Edward I. George

Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja, Edward I. George, Linda Zhao, A Model Free Perspective for Linear Regression: Uniform-in-model Bounds for Post Selection Inference.

Abstract: For the last two decades, high-dimensional data and methods have proliferated throughout the literature. The classical technique of linear regression, however, has not lost its touch in applications. Most high-dimensional estimation techniques can be seen as variable selection tools which lead to a smaller set of variables where classical linear regression technique applies. In this paper, we prove estimation error and linear representation bounds for the linear regression estimator uniformly over (many) subsets of variables. Based on deterministic inequalities, our results provide “good” rates when applied to both independent and dependent data. These results are useful in correctly interpreting the linear regression estimator obtained after exploring the data and also in post model-selection inference. All the results are derived under no model assumptions and are non-asymptotic in nature.

Andreas Buja, Richard A. Berk, Lawrence D. Brown, Edward I. George, Emil Pitkin, Mikhail Traskin, Linda Zhao, Kai Zhang (2017), Models as Approximations, Part I: A Conspiracy of Nonlinearity and Random Regressors in Linear Regression, Statistical Science, (revision submitted).

Matthew T. Pratola, Hugh A. Chipman, Edward I. George, Robert E. McCulloch (Under Review), Heteroscedastic BART Using Multiplicative Regression Trees.

Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja, Richard A. Berk, Linda Zhao, Edward I. George (Working), Valid Post-selection Inference in Assumption-lean Linear Regression.

Abstract: This paper provides multiple approaches to perform valid post-selection inference in an assumption-lean regression analysis. To the best of our knowledge, this is the first work that provides valid post-selection inference for regression analysis in such a general settings that include independent, m-dependent random variables.

Richard A. Berk, Lawrence D. Brown, Andreas Buja, Edward I. George, Linda Zhao (2017), Working with Misspecified Regression Models, Journal of Quantitative Criminology, (in press).

Edward I. George, Veronika Rockova, Paul R. Rosenbaum, Ville Satopää, Jeffrey H. Silber (2017), Mortality Rate Estimation and Standardization for Public Reporting: Medicare's Hospital Compare, Journal of the American Statistical Association, Applications, (in press).

Abstract: Bayesian models are increasingly fit to large administrative data sets and then used to make individualized recommendations. In particular, Medicare's Hospital Compare webpage provides information to patients about specific hospital mortality rates for a heart attack or Acute Myocardial Infarction (AMI). Hospital Compare's current recommendations are based on a random-effects logit model with a random hospital indicator and patient risk factors. Except for the largest hospitals, these individual recommendations or predictions are not checkable against data, because data from smaller hospitals are too limited to provide a meaningful check. Before individualized Bayesian recommendations, people derived general advice from empirical studies of many hospitals; e.g., prefer hospitals of type 1 to type 2 because the risk is lower at type 1 hospitals. Here we calibrate these Bayesian recommendation systems by checking, out of sample, whether their predictions aggregate to give correct general advice derived from another sample. This process of calibrating individualized predictions against general empirical advice leads to substantial revisions in the Hospital Compare model for AMI mortality. In order to make appropriately calibrated predictions, our revised models incorporate information about hospital volume, nursing staff, medical residents, and the hospital's ability to perform cardiovascular procedures. For the ultimate purpose of comparisons, hospital mortality rates must be standardized to adjust for patient mix variation across hospitals. We find that indirect standardization, as currently used by Hospital Compare, fails to adequately control for differences in patient risk factors and systematically underestimates mortality rates at the low volume hospitals. To provide good control and correctly calibrated rates, we propose direct standardization instead.  

Daniel McCarthy, Kai Zhang, Lawrence D. Brown, Richard A. Berk, Andreas Buja, Edward I. George, Linda Zhao (2017), Calibrated Percentile Double Bootstrap For Robust Linear Regression Inference, Statistica Sinica, (in press).

Veronika Rockova and Edward I. George (2017), Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity, Journal of the American Statistical Association, Theory and Methods, 111, pp. 1608-1622.

Abstract: Rotational transformations have traditionally played a key role in enhancing the interpretability of factor analysis via post-hoc modifications of the factor model orientation. Regularization methods also serve to achieve this goal by prioritizing sparse loading matrices. In this work, we cross-fertilize these two paradigms within a unifying Bayesian framework. Our approach deploys intermediate factor rotations throughout the learning process, greatly enhancing the effectiveness of sparsity inducing priors. These automatic rotations to sparsity are embedded within a PXL-EM algorithm, a Bayesian variant of parameter-expanded EM for posterior mode detection. By iterating between soft-thresholding of small factor loadings and transformations of the factor basis, we obtain (a) dramatic accelerations, (b) robustness against poor initializations and (c) better oriented sparse solutions. For accurate recovery of factor loadings, we deploy a two-component refinement of the Laplace prior, the spike-and-slab LASSO prior. The potential of the proposed procedure is demonstrated on both simulated and real high-dimensional data, which would render posterior simulation impractical.

Veronika Rockova and Edward I. George (2016), The Spike-and-Slab LASSO, Journal of the American Statistical Association, Theory and Methods, (in press).

Andreas Buja, Richard A. Berk, Lawrence D. Brown, Edward I. George, Arun Kumar Kuchibhotla, Linda Zhao (2016), Models as Approximations, Part II: A General Theory of Model-Robust Regression, Statistical Science, (submitted).