Bayesian variable selection for multioutcome models through shared shrinkage

Kundu, Debamita; Mitra, Riten; Gaskins, Jeremy

doi:10.1111/sjos.12455

Cited by 11 publications

(8 citation statements)

References 27 publications

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“…. , m. A version of this prior has previously been used by one of the authors for a multi-outcome regression model [27]. There the local shrinkage effects, while varying among individual predictor values, were shared across multiple dimensions of the same predictor, and the global component varied across different dimensions.…”

Section: • Inverse Wishart Prior On the Hyperparameter λmentioning

confidence: 99%

“…There the local shrinkage effects, while varying among individual predictor values, were shared across multiple dimensions of the same predictor, and the global component varied across different dimensions. While these types of priors may be more natural for the multi-outcome regression models of [27] to allow more intra-dimensional variability, their use in the context of multidimensional dynamical systems lacks strong justification. Rather the significantly higher number of additional hyperparameters that these priors require will lead to substantial increase in the complexity and run-time of the resulting Gibb's algorithm.…”

Section: • Inverse Wishart Prior On the Hyperparameter λmentioning

confidence: 99%

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Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations

Ganguly¹,

Mitra²,

Zhou³

2022

Preprint

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The paper has two major themes. The first part of the paper establishes certain general results for infinite-dimensional optimization problems on Hilbert spaces. These results cover the classical representer theorem and many of its variants as special cases and offer a wider scope of applications. The second part of the paper then develops a systematic approach for learning the drift function of a stochastic differential equation by integrating the results of the first part with Bayesian hierarchical framework. Importantly, our Baysian approach incorporates low-cost sparse learning through proper use of shrinkage priors while allowing proper quantification of uncertainty through posterior distributions. Several examples at the end illustrate the accuracy of our learning scheme.

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Section: • Inverse Wishart Prior On the Hyperparameter λmentioning

confidence: 99%

Section: • Inverse Wishart Prior On the Hyperparameter λmentioning

confidence: 99%

Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations

Ganguly¹,

Mitra²,

Zhou³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Under this setting, the implementation of shrinkage or regularization methods is common (9)(10)(11). Other authors have addressed variable selection for multivariate modelling using a Bayesian framework (12)(13)(14). However, in clinical settings, where the sample size is frequently large relative to the number of predictors and outcomes, a simpler and easy-to-implement procedure that does not require complex software solutions could be of great utility.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Identifying a Parsimonious and Accurate Predictive Model for Multiple Clinical Outcomes

Diaz‐Ramirez

Lee

Smith

et al. 2021

Computer Methods and Programs in Biomedicine

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Background: Most methods for developing clinical prognostic models focus on identifying parsimonious and accurate models to predict a single outcome; however, patients and providers often want to predict multiple outcomes simultaneously. For example, older adults are often interested in predicting nursing home admission as well as mortality. We propose and evaluate a novel predictor selection method for multiple outcomes.Methods: Our proposed method selected the best subset of common predictors based on the minimum average normalized Bayesian Information Criterion (BIC) across outcomes: the Best Average BIC (baBIC) model. We compared the predictive accuracy (Harrell's C-statistic) and parsimony (number of predictors) of the baBIC model with a subset of common predictors obtained from the union of optimal models for each outcome (Union model). We used example data from the Health and Retirement Study (HRS) to demonstrate our method and conducted a simulation study to investigate performance considering correlated and uncorrelated outcomes. Results:In the example data, the average Harrell's C-statistics across outcomes of the baBIC and Union models were comparable (0.657 vs. 0.662 respectively). Despite the similar discrimination, the baBIC model was more parsimonious than the Union model (15 vs. 23 predictors respectively).Likewise, in the simulations with correlated outcomes, the mean C-statistic across outcomes of the baBIC and Union models were the same after rounding: 0.650, and the baBIC model had an average

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“…Under this setting, the implementation of shrinkage or regularization methods is common [10][11][12][13]. Other authors have addressed variable selection for multivariate modelling using a Bayesian framework [14][15][16]. However, in clinical settings, where the sample size is frequently large relative to the number of predictors and outcomes, a simpler and easy-to-implement procedure that does not require complex software solutions could be of great utility.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Identifying a Parsimonious and Accurate Predictive Model for Multiple Clinical Outcomes

Diaz‐Ramirez

Lee

Smith

et al. 2021

Preprint

View full text Add to dashboard Cite

Background and Objective: Most methods for developing clinical prognostic models focus on identifying parsimonious and accurate models to predict a single outcome; however, patients and providers often want to predict multiple outcomes simultaneously. As an example, for older adults one is often interested in predicting nursing home admission as well as mortality. We propose and evaluate a novel predictor-selection computing method for multiple outcomes and provide the code for its implementation.Methods: Our proposed algorithm selected the best subset of common predictors based on the minimum average normalized Bayesian Information Criterion (BIC) across outcomes: the Best Average BIC (baBIC) method. We compared the predictive accuracy (Harrell’s C-statistic) and parsimony (number of predictors) of the model obtained using the baBIC method with: 1) a subset of common predictors obtained from the union of optimal models for each outcome (Union method), 2) a subset obtained from the intersection of optimal models for each outcome (Intersection method), and 3) a model with no variable selection (Full method). We used a case-study data from the Health and Retirement Study (HRS) to demonstrate our method and conducted a simulation study to investigate performance.Results: In the case-study data and simulations, the average Harrell’s C-statistics across outcomes of the models obtained with the baBIC and Union methods were comparable. Despite the similar discrimination, the baBIC method produced more parsimonious models than the Union method. In contrast, the models selected with the Intersection method were the most parsimonious, but with worst predictive accuracy, and the opposite was true in the Full method. In the simulations, the baBIC method performed well by identifying many of the predictors selected in the baBIC model of the case-study data most of the time and excluding those not selected in the majority of the simulations.Conclusions: Our method identified a common subset of variables to predict multiple clinical outcomes with superior balance between parsimony and predictive accuracy to current methods.

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Bayesian variable selection for multioutcome models through shared shrinkage

Cited by 11 publications

References 27 publications

Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations

Infinite-dimensional optimization and Bayesian nonparametric learning of stochastic differential equations

A Novel Method for Identifying a Parsimonious and Accurate Predictive Model for Multiple Clinical Outcomes

A Novel Method for Identifying a Parsimonious and Accurate Predictive Model for Multiple Clinical Outcomes

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