly detection is dominated by classical density-proxy methods (Isolation Forest, OCSVM, LOF), reconstruction-based detectors (Autoencoders, VAEs), and modern non-parametric scorers (COPOD, ECOD, Deep SVDD), all of which approximate the inlier distribution only indirectly; explicit energy-based models are largely absent. Motivated by the recent revival of EBMs in deep learning (e.g., Energy-Based Transformers, JEPA), we revisit the classical Deep Boltzmann Machine (DBM) for this task and hypothesize that its mean-field energy combines more effectively with a reconstruction-based score than same-lineage pairs do. We evaluate a two-hidden-layer DBM on two tabular benchmarks spanning distinct domains (UCI Bank Marketing and NSL-KDD) against eight classical and modern baselines across twenty random seeds. The DBM mean-field energy matches the strongest baseline (the Autoencoder) on Bank Marketing and statistically beats it on NSL-KDD, while significantly outperforming the remaining seven on both datasets. When fused with the Autoencoder via rank fusion, the DBM energy yields a statistically significant improvement on both datasets (AUROC=+0.014, p<0.01 on Bank Marketing; +0.002, p<0.001 on NSL-KDD); every non-DBM-derived base model instead fails to improve or significantly degrades the AE-paired ensemble. Our position is that classical EBMs, exemplified by the DBM, deserve a place in the tabular anomaly detection toolbox as a non-redundant complementary view to the reconstruction-based scores that dominate current practice.

Spillover of volatility shocks across borders during turbulent periods makes accurate equity market volatility forecasts especially critical for risk management, derivatives pricing, and regulatory capital. In this paper, we examine whether volatility forecasts improve when models incorporate information on how markets are connected, and whether the choice of connection measure matters. Using daily data on 29 equity indices from every major region over 2015-2025, we let each market's forecast draw on the recent volatility of the markets linked to it, with the strength of each link set either by geography, return correlation, or the Diebold-Yilmaz (DY) spillover network estimated from the data. The spillover-informed forecasting model achieved an approximately 13% reduction in out-of-sample QLIKE loss relative to the standard Heterogeneous AutoRegressive benchmark ($p<0.001$) and attained the highest model confidence set $p$-value among the models considered. Several benchmark models that do not explicitly incorporate cross-market structure were excluded from the 90% model confidence set. The greatest improvements were observed during periods of elevated market stress: the COVID-19 crash, the Russian invasion of Ukraine, and the $2025$ US tariff shock, spillover-informed forecasts achieved approximately 21% lower QLIKE loss than an otherwise identical network-blind model ($p = 0.018$), with no significant performance loss during calm periods. The advantage is economically material: a volatility-targeting investor would pay $322$-$373$ basis points per year, net of transaction costs, for spillover-informed forecasts, versus an insignificant $85$-$102$ basis point for the alternatives. Finally, when the model is left to infer connections on its own, it recovers the DY network from the forecast objective alone (permutation $p=0.0005$).

Network data obtained through link-tracing designs, such as snowball sampling, are collected through a mechanism that depends on the very structure the analysis seeks to estimate. Ignoring this dependence and treating the observed sample as though it were itself a complete network can lead to substantially biased inference. While the resulting selection problem is intractable in general, we show that it admits an exact solution for $r$-wave snowball samples, with full-neighbourhood recruitment, drawn from an Erdős–Rényi population. We derive the exact likelihood of such a sample and show that it defines a curved exponential family in the edge probability $\pi$, with a low-dimensional sufficient statistic. Building on this result, we obtain the maximum likelihood estimator of $\pi$ that correctly accounts for the sampling design and, as a function of the minimal sufficient statistic, makes full use of the information in the sample. Simulation studies show that this correction substantially reduces bias relative to the naive estimator, remaining effectively unbiased even when the sample covers as little as 0.1% of the network. We further construct valid confidence intervals for $\pi$ by inverting a test built on the exact sampling distribution, approximated via Monte Carlo simulation. Simulation studies confirm that these confidence intervals attain the nominal coverage level within Monte Carlo error across a range of edge probabilities and numbers of waves.

Joint models provide a flexible framework for characterizing the association between longitudinal and time-to-event processes and have been widely applied in biomedical research. However, fitting joint models can be computationally challenging for large-scale and complex biomedical data. This paper introduces the \proglang{R} package \pkg{FastJM}, which provides computationally efficient frequentist estimation for three classes of semiparametric joint models: joint models with a single longitudinal biomarker, joint models with multiple longitudinal biomarkers, and joint models with a single longitudinal biomarker with heterogeneous within-subject (WS) variability. Within an expectation–maximization framework, \pkg{FastJM} employs customized linear-scan algorithms to efficiently update the nonparametric baseline hazards, thereby addressing a major computational bottleneck in semiparametric joint modeling. The package also supports commonly used time-dependent latent association structures by integrating these algorithms with a landmark multivariate joint modeling framework. \pkg{FastJM} provides a unified interface for model specification, estimation, inference, visualization, dynamic prediction, and prediction performance assessment, including cross-validated time-dependent accuracy measures and time-independent concordance statistics. We describe the underlying methodology and software implementation and demonstrate the main functionality of \pkg{FastJM} through reproducible examples.

When forecasting hourly returns for 1,000 US equities, we observe an unexpected phenomenon: predictions become nearly flat and show poor stock ranking, as measured by cross-sectional correlation. We call this forecast collapse. Surprisingly, the phenomenon largely disappears when forecasting trading volume under the same setting. We investigate forecast collapse across time-series foundation models (TSFMs), twelve deep-learning forecasting models, and 97 public benchmark configurations, and find that it is closely tied to target predictability. We identify two distinct reasons behind it: low predictability limits the amplitude of calibrated point forecasts, while per-series objectives leave cross-series structure unidentified. These findings reveal a calibration-ranking tradeoff: optimizing squared error leads to flat predictions, whereas directly optimizing cross-sectional correlation improves ranking but can inflate forecast amplitude by more than an order of magnitude. To address this tradeoff, we introduce CalibRank, a simple objective that balances calibration and ranking. On Finance1K, CalibRank nearly triples cross-sectional correlation while keeping amplitude close to the target, and improves correlation on all tested models. Our results reveal a blind spot in conventional time-series evaluation: per-series metrics can hide failures in cross-series structure needed by downstream decisions.

We propose a novel methodology for fitting decision trees to latent classes. The latent class analysis methodological literature has previously been focusing on logistic models of class membership given covariates, which has important drawbacks in the presence of complex interactions between covariates: logistic models are easily misspecified by omitting some interaction terms and complexity of interpretation increases rapidly with inclusion of higher-order interaction terms. Our proposed approach directly integrates decision tree modeling into the latent class analysis framework to model the covariate effects as an easily interpretable tree leading the eye through combinations of predictors to a final conditional classification. The novel methodology does not require any non-traditional assumptions for latent class models with covariates, is based on well-established routines of model estimation, and can be readily implemented in existing software. In the present paper, we focus on decision trees for binary covariates. We present the proposed approach, describe two tree pruning strategies, and provide a real-data illustration. Important extensions include generalizing the approach to multinomial and continuous covariates by developing more advanced within-predictor splitting procedures, and developing and evaluating alternative tree pruning strategies. The ultimate aim of this work is to initiate a novel research line in the latent class analysis methodological literature, and to facilitate the advancement of applied research via a novel data analytical tool.

Accurate small-area estimation of voter turnout for demographic subgroups is crucial for political analysis but methodologically challenging. Survey data suffer from over-reporting, non-representativeness, and non-ignorable non-response, while ecological inference (EI) from aggregate data is vulnerable to the ecological fallacy. We propose a Bayesian hierarchical framework that jointly integrates individual-level survey data, official aggregate turnout margins, and census cell counts. The framework comprises three models: a multilevel ecological inference (EI) model that extends MRP-style structure to aggregate data, a Poll-and-Margin (PM) model that jointly fits survey and margins in one coherent likelihood, and a Full Selection (FS) model that adds a Heckman-style selection correction under a random-contact assumption and uses informative priors for identification. In simulations with controlled selection mechanisms based on empirical census demographics, FS substantially improves over established benchmarks, particularly under strong selection bias or heavy censoring, but is sensitive to unmodeled selection noise. In an application to the 2023 Estonian parliamentary election, PM performs similarly to the current state of the art on available validation margins, with FS showing a modest improvement that depends on the informative priors.

Distributional mismatch between the data used to construct a statistical procedure and the population to which it is ultimately applied is pervasive in modern data analysis. We study covariate shift, a fundamental instance of this problem, and develop an adaptive importance-weighted model averaging method for prediction when labeled observations are available from a source distribution, whereas only unlabeled covariates are observed from the target distribution. Procedures fitted directly to the source sample generally optimize prediction risk under the source distribution and may therefore be suboptimal for target prediction. Importance weighting by the density ratio between the target and source covariate marginals provides a natural correction, but a small number of large density-ratio values can substantially inflate the variance of the resulting estimator in finite samples. We address this bias-variance trade-off by treating the degree of importance-weighting correction as a source of model uncertainty. Specifically, we construct a family of adaptive importance-weighted least-squares estimators by raising the estimated density ratio to a range of exponents, with the endpoints corresponding to ordinary least squares and standard importance-weighted least squares, and form a data-driven average over these candidates. Under model misspecification, the proposed model averaging estimator is shown to be asymptotically optimal relative to the infeasible best convex combination of the candidate estimators. Under correct specification, a diverging penalty is shown to make the selected weights concentrate near the ordinary least-squares endpoint. Simulations and a real-data application show that the proposed method achieves competitive target-prediction performance across the settings considered.

Adding data known to be correct ought to be safe. Not always. Larsen, Pabbaraju and Shetty model the failure with a monotone adversary, which reads an i.i.d. training sample and may append as many further examples as it likes, provided the target hypothesis labels them all. Mehrotra has since settled the cost, showing that for classes of VC dimension d >= 2 no learner can guarantee expected error better than Theta((d/n)log(en/d)), a logarithmic factor above the clean PAC rate. Because that rate is a worst case over all classes, it says nothing about which classes actually suffer the penalty, and the answer turns on the learner. We call a learner insertion-stable if feeding it more correctly labeled examples can only shrink the region where it errs. Such learners are immune to the adversary, since on any given sample the risk after insertions never exceeds the risk on the clean part alone, however much is added and however cleverly it is chosen. High- probability guarantees carry over unchanged, and because Closure is insertion-stable every intersection-closed class keeps its clean rate of E[Err] <= (21d+34)/n. Immunity is not something the classical dimensions can predict. Two classes can agree on VCdim = Ldim = 2 and still split, one at Theta(1/n) and the other at Theta(log(en)/n), while intervals have unbounded Littlestone dimension and are immune anyway. On Mehrotra's hard class we prove more than the failure of a single algorithm, showing that no monotone permutation-invariant compression scheme of any finite size attains the clean rate. The question is therefore not whether a class is hard, nor whether a learner is good, but whether the two suit each other. Given an insertion-stable learner that is optimal on clean data, correct additions are free, and without one the cost belongs to the class, so changing the learner will not avoid it.

Bayesian statistics rests on a few familiar distinctions: frequentist vs. Bayesian, objective versus subjective probability, a model versus the data it is fitted to, a prior versus a posterior. Here, I use Donald Davidson's "third dogma of empiricism" to critique such distinctions in terms of scheme/content dualisms. With a single running example – estimating how often a football (soccer) team scores – I argue that a degree of belief is in itself objective, that model and data are better seen as parts of one belief system than as different kinds of things, and that Bayes' theorem describes relations within that system rather than data updating a model from outside. What matters instead is how belief systems are built, checked and rebuilt. To this end, I use Davidson's constructive programme of radical interpretation to suggest that a belief system should be not only coherent (as statisticians already require) but also charitable and triangulated, answerable to other people and to a shared world. I argue that these three constraints are exactly what good statistical practice – from eliciting priors to checking models – already tries to satisfy and talking about them explicitly could improve this practice.

The Weibull distribution is one of the most flexible continuous probability distributions used to model various failure rates and skewed data in reliability engineering, industry, weather studies and cancer studies. It is a common scenario in statistical inference that several Weibull populations share the same shape parameter, which also implies that they have the same coefficient of variation. While the inferential study of the common shape parameter is often considered for complete samples, the presence of censored data requires a separate investigation that has not received enough attention in the existing literature. Therefore, the focus of this article is on a comparative study of interval estimators for the common shape parameter and the common coefficient of variation under progressive type-II censoring using frequentist methods based on large-sample theory, variance estimates recovery, generalized pivots, and Bayesian inference. An optimal censoring scheme is also proposed to enhance the robustness of interval estimation. Numerical data analyses using a simulation study and a real carbon fiber strength data example are carried out for comparison, and the results recommend the intervals based on Bayesian and variance estimates recovery methods for their satisfactory performance.

As large language model inference shifts toward lower precision, post-training quantization (PTQ) becomes increasingly brittle, making quantization-aware training (QAT) essential for preserving model quality. However, QAT has a structural mismatch: gradient updates are applied to latent full-precision weights, while the loss and gradients are computed on lossy reconstructions of those weights. This mismatch can lead to suboptimal training trajectories and a higher loss floor. Second-order PTQ methods address a similar problem by minimizing loss-aware reconstruction error, but applying such expensive reconstruction repeatedly during QAT as the weights evolve is impractical. We introduce QUASAR, a QAT method that brings lightweight, loss-aware reconstruction into the training loop. At each training step, QUASAR reconstructs the latent weights by searching over a small set of clipping ranges and fitting dequantization parameters through saliency-weighted least squares. We use an exponential moving average of squared gradients as the per-parameter saliency signal. Our theoretical analysis shows that optimizing QUASAR's reconstruction objective tightens both the convergence and final-loss bounds of QAT. We evaluate QUASAR across four model families and across INT4, INT3, INT2, and NVFP4 quantization formats. QUASAR consistently achieves lower training and evaluation loss than competitive QAT methods and outperforms QAT and PTQ baselines on downstream benchmarks. At INT2, QUASAR improves average accuracy over the best QAT baseline by 13.3 points with quantization-aware distillation and by 10.9 points with QAT on mathematical reasoning data. Notably, after distillation on only about 600M tokens, QUASAR's INT4 Gemma-4 E4B checkpoint outperforms the corresponding QAT checkpoint released by Google, with 66% lower KL divergence and 1.8 points higher average accuracy.

Finding the optimal individualized treatment rule that maps individual characteristics or contextual information to treatment assignments has been extensively investigated in existing literature, with widespread practical applications. This paper considers the estimation of optimal treatment regimes within a semi-supervised data framework (exemplified by electronic medical record data). In such settings, only a tiny proportion of observations have observed outcome labels, owing to high labeling costs, time limitations, data privacy concerns, and other constraints, while covariates and treatment assignments are available for all study subjects. We develop a semi-parametric inference method for optimal treatment regimes, which leverages outcome- unlabeled samples with complete covariate and treatment information to enhance estimation efficiency. The proposed estimation framework consists of two key steps: first, flexible nonparametric imputation via single-index kernel smoothing; second, subsequent estimation of the optimal treatment regime based on concordance-assisted learning. We establish the consistency and asymptotic normality of our proposed estimators. Numerical simulation studies demonstrate that our method achieves higher efficiency and stronger robustness relative to fully supervised estimators under finite-sample settings. We further validate the practical value of our proposed framework using the MIMIC-III and ACTG175 datasets.

Smart manufacturing processes are often installed with a large number of sensors, imaging devices and computers, which not only enable instant communication across various modules of a production system but also aid in intelligent manufacturing management. In this paper, we introduce MODERN, a deep learning framework for quality monitoring and fault isolation, which integrates these enhanced capabilities into the practice of industrial quality control. Using the architecture of an inception residual neural network, we develop a control chart that monitors the likelihood of a product containing defects. We also propose a faulty region estimator that identifies the defective area using transfer learning. To extend our framework to cases where there are not sufficient training data, we suggest a transfer monitoring technique that requires only a small sample size and a hypothesis testing approach for quantitatively assessing the applicability of our method. Theoretically, we establish the minimax optimal convergence rate for both our defect likelihood estimation and fault diagnosis. Our results lead to a seemingly counter-intuitive managerial implication - it may not always be in a manufacturer's best interests to keep upgrading its monitoring equipment regardless of the cost. Empirically, we demonstrate the superior performance of our method in comparison with a state-of-the-art approach using both simulated experiments and real data.