Valid statistical inference is challenging when the sample is subject to unknown selection bias. Data integration can be used to correct for selection bias when we have a parallel probability sample from the same population with some common measurements. How to model and estimate the selection probability or the propensity score (PS) of a non-probability sample using an independent probability sample is the challenging part of the data integration. We approach this difficult problem by employing multiple candidate models for PS combined with empirical likelihood. By incorporating multiple propensity score models into the internal bias calibration constraint in the empirical likelihood setup, the selection bias can be eliminated so long as the multiple candidate models contain a true PS model. The bias calibration constraint under the multiple PS models is called multiple bias calibration. Multiple PS models can include both missing-at-random and missing-not-at-random models. Asymptotic properties are discussed, and some limited simulation studies are presented to compare the proposed method with some existing competitors. Plasmode simulation studies using the Culture \& Community in a Time of Crisis dataset demonstrate the practical usage and advantages of the proposed method.
相關內容
We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $l$ in an infinite heterogeneous correlated random medium, in a situation where the medium is only known in a box of diameter $L\gg l$ around the support of the charge. We show that the algorithm of Lu, Otto and Wang, suggesting optimal Dirichlet boundary conditions motivated by the multipole expansion of Bella, Giunti and Otto, still performs well in correlated media. With overwhelming probability, we obtain a convergence rate in terms of $l$, $L$ and the size of the correlations for which optimality is supported with numerical simulations. These estimates are provided for ensembles which satisfy a multi-scale logarithmic Sobolev inequality, where our main tool is an extension of the semi-group estimates established by the first author. As part of our strategy, we construct sub-linear second-order correctors in this correlated setting which is of independent interest.
This paper presents a numerical method for the simulation of elastic solid materials coupled to fluid inclusions. The application is motivated by the modeling of vascularized tissues and by problems in medical imaging which target the estimation of effective (i.e., macroscale) material properties, taking into account the influence of microscale dynamics, such as fluid flow in the microvasculature. The method is based on the recently proposed Reduced Lagrange Multipliers framework. In particular, the interface between solid and fluid domains is not resolved within the computational mesh for the elastic material but discretized independently, imposing the coupling condition via non-matching Lagrange multipliers. Exploiting the multiscale properties of the problem, the resulting Lagrange multipliers space is reduced to a lower-dimensional characteristic set. We present the details of the stability analysis of the resulting method considering a non-standard boundary condition that enforces a local deformation on the solid-fluid boundary. The method is validated with several numerical examples.
Science mapping is an important tool to gain insight into scientific fields, to identify emerging research trends, and to support science policy. Understanding the different ways in which different science mapping approaches capture the structure of scientific fields is critical. This paper presents a comparative analysis of two commonly used approaches, topic modeling (TM) and citation-based clustering (CC), to assess their respective strengths, weaknesses, and the characteristics of their results. We compare the two approaches using cluster-to-topic and topic-to-cluster mappings based on science maps of cardiovascular research (CVR) generated by TM and CC. Our findings reveal that relations between topics and clusters are generally weak, with limited overlap between topics and clusters. Only in a few exceptional cases do more than one-third of the documents in a topic belong to the same cluster, or vice versa. CC excels at identifying diseases and generating specialized clusters in Clinical Treatment & Surgical Procedures, while TM focuses on sub-techniques within diagnostic techniques, provides a general perspective on Clinical Treatment & Surgical Procedures, and identifies distinct topics related to practical guidelines. Our work enhances the understanding of science mapping approaches based on TM and CC and delivers practical guidance for scientometricians on how to apply these approaches effectively.
It is crucial to detect when an instance lies downright too far from the training samples for the machine learning model to be trusted, a challenge known as out-of-distribution (OOD) detection. For neural networks, one approach to this task consists of learning a diversity of predictors that all can explain the training data. This information can be used to estimate the epistemic uncertainty at a given newly observed instance in terms of a measure of the disagreement of the predictions. Evaluation and certification of the ability of a method to detect OOD require specifying instances which are likely to occur in deployment yet on which no prediction is available. Focusing on regression tasks, we choose a simple yet insightful model for this OOD distribution and conduct an empirical evaluation of the ability of various methods to discriminate OOD samples from the data. Moreover, we exhibit evidence that a diversity of parameters may fail to translate to a diversity of predictors. Based on the choice of an OOD distribution, we propose a new way of estimating the entropy of a distribution on predictors based on nearest neighbors in function space. This leads to a variational objective which, combined with the family of distributions given by a generative neural network, systematically produces a diversity of predictors that provides a robust way to detect OOD samples.
Permutation tests are widely recognized as robust alternatives to tests based on the normal theory. Random permutation tests have been frequently employed to assess the significance of variables in linear models. Despite their widespread use, existing random permutation tests lack finite-sample and assumption-free guarantees for controlling type I error in partial correlation tests. To address this standing challenge, we develop a conformal test through permutation-augmented regressions, which we refer to as PALMRT. PALMRT not only achieves power competitive with conventional methods but also provides reliable control of type I errors at no more than $2\alpha$ given any targeted level $\alpha$, for arbitrary fixed-designs and error distributions. We confirmed this through extensive simulations. Compared to the cyclic permutation test (CPT), which also offers theoretical guarantees, PALMRT does not significantly compromise power or set stringent requirements on the sample size, making it suitable for diverse biomedical applications. We further illustrate their differences in a long-Covid study where PALMRT validated key findings previously identified using the t-test, while CPT suffered from a drastic loss of power. We endorse PALMRT as a robust and practical hypothesis test in scientific research for its superior error control, power preservation, and simplicity.
Reinforcement learning of real-world tasks is very data inefficient, and extensive simulation-based modelling has become the dominant approach for training systems. However, in human-robot interaction and many other real-world settings, there is no appropriate one-model-for-all due to differences in individual instances of the system (e.g. different people) or necessary oversimplifications in the simulation models. This requires two approaches: 1. either learning the individual system's dynamics approximately from data which requires data-intensive training or 2. using a complete digital twin of the instances, which may not be realisable in many cases. We introduce two approaches: co-kriging adjustments (CKA) and ridge regression adjustment (RRA) as novel ways to combine the advantages of both approaches. Our adjustment methods are based on an auto-regressive AR1 co-kriging model that we integrate with GP priors. This yield a data- and simulation-efficient way of using simplistic simulation models (e.g., simple two-link model) and rapidly adapting them to individual instances (e.g., biomechanics of individual people). Using CKA and RRA, we obtain more accurate uncertainty quantification of the entire system's dynamics than pure GP-based and AR1 methods. We demonstrate the efficiency of co-kriging adjustment with an interpretable reinforcement learning control example, learning to control a biomechanical human arm using only a two-link arm simulation model (offline part) and CKA derived from a small amount of interaction data (on-the-fly online). Our method unlocks an efficient and uncertainty-aware way to implement reinforcement learning methods in real world complex systems for which only imperfect simulation models exist.
A fundamental aspect of statistics is the integration of data from different sources. Classically, Fisher and others were focused on how to integrate homogeneous (or only mildly heterogeneous) sets of data. More recently, as data is becoming more accessible, the question of if data sets from different sources should be integrated is becoming more relevant. The current literature treats this as a question with only two answers: integrate or don't. Here we take a different approach, motivated by information-sharing principles coming from the shrinkage estimation literature. In particular, we deviate from the do/don't perspective and propose a dial parameter that controls the extent to which two data sources are integrated. How far this dial parameter should be turned is shown to depend, for example, on the informativeness of the different data sources as measured by Fisher information. In the context of generalized linear models, this more nuanced data integration framework leads to relatively simple parameter estimates and valid tests/confidence intervals. Moreover, we demonstrate both theoretically and empirically that setting the dial parameter according to our recommendation leads to more efficient estimation compared to other binary data integration schemes.
Besov priors are nonparametric priors that can model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of work has initiated the study of their asymptotic frequentist convergence properties. In the present paper, we consider the theoretical recovery performance of the posterior distributions associated to Besov-Laplace priors in the density estimation model, under the assumption that the observations are generated by a possibly spatially inhomogeneous true density belonging to a Besov space. We improve on existing results and show that carefully tuned Besov-Laplace priors attain optimal posterior contraction rates. Furthermore, we show that hierarchical procedures involving a hyper-prior on the regularity parameter lead to adaptation to any smoothness level.
Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic -- primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms introduces added complexity to the workflow, leading to longer computation times. This poses a notable challenge to ML applications, as suboptimal hyperparameter selections curtail the potential of ML model performance, ultimately obstructing the full exploitation of ML techniques. In this article, we present a two-step HPO method as a strategic solution to curbing computational demands and wait times, gleaned from practical experiences in applied ML parameterization work. The initial phase involves a preliminary evaluation of hyperparameters on a small subset of the training dataset, followed by a re-evaluation of the top-performing candidate models post-retraining with the entire training dataset. This two-step HPO method is universally applicable across HPO search algorithms, and we argue it has attractive efficiency gains. As a case study, we present our recent application of the two-step HPO method to the development of neural network emulators for aerosol activation. Although our primary use case is a data-rich limit with many millions of samples, we also find that using up to 0.0025% of the data (a few thousand samples) in the initial step is sufficient to find optimal hyperparameter configurations from much more extensive sampling, achieving up to 135-times speedup. The benefits of this method materialize through an assessment of hyperparameters and model performance, revealing the minimal model complexity required to achieve the best performance. The assortment of top-performing models harvested from the HPO process allows us to choose a high-performing model with a low inference cost for efficient use in global climate models (GCMs).
Gene set analysis is a mainstay of functional genomics, but it relies on manually curated databases of gene functions that are incomplete and unaware of biological context. Here we evaluate the ability of OpenAI's GPT-4, a Large Language Model (LLM), to develop hypotheses about common gene functions from its embedded biomedical knowledge. We created a GPT-4 pipeline to label gene sets with names that summarize their consensus functions, substantiated by analysis text and citations. Benchmarking against named gene sets in the Gene Ontology, GPT-4 generated very similar names in 50% of cases, while in most remaining cases it recovered the name of a more general concept. In gene sets discovered in 'omics data, GPT-4 names were more informative than gene set enrichment, with supporting statements and citations that largely verified in human review. The ability to rapidly synthesize common gene functions positions LLMs as valuable functional genomics assistants.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191