{"title":"A statistical view of column subset selection.","authors":"Anav Sood, Trevor Hastie","doi":"10.1093/jrsssb/qkaf023","DOIUrl":"10.1093/jrsssb/qkaf023","url":null,"abstract":"<p><p>We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as column subset selection (CSS). Meanwhile, the typical statistical formalization is to find an information-maximizing set of principal variables. This paper shows that these two approaches are equivalent, and moreover, both can be viewed as maximum-likelihood estimation within a certain semi-parametric model. Within this model, we establish suitable conditions under which the CSS estimate is consistent in high dimensions, specifically in the proportional asymptotic regime where the number of variables over the sample size converges to a constant. Using these connections, we show how to efficiently (1) perform CSS using only summary statistics from the original dataset; (2) perform CSS in the presence of missing and/or censored data; and (3) select the subset size for CSS in a hypothesis testing framework.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":" ","pages":""},"PeriodicalIF":3.6,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12288642/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144734981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Product Centred Dirichlet Processes for Bayesian Multiview Clustering.","authors":"Alexander Dombowsky, David B Dunson","doi":"10.1093/jrsssb/qkaf021","DOIUrl":"10.1093/jrsssb/qkaf021","url":null,"abstract":"<p><p>While there is an immense literature on Bayesian methods for clustering, the multiview case has received little attention. This problem focuses on obtaining distinct but statistically dependent clusterings in a common set of entities for different data types. For example, clustering patients into subgroups with subgroup membership varying according to the domain of the patient variables. A challenge is how to model the across-view dependence between the partitions of patients into subgroups. The complexities of the partition space make standard methods to model dependence, such as correlation, infeasible. In this article, we propose CLustering with Independence Centring (CLIC), a clustering prior that uses a single parameter to explicitly model dependence between clusterings across views. CLIC is induced by the product centred Dirichlet process (PCDP), a novel hierarchical prior that bridges between independent and equivalent partitions. We show appealing theoretic properties, provide a finite approximation and prove its accuracy, present a marginal Gibbs sampler for posterior computation, and derive closed form expressions for the marginal and joint partition distributions for the CLIC model. On synthetic data and in an application to epidemiology, CLIC accurately characterizes view-specific partitions while providing inference on the dependence level.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":" ","pages":""},"PeriodicalIF":3.6,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12392789/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144976818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Two-phase rejective sampling and its asymptotic properties.","authors":"Shu Yang, Peng Ding","doi":"10.1093/jrsssb/qkaf002","DOIUrl":"10.1093/jrsssb/qkaf002","url":null,"abstract":"<p><p>Rejective sampling improves design and estimation efficiency of single-phase sampling when auxiliary information in a finite population is available. When such auxiliary information is unavailable, we propose to use two-phase rejective sampling (TPRS), which involves measuring auxiliary variables for the sample of units in the first phase, followed by the implementation of rejective sampling for the outcome in the second phase. We explore the asymptotic design properties of double expansion and regression estimators under TPRS. We show that TPRS enhances the efficiency of the double-expansion estimator, rendering it comparable to a regression estimator. We further refine the design to accommodate varying importance of covariates and extend it to multi-phase sampling. We start with the theory for the population mean and then extend the theory to parameters defined by general estimating equations. Our asymptotic results for TPRS immediately cover the existing single-phase rejective sampling, under which the asymptotic theory has not been fully established.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":" ","pages":""},"PeriodicalIF":3.6,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12355938/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144876438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chris J Oates, Toni Karvonen, Aretha L Teckentrup, Marina Strocchi, Steven A Niederer
{"title":"Probabilistic Richardson extrapolation.","authors":"Chris J Oates, Toni Karvonen, Aretha L Teckentrup, Marina Strocchi, Steven A Niederer","doi":"10.1093/jrsssb/qkae098","DOIUrl":"https://doi.org/10.1093/jrsssb/qkae098","url":null,"abstract":"<p><p>For over a century, extrapolation methods have provided a powerful tool to improve the convergence order of a numerical method. However, these tools are not well-suited to modern computer codes, where multiple continua are discretized and convergence orders are not easily analysed. To address this challenge, we present a probabilistic perspective on Richardson extrapolation, a point of view that unifies classical extrapolation methods with modern multi-fidelity modelling, and handles uncertain convergence orders by allowing these to be statistically estimated. The approach is developed using Gaussian processes, leading to <i>Gauss-Richardson Extrapolation</i>. Conditions are established under which extrapolation using the conditional mean achieves a polynomial (or even an exponential) speed-up compared to the original numerical method. Further, the probabilistic formulation unlocks the possibility of experimental design, casting the selection of fidelities as a continuous optimization problem, which can then be (approximately) solved. A case study involving a computational cardiac model demonstrates that practical gains in accuracy can be achieved using the GRE method.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"87 2","pages":"457-479"},"PeriodicalIF":3.1,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11985099/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144058583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust evaluation of longitudinal surrogate markers with censored data.","authors":"Denis Agniel, Layla Parast","doi":"10.1093/jrsssb/qkae119","DOIUrl":"10.1093/jrsssb/qkae119","url":null,"abstract":"<p><p>The development of statistical methods to evaluate surrogate markers is an active area of research. In many clinical settings, the surrogate marker is not simply a single measurement but is instead a longitudinal trajectory of measurements over time, e.g. fasting plasma glucose measured every 6 months for 3 years. In general, available methods developed for the single-surrogate setting cannot accommodate a longitudinal surrogate marker. Furthermore, many of the methods have not been developed for use with primary outcomes that are time-to-event outcomes and/or subject to censoring. In this paper, we propose robust methods to evaluate a longitudinal surrogate marker in a censored time-to-event outcome setting. Specifically, we propose a method to define and estimate the proportion of the treatment effect on a censored primary outcome that is explained by the treatment effect on a longitudinal surrogate marker measured up to time <math><msub><mi>t</mi> <mn>0</mn></msub> </math> . We accommodate both potential censoring of the primary outcome and of the surrogate marker. A simulation study demonstrates a good finite-sample performance of our proposed methods. We illustrate our procedures by examining repeated measures of fasting plasma glucose, a surrogate marker for diabetes diagnosis, using data from the diabetes prevention programme.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"87 3","pages":"891-907"},"PeriodicalIF":3.1,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12256123/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144638525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Robust angle-based transfer learning in high dimensions.","authors":"Tian Gu, Yi Han, Rui Duan","doi":"10.1093/jrsssb/qkae111","DOIUrl":"10.1093/jrsssb/qkae111","url":null,"abstract":"<p><p>Transfer learning improves target model performance by leveraging data from related source populations, especially when target data are scarce. This study addresses the challenge of training high-dimensional regression models with limited target data in the presence of heterogeneous source populations. We focus on a practical setting where only parameter estimates of pretrained source models are available, rather than individual-level source data. For a single source model, we propose a novel angle-based transfer learning (angleTL) method that leverages concordance between source and target model parameters. AngleTL adapts to the signal strength of the target model, unifies several benchmark methods, and mitigates negative transfer when between-population heterogeneity is large. We extend angleTL to incorporate multiple source models, accounting for varying levels of relevance among them. Our high-dimensional asymptotic analysis provides insights into when a source model benefits the target model and demonstrates the superiority of angleTL over other methods. Extensive simulations validate these findings and highlight the feasibility of applying angleTL to transfer genetic risk prediction models across multiple biobanks.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"87 3","pages":"723-745"},"PeriodicalIF":3.6,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12256125/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144638524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jeremiah Jones, Ashkan Ertefaie, Robert L Strawderman
{"title":"Causal mediation analysis: selection with asymptotically valid inference.","authors":"Jeremiah Jones, Ashkan Ertefaie, Robert L Strawderman","doi":"10.1093/jrsssb/qkae109","DOIUrl":"10.1093/jrsssb/qkae109","url":null,"abstract":"<p><p>Researchers are often interested in learning not only the effect of treatments on outcomes, but also the mechanisms that transmit these effects. A mediator is a variable that is affected by treatment and subsequently affects outcome. Existing methods for penalized mediation analyses may lead to ignoring important mediators and either assume that finite-dimensional linear models are sufficient to remove confounding bias, or perform no confounding control at all. In practice, these assumptions may not hold. We propose a method that considers the confounding functions as nuisance parameters to be estimated using data-adaptive methods. We then use a novel regularization method applied to this objective function to identify a set of important mediators. We consider natural direct and indirect effects as our target parameters. We then proceed to derive the asymptotic properties of our estimators and establish the oracle property under specific assumptions. Asymptotic results are also presented in a local setting, which contrast the proposal with the standard adaptive lasso. We also propose a perturbation bootstrap technique to provide asymptotically valid postselection inference for the mediated effects of interest. The performance of these methods will be discussed and demonstrated through simulation studies.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"87 3","pages":"678-700"},"PeriodicalIF":3.6,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12256126/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144638523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A focusing framework for testing bi-directional causal effects in Mendelian randomization.","authors":"Sai Li, Ting Ye","doi":"10.1093/jrsssb/qkae101","DOIUrl":"10.1093/jrsssb/qkae101","url":null,"abstract":"<p><p>Mendelian randomization (MR) is a powerful method that uses genetic variants as instrumental variables to infer the causal effect of a modifiable exposure on an outcome. We study inference for bi-directional causal relationships and causal directions with possibly pleiotropic genetic variants. We show that assumptions for common MR methods are often impossible or too stringent given the potential bi-directional relationships. We propose a new focusing framework for testing bi-directional causal effects and it can be coupled with many state-of-the-art MR methods. We provide theoretical guarantees for our proposal and demonstrate its performance using several simulated and real datasets.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"87 2","pages":"529-548"},"PeriodicalIF":3.6,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11985100/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144047748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric estimation via partial derivatives.","authors":"Xiaowu Dai","doi":"10.1093/jrsssb/qkae093","DOIUrl":"https://doi.org/10.1093/jrsssb/qkae093","url":null,"abstract":"<p><p>Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically large dataset sizes for reliable conclusions. We develop an approach based on partial derivatives, either observed or estimated, to effectively estimate the function at near-parametric convergence rates. This novel approach and computational algorithm could lead to methods useful to practitioners in many areas of science and engineering. Our theoretical results reveal behaviour universal to this class of nonparametric estimation problems. We explore a general setting involving tensor product spaces and build upon the smoothing spline analysis of variance framework. For <i>d</i>-dimensional models under full interaction, the optimal rates with gradient information on <i>p</i> covariates are identical to those for the <math><mo>(</mo> <mi>d</mi> <mo>-</mo> <mi>p</mi> <mo>)</mo></math> -interaction models without gradients and, therefore, the models are immune to the <i>curse of interaction</i>. For additive models, the optimal rates using gradient information are <math><msqrt><mi>n</mi></msqrt> </math> , thus achieving the <i>parametric rate</i>. We demonstrate aspects of the theoretical results through synthetic and real data applications.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"87 2","pages":"319-336"},"PeriodicalIF":3.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11985098/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144064677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Mode-wise principal subspace pursuit and matrix spiked covariance model.","authors":"Runshi Tang, Ming Yuan, Anru R Zhang","doi":"10.1093/jrsssb/qkae088","DOIUrl":"10.1093/jrsssb/qkae088","url":null,"abstract":"<p><p>This paper introduces a novel framework called Mode-wise Principal Subspace Pursuit (MOP-UP) to extract hidden variations in both the row and column dimensions for matrix data. To enhance the understanding of the framework, we introduce a class of matrix-variate spiked covariance models that serve as inspiration for the development of the MOP-UP algorithm. The MOP-UP algorithm consists of two steps: Average Subspace Capture (ASC) and Alternating Projection. These steps are specifically designed to capture the row-wise and column-wise dimension-reduced subspaces which contain the most informative features of the data. ASC utilizes a novel average projection operator as initialization and achieves exact recovery in the noiseless setting. We analyse the convergence and non-asymptotic error bounds of MOP-UP, introducing a blockwise matrix eigenvalue perturbation bound that proves the desired bound, where classic perturbation bounds fail. The effectiveness and practical merits of the proposed framework are demonstrated through experiments on both simulated and real datasets. Lastly, we discuss generalizations of our approach to higher-order data.</p>","PeriodicalId":49982,"journal":{"name":"Journal of the Royal Statistical Society Series B-Statistical Methodology","volume":"87 1","pages":"232-255"},"PeriodicalIF":3.6,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11809223/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143411335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}