Rejoinder: One-step sparse estimates in nonconcave penalized likelihood models

We would like to take this opportunity to thank the discussants for their thoughtful comments and encouragements on our work [arXiv:0808.1012]. The discussants raised a number of issues from theoretical as well as computational perspectives. Our rejoinder will try to provide some insights into these issues and address specific questions asked by the discussants.Comment: Published in at http://dx.doi.org/10.1214/07-AOS0316REJ the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Monitoring Networked Applications With Incremental Quantile Estimation

Networked applications have software components that reside on different computers. Email, for example, has database, processing, and user interface components that can be distributed across a network and shared by users in different locations or work groups. End-to-end performance and reliability metrics describe the software quality experienced by these groups of users, taking into account all the software components in the pipeline. Each user produces only some of the data needed to understand the quality of the application for the group, so group performance metrics are obtained by combining summary statistics that each end computer periodically (and automatically) sends to a central server. The group quality metrics usually focus on medians and tail quantiles rather than on averages. Distributed quantile estimation is challenging, though, especially when passing large amounts of data around the network solely to compute quality metrics is undesirable. This paper describes an Incremental Quantile (IQ) estimation method that is designed for performance monitoring at arbitrary levels of network aggregation and time resolution when only a limited amount of data can be transferred. Applications to both real and simulated data are provided.Comment: This paper commented in: [arXiv:0708.0317], [arXiv:0708.0336], [arXiv:0708.0338]. Rejoinder in [arXiv:0708.0339]. Published at http://dx.doi.org/10.1214/088342306000000583 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Machine Learning Framework to Identify Individuals at Risk of Rapid Progression of Coronary Atherosclerosis: From the PARADIGM Registry.

Background Rapid coronary plaque progression (RPP) is associated with incident cardiovascular events. To date, no method exists for the identification of individuals at risk of RPP at a single point in time. This study integrated coronary computed tomography angiography-determined qualitative and quantitative plaque features within a machine learning (ML) framework to determine its performance for predicting RPP. Methods and Results Qualitative and quantitative coronary computed tomography angiography plaque characterization was performed in 1083 patients who underwent serial coronary computed tomography angiography from the PARADIGM (Progression of Atherosclerotic Plaque Determined by Computed Tomographic Angiography Imaging) registry. RPP was defined as an annual progression of percentage atheroma volume ≥1.0%. We employed the following ML models: model 1, clinical variables; model 2, model 1 plus qualitative plaque features; model 3, model 2 plus quantitative plaque features. ML models were compared with the atherosclerotic cardiovascular disease risk score, Duke coronary artery disease score, and a logistic regression statistical model. 224 patients (21%) were identified as RPP. Feature selection in ML identifies that quantitative computed tomography variables were higher-ranking features, followed by qualitative computed tomography variables and clinical/laboratory variables. ML model 3 exhibited the highest discriminatory performance to identify individuals who would experience RPP when compared with atherosclerotic cardiovascular disease risk score, the other ML models, and the statistical model (area under the receiver operating characteristic curve in ML model 3, 0.83 [95% CI 0.78-0.89], versus atherosclerotic cardiovascular disease risk score, 0.60 [0.52-0.67]; Duke coronary artery disease score, 0.74 [0.68-0.79]; ML model 1, 0.62 [0.55-0.69]; ML model 2, 0.73 [0.67-0.80]; all P<0.001; statistical model, 0.81 [0.75-0.87], P=0.128). Conclusions Based on a ML framework, quantitative atherosclerosis characterization has been shown to be the most important feature when compared with clinical, laboratory, and qualitative measures in identifying patients at risk of RPP

High-dimensional regression adjustments in randomized experiments

We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information, and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the average treatment effect. Our results considerably extend the range of settings where high-dimensional regression adjustments are guaranteed to provide valid inference about the population average treatment effect. We then propose cross-estimation, a simple method for obtaining finite-sample-unbiased treatment effect estimates that leverages high-dimensional regression adjustments. Our method can be used when the regression model is estimated using the lasso, the elastic net, subset selection, etc. Finally, we extend our analysis to allow for adaptive specification search via cross-validation, and flexible non-parametric regression adjustments with machine learning methods such as random forests or neural networks.Comment: To appear in the Proceedings of the National Academy of Sciences. The present draft does not reflect final copyediting by the PNAS staf

Variable selection using MM algorithms

Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and/or nonconcave. This article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions. These algorithms operate by perturbing the penalty function slightly to render it differentiable, then optimizing this differentiable function using a minorize-maximize (MM) algorithm. MM algorithms are useful extensions of the well-known class of EM algorithms, a fact that allows us to analyze the local and global convergence of the proposed algorithm using some of the techniques employed for EM algorithms. In particular, we prove that when our MM algorithms converge, they must converge to a desirable point; we also discuss conditions under which this convergence may be guaranteed. We exploit the Newton-Raphson-like aspect of these algorithms to propose a sandwich estimator for the standard errors of the estimators. Our method performs well in numerical tests.Comment: Published at http://dx.doi.org/10.1214/009053605000000200 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org