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1. A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2)

   https://doi.org/10.5194/gmd-17-8853-2024  

   Sabaté_Landman, Malena; Chung, Julianne; Jiang, Jiahua; Miller, Scot M; Saibaba, Arvind K (December 2024, Geoscientific Model Development)

   Inverse models arise in various environmental applications, ranging from atmospheric modeling to geosciences. Inverse models can often incorporate predictor variables, similar to regression, to help estimate natural processes or parameters of interest from observed data. Although a large set of possible predictor variables may be included in these inverse or regression models, a core challenge is to identify a small number of predictor variables that are most informative of the model, given limited observations. This problem is typically referred to as model selection. A variety of criterion-based approaches are commonly used for model selection, but most follow a two-step process: first, select predictors using some statistical criteria, and second, solve the inverse or regression problem with these predictor variables. The first step typically requires comparing all possible combinations of candidate predictors, which quickly becomes computationally prohibitive, especially for large-scale problems. In this work, we develop a one-step approach for linear inverse modeling, where model selection and the inverse model are performed in tandem. We reformulate the problem so that the selection of a small number of relevant predictor variables is achieved via a sparsity-promoting prior. Then, we describe hybrid iterative projection methods based on flexible Krylov subspace methods for efficient optimization. These approaches are well-suited for large-scale problems with many candidate predictor variables. We evaluate our results against traditional, criteria-based approaches. We also demonstrate the applicability and potential benefits of our approach using examples from atmospheric inverse modeling based on NASA's Orbiting Carbon Observatory-2 (OCO-2) satellite. 

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2. Bayesian network-guided sparse regression with flexible varying effects

   https://doi.org/10.1093/biomtc/ujae111  

   Ren, Yangfan; Peterson, Christine_B; Vannucci, Marina (October 2024, Biometrics)

   ABSTRACT In this paper, we propose Varying Effects Regression with Graph Estimation (VERGE), a novel Bayesian method for feature selection in regression. Our model has key aspects that allow it to leverage the complex structure of data sets arising from genomics or imaging studies. We distinguish between the predictors, which are the features utilized in the outcome prediction model, and the subject-level covariates, which modulate the effects of the predictors on the outcome. We construct a varying coefficients modeling framework where we infer a network among the predictor variables and utilize this network information to encourage the selection of related predictors. We employ variable selection spike-and-slab priors that enable the selection of both network-linked predictor variables and covariates that modify the predictor effects. We demonstrate through simulation studies that our method outperforms existing alternative methods in terms of both feature selection and predictive accuracy. We illustrate VERGE with an application to characterizing the influence of gut microbiome features on obesity, where we identify a set of microbial taxa and their ecological dependence relations. We allow subject-level covariates, including sex and dietary intake variables to modify the coefficients of the microbiome predictors, providing additional insight into the interplay between these factors. 

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3. Automated Search for Logistic Knowledge Tracing Models

   Philip I. Pavlik Jr., & Luke (July 2023, Proceedings of the 16th International Conference on Educational Data Mining, 17–27)

   This paper presents a tool for creating student models in logistic regression. Creating student models has typically been done by expert selection of the appropriate terms, beginning with models as simple as IRT or AFM but more recently with highly complex models like BestLR. While alternative methods exist to select the appropriate predictors for the regression-based models (e.g., step-wise selection or LASSO), we are unaware of their application to student modeling. Such automatic methods of model creation offer the possibility of better student models with either reduced complexity or better fit, in addition to relieving experts from the burden of searching for better models by hand with possible human error. Our tool builds on top of the preexisting R package LKT. We explain our search methods with two datasets demonstrating the advantages of using the tool with stepwise regression and regularization (LASSO) methods to aid in feature selection. For the stepwise method using BIC, the models are simpler (due to the BIC penalty for parameters) than alternatives like BestLR with little lack of fit. For the LASSO method, the models can be made simpler due to the fitting procedure involving a regularization parameter that penalizes large absolute coefficient values. However, LASSO also offers the possibility of highly complex models with exceptional fit. 

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4. Wasserstein regression with empirical measures and density estimation for sparse data

   https://doi.org/10.1093/biomtc/ujae127  

   Zhou, Yidong; Müller, Hans-Georg (November 2024, Biometrics)

   Abstract The problem of modeling the relationship between univariate distributions and one or more explanatory variables lately has found increasing interest. Existing approaches proceed by substituting proxy estimated distributions for the typically unknown response distributions. These estimates are obtained from available data but are problematic when for some of the distributions only few data are available. Such situations are common in practice and cannot be addressed with currently available approaches, especially when one aims at density estimates. We show how this and other problems associated with density estimation such as tuning parameter selection and bias issues can be side-stepped when covariates are available. We also introduce a novel version of distribution-response regression that is based on empirical measures. By avoiding the preprocessing step of recovering complete individual response distributions, the proposed approach is applicable when the sample size available for each distribution varies and especially when it is small for some of the distributions but large for others. In this case, one can still obtain consistent distribution estimates even for distributions with only few data by gaining strength across the entire sample of distributions, while traditional approaches where distributions or densities are estimated individually fail, since sparsely sampled densities cannot be consistently estimated. The proposed model is demonstrated to outperform existing approaches through simulations and Environmental Influences on Child Health Outcomes data. 

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5. Consistent Estimation of Generalized Linear Models with High Dimensional Predictors via Stepwise Regression

   https://doi.org/10.3390/e22090965  

   Pijyan, Alex; Zheng, Qi; Hong, Hyokyoung G.; Li, Yi (September 2020, Entropy)

   null (Ed.)

   Predictive models play a central role in decision making. Penalized regression approaches, such as least absolute shrinkage and selection operator (LASSO), have been widely used to construct predictive models and explain the impacts of the selected predictors, but the estimates are typically biased. Moreover, when data are ultrahigh-dimensional, penalized regression is usable only after applying variable screening methods to downsize variables. We propose a stepwise procedure for fitting generalized linear models with ultrahigh dimensional predictors. Our procedure can provide a final model; control both false negatives and false positives; and yield consistent estimates, which are useful to gauge the actual effect size of risk factors. Simulations and applications to two clinical studies verify the utility of the method. 

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