AI 速览：提出一种差分隐私两阶段协变量平衡加权估计器，在保护隐私的同时从观察数据中推断因果效应，并提供统计保证。
Differential privacy is the leading mathematical framework for privacy protection, providing a probabilistic guarantee that safeguards individuals' private information when publishing statistics from a dataset. This guarantee is achieved by applying a randomized algorithm to the original data, which introduces unique challenges in data analysis by distorting inherent patterns. In particular, causal inference using observational data while preserving privacy is challenging because it requires a good covariate balance between treatment groups, but checking the covariate balance is challenging when privacy is a primary concern because releasing any statistic (e.g., t-statistic) for the balance check compromises privacy. Additionally, the performance of the privatized estimator critically depends on the choice of differential privacy mechanisms, and it remains unexplored how privacy-protecting causal inference could be conducted with observational data. In this article, we present a differentially private two-stage covariate balancing weighting estimator to infer causal effects from observational data. Our algorithm produces both point and interval estimators with statistical guarantees, such as covariate balance, rate optimality, and oracle budget allocation, under a given privacy budget.
Albert Gong, Annabelle Michael Carrell, Raaz Dwivedi, Lester Mackey
AI 速览：提出 Express 工具，将非因果注意力近似转化为因果近似，并结合 Thinformer 实现更优的因果注意力保证与高效实现。
We introduce a new tool, Express, for converting a non-causal attention approximation into a causal approximation with matching approximation guarantees. When combined with the state-of-the-art Thinformer approximation, Express improves upon the best known causal attention guarantees, delivering $\log^{3/2}(n)/s$ approximation error with only $O(s)$ memory and $O(s^2 \log^2(n))$ compression overhead for a sequence of length $n$. We pair these developments with an efficient I/O-aware Triton implementation, demonstrate substantial speedups over FlashAttention 2, and use Express to overcome four resource bottlenecks in the language modeling pipeline: long-context prefill, KV cache compression, long-form memory-constrained decoding, and long-form compute-constrained decoding.
Agentic Distributional Regression: Conditional Density Estimation through Agent-Written Programs
Lorenzo Tedesco, Francesco Finazzi
AI 速览：提出让大语言模型智能体根据样本自动选择条件分布模型并输出拟合程序，从而估计条件密度的方法（ADR）。
Artificial intelligence offers statisticians a new paradigm for modelling and analysing complex datasets. Agents based on large language models can reason about data and automate key stages of the statistical modelling workflow, from model fitting to validation. In this paper we propose a method that uses such an agent to estimate the conditional density of a response given a vector of covariates from an iid sample. The agent examines the sample, chooses a model for the conditional distribution of the response and the procedure to fit it, and returns the estimator as a short computer program. The program is built from a library of probability distributions. The returned law can therefore be a parametric distribution, a mixture or a multivariate factorization, with distribution parameters given by explicit formulas in the covariates. We call this approach agentic distributional regression (ADR). Unlike in the classical approach, the statistician no longer chooses the estimator, but asks an agent to build one. Treating the returned program as a random conditional density estimator, we derive a finite-sample error bound under assumptions on the number of admissible models and on the accuracy of the agent's fit, and an oracle inequality for the selection of a model among fitted candidates using independent validation data. Finally, assuming that, as the sample size grows, the agent selects the same smooth parametric model with probability tending to one and fits it accurately, we show that the estimated parameters are asymptotically normal. In simulation studies, on twelve real datasets and on a new dataset whose responses postdate the agents' training data, ADR with Claude Opus 5.5 has the best average performance among the existing methods from the statistical literature with which it is compared.
Optimal Neural Estimation for High-Dimensional Nonparametric Regression under Multisource Covariate Shift
Chenghao Xu, Haotian Xu, Shivam Kumar, Daren Wang
AI 速览：研究多源协变量偏移下高维非参数回归，提出oracle加权神经估计并给出minimax最优收敛率，同时给出无需已知噪声方差与偏移参数的自适应方法。
We study high-dimensional nonparametric regression under multisource covariate shift, where $\mathrm J$ sources of training data share a common regression function but differ in their covariate distributions, sample sizes, and noise variances. Our goal is to combine these sources to estimate the regression function accurately under a target covariate distribution. We propose an oracle weighted neural estimator and establish its minimax optimality up to logarithmic factors through matching upper and lower bounds. The resulting rate is $\mathsf n_{\rm eff}^{-2p/(2p+K)}$, where $p$ and $K$ denote the effective smoothness and dimension of the regression function, and the effective sample size is \begin{align} \mathsf n_{\rm eff} =\sum_{j=1}^{\mathrm J} \frac{n_j}{(1+σ_{ρ,j})σ_{ε,j}^{2}}. \nonumber \end{align} Here, $n_j$ is the sample size of source $j$, $σ_{ε,j}^{2}$ is its noise variance, and $σ_{ρ,j}$ controls the deviation between the covariate distribution of source $j$ and the target covariate distribution. We also develop an adaptive procedure that requires no knowledge of source noise variances or covariate-shift parameters. Under suitable conditions, this procedure attains the oracle minimax rate up to logarithmic factors.
Statistical Inference for Matching Decisions via Matrix Completion under Dependent Missingness
Congyuan Duan, Wanteng Ma, Dong Xia, Kan Xu
AI 速览：针对匹配容量导致的观测条目依赖性问题，提出基于 Grassmannian 梯度下降的非凸矩阵补全方法，并构建去偏与投影框架，用于匹配决策的统计推断。
This paper studies decision-making and statistical inference for two-sided matching markets via matrix completion. In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise from past matching data, are constrained by matching capacity. This matching-induced dependence poses new challenges for both estimation and inference in the matrix completion framework. We propose a non-convex algorithm based on Grassmannian gradient descent and establish near-optimal entrywise convergence rates for three canonical mechanisms, i.e., one-to-one matching, one-to-many matching with one-sided random arrival, and two-sided random arrival. To facilitate valid uncertainty quantification and hypothesis testing on matching decisions, we further develop a general debiasing and projection framework for arbitrary linear forms of the reward matrix, deriving asymptotic normality with finite-sample guarantees under matching-induced dependent sampling. Our empirical experiments demonstrate that the proposed approach provides accurate estimation, valid confidence intervals, and efficient evaluation of matching policies.
Hongqi Chen, Chengwang Liao, Ziwei Mei, Zhentao Shi
LASSO is one of the most popular regularization methods for high-dimensional regression models. While cointegration is common in practical applications of predictive regressions with many regressors, the convex penalty of LASSO overly suppresses the coefficients of cointegrated regressors and therefore fails to deliver consistent parameter estimation. We employ folded concave penalties (FCP), including the well-known SCAD and MCP, to address this issue. Using FCP, we establish two asymptotic results: (i) a local oracle property for the penalized regression, and (ii) a global oracle property for regressions with a penalty-level constraint. In particular, the latter guarantees a global solution that consistently estimates the true coefficients and enjoys oracle prediction performance. Simulation studies and an application to predicting the euro area unemployment rate show that FCP improves variable selection and out-of-sample prediction relative to LASSO.
Artificial intelligence (AI) models can accelerate cell-type annotation in digital pathology, but safely scaling their use requires determining, with error control, which model-generated labels can be accepted without expert review. This is challenging in evolving workflows because cell morphology and type composition may change across tissue regions and slides, making one-time calibration unreliable. We propose Conformal Annotation with Randomized Expert review under Distribution shift (CARED), a distribution-free framework that leverages randomized expert audit to achieve long-run error control for AI-assisted annotation under distribution shift. For each incoming batch, CARED uniformly selects a subset of cases for expert review and uses the acquired labels to calibrate later decisions. Among unreviewed cases, CARED determines a subset of them to safely skip expert labeling, while suggesting candidate labels for the others for downstream resolution. We prove that this workflow provides long-run control of cumulative error over both the full stream and the cells outside of the audit sample, without stationarity or exchangeability assumptions. We further enhance the framework by introducing class-conditional guarantees to ensure error control within important but rare cell types, together with a utility module to target more automatic resolutions, smaller candidate sets, and greater biological coherence, without compromising validity. Experiments on pancreas, lung, and ovary annotation streams, together with a stream constructed from real expert annotations, show that CARED controls the cumulative errors while a substantial fraction of cells (up to 70%) bypass expert review.
We consider the problem of dynamically selecting among competing strategies using observable predictors. To mitigate estimation noise and excessive switching, we regularise the estimated policy with a switching cost, which may exceed actual transaction costs when these are too small to provide sufficient regularisation. Since switching costs make current choices affect future decisions, we formulate the problem using dynamic programming. The optimal policy is estimated using a reinforcement learning algorithm based on iterated regressions, making the procedure simple to implement. We apply the method to monthly rotation among momentum, value, profitability, and defensive U.S. equity factors over a sample of about 60 years. Using a parsimonious set of state variables, the estimated policy outperforms both the myopic dynamic policy and the best fixed factor in hindsight in out-of-sample evaluation. Under weak conditions, we show theoretically that the decision rule estimated from empirical data is asymptotically consistent for the unknown optimal decision rule. Simulation results illustrate the finite-sample relevance of these asymptotic results.
Raphael Kim, Michele Santacatterina, Ramin Zabih, Keith Barnatchez
Reinforcement learning (RL) is increasingly used to train robust, adaptable systems across healthcare, e-commerce, and robotics. In these settings, legal, ethical, or logistical concerns may preclude certain key variables that drive decisions from being collected during deployment time. This gives rise to a setting known as runtime confounding: the logged data hold full observability, but deployment time lacks knowledge of certain variables, known as runtime confounders. Unlike single timepoint and non-adaptive settings, runtime confounding under reinforcement learning has the potential to propagate over time, as earlier decisions affect future states, observations, and action assignments, leading to biased learning. We address these problems with three contributions: we (1) develop policy learning algorithms under runtime-confounding, (2) develop semi-parametric efficient off-policy estimation procedures, and (3) provide diagnostics for understanding the price of runtime confounding.
Video-based gait assessment often keeps only high-confidence pose observations, which can lower measurement error but change the movement assessed. We compared confidence selection with budget-matched random selection in a Parkinson-related cohort (n = 96) and an NF2-related replication cohort (n = 18). In the Parkinson-related cohort, confidence selection produced a small but consistent shift in the observed movement summary (+0.05 SD, 95% CI 0.03 to 0.07), while held-out Mini-BESTest error stayed flat (-0.04 points, -0.13 to 0.05); a policy preserving motion-group proportions reduced the shift, while NF2 showed no shift and its predictor did not beat a constant baseline. Because this shift mixes measurement error with selection shift, we decompose and simulate both on the cohort's window structure. Filtering lowers local error when error depends on confidence, but biases the endpoint once confidence tracks movement more than error. In the Parkinson-related data, confidence was only weakly tied to movement (rho = 0.14). There, filtering is harmless if well-tracked windows are unbiased. If instead systematic error only redistributes within participants, filtering can add up to 0.58 degrees. Unchanged clinical error from such small-cohort predictors therefore cannot show that quality filtering preserves the assessed movement.
We show that established performance metrics in binary classification, such as Matthews' correlation coefficient (MCC), Cohen's $κ$, the F-score or the Jaccard similarity coefficient are not robust to class imbalance in the sense that if the proportion of the minority class tends to $0$, the true positive rate (TPR) of the Bayes classifier under these metrics {becomes very small or even tends to $0$}. Thus, in imbalanced classification problems, these metrics favour classifiers which ignore the minority class. To alleviate this issue we introduce robustified modifications of the MCC, of Cohen's $κ$ and of the F-score with an additional tuning parameter which allows to adapt the amount of robustness against class imbalance. As theoretical guarantee we show that the Bayes-optimal classifier for these robustified performance metrics, when expressed in terms of the density ratio $f_1/f_0$ of the class-conditional densities $f_i$, has a threshold parameter which is upper-bounded in terms of the tuning parameters. Therefore, even in strongly imbalanced settings, the TPR associated to this classifier will be bounded away from $0${, provided that $f_1/f_0$ exceeds this bound with positive probability under the positive class}. We numerically illustrate the behaviour of the various performance metrics and the effect of the tuning parameters in simulations as well as on a credit default data set. We also discuss connections to the receiver operating characteristic and precision-recall curves, which provide an alternative perspective on the proposed notion of robustness, and give recommendations on how to combine their usage with performance metrics.
Nan Lu, Ethan Lee, Ruicheng Ao, James M. Robins, David Simchi-Levi, Junwei Lu
We study offline inference for the optimal value in reinforcement learning under finite state and action spaces. Two new nuisances are derived as fixed points of a self-induced Bellman equation, in which we approximate the maximum Bellman operator by its softmax correspondence. We propose a debiased estimator through the Neyman orthogonality and establish its asymptotic normality under diverging horizons even when the behavior policy changes with time, as long as the nuisances have the statistical rates that can be achieved by many machine learning methods. We provide a concrete estimating procedure for these nuisances and show they can lead to valid inference. Synthetic experiments validate the numerical performance of our inference method, and we implement it in real-life decision-making problems, including bike repositioning and AI agentic tool use.
Parameter estimation and classification in binary logistic regression deteriorate severely when the number of minority class observations ($n_1$) is smaller than the feature dimension ($p$). Under such rank-deficient rarity ($n_1 < p$), maximum likelihood estimators suffer from quasi-complete separation, penalized likelihood methods exhibit severe intercept bias, and convex minority oversampling techniques such as SMOTE collapse into an $(n_1 - 1)$-dimensional affine subspace. In this paper, we propose a novel \textit{Self-Calibrated Zero-Complement} estimator that shifts the paradigm from minority interpolation to majority fringe extrapolation. Grounded in Stein's Lemma, we prove that the conditional expectation shift of the abundant majority class ($Y=0$) induced by logistic truncation uniquely identifies the true hyperplane normal $\boldsymbolβ$ after Mahalanobis whitening. We further establish that extrapolating synthetic minority instances outward from the high-quantile density fringe of the majority distribution along the conjugate direction preserves full-rank covariance regularity ($\mathrm{rank} = p$). To accommodate both semi-supervised environments (with an unlabeled background mean) and strictly supervised subsamples, we introduce a hybrid estimator incorporating the intrinsic third-moment skewness of the majority class alongside a location-shift-invariant zero-boundary intercept calibration. Extensive Monte Carlo simulations and real-world benchmark applications (Wisconsin Diagnostic Breast Cancer and Banknote Authentication) under extreme rarity ($n_1 \in \{3, 5\}$) demonstrate that our approach prevents parameter divergence, recovers the oracle hyperplane with high fidelity, and substantially outperforms Firth's regression and SMOTE in F1-score and estimation stability.
This paper introduces iWAR, a system for estimating wins above replacement from historical Retrosheet play-by-play records. We compare its runs-allowed (RA) and fielding-independent pitching (FIP) versions with Baseball-Reference WAR (bWAR), FanGraphs WAR (fWAR) and run-based alternatives. The common historical sample contains 1,471 team-seasons across 79 years and 1,441 consecutive franchise pairs. Under the fixed conversion to wins, same-season mean absolute error was 3.695 credited wins per 162 games for iWAR RA, compared with 4.724 for bWAR and 4.744 for fWAR: reductions of 21.793% and 22.112%. The paired differences were -1.030 and -1.049, with conditional 95% calendar-block intervals of [-1.367, -0.706] and [-1.398, -0.725]. Calibration preserved most of these advantages. A broader bWAR comparison across 118 years retained a smaller advantage; modern differences were smaller or sometimes reversed. PythagenPat reconstructed records more closely than every WAR total. Next-season replay gave nearly identical fixed-map errors for iWAR FIP and fWAR, while calibration changed their ordering. An amended chronological learned-model analysis of 1,552 franchise pairs gave neural RMSE 10.163, versus 9.946 for the development-selected ridge comparator (difference +0.217; conditional interval [0.015, 0.474]). This work provides a new, specialized framework for analyzing WAR across eras and provides context for future work using learning models.
Carole Lunny, Ian Goodman, Stefano Berrone, Connor TA Brenna, Emma K Reid, Ivan Perez-Neri, Shailesh Kolekar, Nityanand Jain 等 15 位作者
LLM read-and-evaluate tasks include study screening, data extraction, risk-of-bias assessment, and critical appraisal in the evidence synthesis field. These task differ in the amount of LLM interpretation they require. Some tasks involve retrieving relatively simple information, such as an author name, sample size, or publication year. Others require the LLM to read source material, interpret it against predefined criteria, and make a judgement. Researchers should assess whether LLM judgements are accurate, supported by appropriate source evidence, and reproducible under specified conditions. A correct judgement does not necessarily indicate that the underlying evaluation process is reliable. We developed a taxonomy for identifying mechanisms that may compromise these properties and for informing the selection and reporting of appropriate evaluation methods. The taxonomy outlines potential ways that LLM judgments from read-and-evaluate tasks can fail, called TRAILS (Taxonomy of Reliability And Instability in LLM-assisted evidence Synthesis). The TRAILS taxonomy addresses two complementary questions. First, what mechanisms can cause the same read-and-evaluate task to produce different judgements across repeated LLM runs? Second, what mechanisms can systematically affect the judgement or required output in a way that is not apparent from the judgement itself? This study presents 38 mechanisms and identifies the deployment settings in which each can operate, approaches for testing them, and mitigation strategies. We also show why repeatability or accuracy does not rule out a hidden judgement failure and why human evaluation should assess whether a judgement is grounded in the supplied evidence, independent of inappropriate external influence, and produced through a process that can be examined and verified.
Tabular foundation models are pretrained networks that predict risk from a table without fitting a model. Whether their risks are correct (calibrated) has been judged on real data, where true risk is unknown. In a pre-registered simulation with known true risks, we compared TabPFN-3.5, TabICLv2 and Mitra-v2 with Firth logistic regression with intercept correction (FLIC) in 58 scenarios and 1,000 random designs, then on four clinical data sets. Foundation models were not a shortcut to calibration. Their calibration slope matched FLIC's within the pre-registered margin in 36 or 37 of 48 core scenarios and was better only at n = 200 with a 3% event rate. Even 3,000 patients were often not enough: with FLIC, TabPFN-3.5 or Mitra-v2, 63%-83% of samples gave risks close to the truth in average, intercept and slope at event rates of 10% and 30%, and 35%-50% at 3%. TabICLv2 did worse (8%-39% and 1%-3%). Across the random designs, foundation models had a lower true calibration error than FLIC beyond the margin in 25%-38% and a higher one in none, though small losses were predicted at n = 3000. On real data, no model resisted a change in event rate between populations; recalibration on 500 local patients largely repaired it.
Principal-agent hypothesis testing studies statistical contracts in which a principal rewards an agent according to data the agent generates. Existing work focuses on the single-shot setting, where the agent produces a single dataset. We extend the framework to sequential settings, where evidence accumulates over time, rewards may be deferred to the end or disbursed incrementally, and the agent may stop the contract at a strategically chosen stopping time. We call a contract null-deterring if no ''null agent'' (those whose data-generating distribution lies in the null hypothesis) can profit in expectation under any stopping rule, and our main conceptual result shows that such contracts are characterized by e-processes. We then turn to the agent's best response and identify the optimal stopping rule through the Snell envelope of the reward process. We develop simpler, more interpretable approximations that often require the agent to have only partial knowledge of its distribution.
Zachary T. Rewolinski, Jan Simson, Frauke Kreuter, Christoph Kern, Bin Yu
Human judgment calls made throughout the data science life cycle can change the conclusions drawn from data. Independent analysts often make different choices when given the same data, leading to often unacceptable variations in results and contributing to the ongoing reproducibility crisis across scientific disciplines. The rapid adoption of agentic tools threatens to amplify this crisis. Several approaches have been developed to address this variation by following the same strategy: repeating an analysis under different combinations of analytical decisions and inspecting the distribution of outcomes. Examples include multiverse analysis, specification curve analysis, and vibration of effects. More broadly, the Predictability-Computability-Stability (PCS) framework assesses how documented judgment calls across the data science life cycle affect conclusions, with predictability serving as a reality-check that a model captures signal. Each of these approaches results in a "multiverse" object. While the distribution of outcomes reflects the overall variability of conclusions, estimating the influence of each individual decision requires additional tools. A common heuristic is to train a model to predict the outcome from these decisions and treat its coefficients or feature importances as proxies for each decision's influence. Although this strategy may work in certain cases, it assumes the model is correctly specified and accurately predicts the outcome, which we show is not always the case. In this work, we introduce DECIDE, a model-free framework that quantifies each decision's importance from the actual outcomes across the plausible decision space, avoiding issues of predictability by design. We demonstrate the effectiveness of DECIDE by applying it to real-world multiverse analyses. We further provide what is, to our knowledge, the first formal definition of the multiverse.
Particle Gibbs samplers with backward sampling are widely used for sampling the smoothing distribution of state-space models, but, with few particles, the new trajectory often coincides with the current one at many time steps. A known but rarely used remedy replaces the random selection of the final particle by a Metropolis--Hastings move which avoids the current particle. We show that, with backward sampling, this remedy only helps at the last time steps, because its effect on the update rates decays geometrically with the distance to the final time. We propose instead Metropolized backward sampling, which makes such a move at every step of the backward pass, forcibly switching trajectories whenever possible. Additionally, we introduce a coupled version which prevents proposing the current trajectory, maximizing the chances of an actual switch versus the current trajectory and performing perfect sampling when the state-space model has no observations, a feature not shared by backward sampling. We prove that, at every time step, both methods dominate backward sampling as they update the state more often and have smaller lag-one autocorrelations than it does. Our methods are drop-in replacements for backward sampling, and can be used to improve any particle Gibbs sampler.
Graphical models are widely used to represent conditional independence structures, but learning them is challenging when data are fragmented across sources that measure different subsets of variables and may not be directly shareable. We develop a general framework for reconstructing a shared global graph from heterogeneous, partially observed sources. Our framework permits both the observed variable sets and source-specific distributions to differ. Under a source-wise faithfulness condition, local conditional independence graphs correspond to latent projections of the shared global graph, which is identifiable up to the equivalence class induced by the observed variable sets. The framework integrates raw data, estimated source graphs, or a combination of both, accommodating settings with restricted access to individual-level data, such as privacy constraints. We develop mixed-integer optimization formulations and scalable approximate algorithms for several classes of graphical models. Unlike standard high-dimensional analyses, our guarantees are governed by new combinatorial notions of signal strength that capture how information propagates across partially observed sources. Extensive simulations further show that integration can substantially improve estimation of source-specific projected graphs relative to separate source methods. Real-data application illustrates the framework's use with partially-observed sources of fatty acid measurements.
Conformal Prediction (CP) provides robust uncertainty guarantees for predictive models, but is typically applied post hoc, which misaligns model training with the conformal goal of producing efficient (i.e., narrow) intervals. We propose SPACR (Single-Pass Adaptive Conformal Regressor), a novel method for directly training uncertainty-aware regressors within a differentiable loss. SPACR jointly optimizes accuracy, efficiency, and validity without batch-splitting or a predefined confidence level during training. As a result, a single SPACR model yields valid prediction intervals at multiple confidence levels during inference, avoiding the costly retraining required by methods like Directly Optimized Inductive Conformal Regression (DOICR). Experiments on diverse tabular and image datasets show that SPACR consistently gives tighter intervals and better coverage-efficiency trade-offs compared to standard CP and DOICR, while significantly reducing computational costs relative to retraining-dependent baselines.
Offline reinforcement learning and off-policy evaluation evaluate dynamic decision rules based on historical data, without the ability to deploy online. In recent artificial intelligence (AI) applications, simple state and reward information is recorded as complex text or image, expert annotation may be available but at a higher cost. Recent AI and machine learning (ML) predictors can label data cheaply but with unknown bias. We show how a limited budget for ground-truth data-annotation can safely make use of plentiful ML predictions in a new estimator for doubly-robust off-policy evaluation with missing rewards. Our method directs where data should be collected by optimizing annotation probabilities for the best downstream estimation variance, which we implement in a feasible batch-adaptive approach. Our work is motivated by a collaboration with a homelessness services nonprofit that writes casenotes for individuals over time. Our method can be used to unlock trustworthy inference from casenote data and answer new inferential questions such as: how does expanding outreach effort over time affect progress towards a housing application and improvement in housing placement? In simulations and on two real datasets -- casenotes from the nonprofit and human-preference votes from LMArena -- we see reductions in RMSE of 37-65% for housing placement and 21-67% for progress towards a housing application at budgets of 50% of full annotation and above, and by 55-62% at every budget on LMArena under an equal-exposure policy.
In this paper, we introduce a model-based boosting approach for fitting structured additive distributional copula regression models for bivariate responses, with particular emphasis on jointly modeling insurance claim frequency and severity. The approach uses regression-type base learners, such as linear terms and splines with low degrees of freedom. It builds on generalized additive models for location, scale, and shape (GAMLSS), which extend generalized additive models (GAMs) by allowing multiple distributional parameters, rather than only the conditional mean, to depend on covariates. The structured additive predictors make the model inherently interpretable, offering greater transparency and auditability than black-box approaches. These features are particularly relevant in regulated actuarial settings and applications requiring explainable artificial intelligence. By estimating the entire conditional joint distribution, the framework also enables insurance practitioners to examine conditional quantiles, tail behavior, and prediction intervals of risks. The copula component captures dependence between claim frequency and severity and allows practitioners to investigate how this dependence varies with policyholder characteristics, potentially improving predictive performance. Moreover, by incorporating modern machine-learning techniques, specifically boosting, the proposed model improves prediction accuracy while retaining interpretability. We assess the proposed framework using both simulated and real data. The results demonstrate its ability to recover the true covariate effects on the marginal distributional parameters and the dependence structure, select informative variables, and achieve predictive performance competitive with standard benchmark models. We also illustrate how to interpret the fitted model.
Ritwik Vashistha, Jeff M. Phillips, Abhra Sarkar, Arya Farahi
Ignoring measurement noise degrades statistical inference. Existing correction techniques are often computationally costly and inefficient. Kernel methods based on maximum mean discrepancy have enabled efficient, likelihood-free inference, but they typically assume clean data. We introduce a framework for inference with samples corrupted by potentially heteroscedastic noise from a known distribution. Central to our method is the convolutional maximum mean discrepancy, which compares distributions after noise convolution and retains metric validity under standard kernel conditions. We establish finite-sample deviation bounds that are unaffected by measurement error and an equivalence between testing under noise and kernel smoothing. Based on this discrepancy, we propose an estimator, establish its consistency and asymptotic normality, and provide an efficient implementation using stochastic gradient descent. We demonstrate the practical effectiveness of our method through simulations and applications in astronomy, anthropometry, and the social sciences. Our method provides a unified, likelihood-free, simulation-based framework for efficient and robust inference for broad classes of problems in noisy data.
Zhenyu Wang, Molei Liu, Jing Lei, Francis Bach, Zijian Guo
When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery of transferable structures and help mitigate systematic biases such as batch effects. We introduce Stable Principal Component Analysis (StablePCA), a distributionally robust framework for constructing stable latent representations by maximizing the worst-case explained variance over multiple sources. A primary challenge in extending classical PCA to the multi-source setting lies in the nonconvex rank constraint, which renders the StablePCA formulation a nonconvex optimization problem. To overcome this challenge, we conduct a convex relaxation of StablePCA and develop an efficient Mirror-Prox algorithm to solve the relaxed problem, with global convergence guarantees. Since the relaxed problem generally differs from the original formulation, we further introduce a data-dependent certificate to assess how well the algorithm solves the original nonconvex problem and establish the condition under which the relaxation is tight. Finally, we explore alternative distributionally robust formulations of multi-source PCA based on different loss functions.
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.
Lasai Barreñada, Andrew Vickers, Laure Wynants, Bieke Tack, Dirk Timmerman, Ewout Steyerberg, Ben Van Calster
Objective: Variable selection for clinical prediction models is commonly done on statistical grounds related to model fit. Statistical approaches ignore the cost of misclassifications and the harm of measuring a variable. We aim to develop a decision-analytic variable selection algorithm based on net benefit. Materials and Methods: The proposed algorithm selects the set of predictors by exhaustively comparing the net benefit of all combinations using cross validation, with an extension based on backward elimination for settings with many predictors. Variables are selected if the increased net benefit from better predictiveness exceeds the net benefit reduction from the harm of variable measurement. Harm includes financial expense, time, resource allocation, and patient burden. We illustrate the algorithm through a simulated example and three real case studies. We compare its performance to traditional backward elimination and LASSO. Results: Across the case studies, parsimonious models were generated that optimized clinical utility with minimal impact on discrimination and calibration. Penalizing predictors based on their cost ensured that expensive or burdensome variables were only selected if they offer sufficient clinical utility. The algorithm was implemented in the R package NBvarsel. Discussion: Decision-analytic variable selection allows prediction models to maximize patient benefit while minimizing unnecessary clinical burden and costs. Conclusion: Clinical utility should not be an afterthought reserved only for implementation. By integrating a harm-adjusted net benefit metric directly into the variable selection process, NBvarsel allows researchers to select only the variables that sufficiently improve clinical utility.
Researchers often choose a proxy dataset from many releases, transformations, or seeds. Search can make an invalid release appear adequate, while one adequate release does not establish that its generator is reliable. ProxyGuard controls both errors using prespecified bounded risks and a sealed target set. Named-release mode corrects for multiplicity and certifies specific releases. Direct shared-target mode evaluates independent mechanism draws on a common target, lower-bounds their favorable-score rate, and subtracts a bound on favorable scores contributed by invalid releases. Conditional on the target, release scores are independent, yielding a finite-sample mechanism-reliability guarantee without independent target batches or assumptions on release-level $p$-value dependence. We show that the mean-only penalty is sharp and derive a smooth-score certificate with additive target concentration. In a registered three-requirement study, direct mode raises power from $5.6\%$ to $64.2\%$ at reliability $0.95$, while named mode remains stronger under high-signal evidence. Prospective audits span full-pipeline Rice--TVAE, which retrains on every draw, and a non-tabular text mechanism.
The ratio of two densities provides a direct characterization of their differences. We consider the two-sample comparison problem by estimating this ratio given i.i.d. observations from two distributions. To this end, we propose additive tree models for density ratio estimation along with efficient algorithms using a new loss function, the balancing loss. The loss allows tree-based models to be trained using several algorithms originally designed for supervised learning, such as forward-stagewise optimization and gradient boosting. Moreover, the balancing loss resembles an exponential family kernel, and it can serve as a pseudo-likelihood with conjugate priors. This property enables generalized Bayesian inference on the density ratio using backfitting samplers designed for Bayesian additive regression trees (BART). Our Bayesian strategy provides uncertainty quantification for the inferred density ratio, which is critical for applications involving high-dimensional and data-limited distributions with potentially substantial uncertainty. We further show connections of the balancing loss to the exponential loss in binary classification and to the variational form of f-divergence, particularly the squared Hellinger distance. Numerical experiments demonstrate that the proposed boosting algorithms achieve high accuracy at low computational cost, and that the Bayesian additive tree is competitive in accuracy while additionally providing uncertainty quantification, which the compared estimators do not offer. Finally, we demonstrate its application to assessing the quality of generative models for microbiome compositional data.
Sølve Langseth, Kristoffer Herland Hellton, Hugo L. Hammer
Prediction models degrade when the deployment population differs from the one used to train them, and training data cannot say which feature-response relationships will transfer. Expert elicitation is slow and unscalable. We ask whether coefficient priors elicited from large language models (LLMs) improve out-of-distribution (OOD) prediction as the shrinkage target of a regularised regression instead of zero, across five tabular datasets split on real covariates, selecting providers and prior structures by source-domain cross-validation alone. The priors help on four of five datasets, by up to 7.9% OOD mean squared error, and ten of twenty-four prior-informed results resolve the mean improvement at conventional confidence; single-deployment intervals are much wider. On classification the gain is in probabilistic accuracy, not ranking, and control tests with corrupted priors attribute the benefit to feature-specific content rather than scale. Two findings temper this. Variation across candidate priors exceeds the average benefit, yet cross-validation margins fall below their own noise, so selection avoids the worst prior rather than finding the best. On three datasets the prior improves in-domain accuracy as much as out-of-domain, making it better regularisation than shift correction. Only where the training data are large enough that the in-domain gain disappears does elicited knowledge demonstrably improve transfer. Code, priors and results: https://github.com/hugohammer/llm-priors-ood.