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Reception to follow.
Reproducibility is imperative for any scientific discovery. Often than not, modern scientific findings rely on statistical analysis of high-dimensional data. At a minimum, reproducibility manifests itself in stability of statistical results relative to “reasonable” perturbations to data and to the model used. Jacknife, bootstrap, and cross-validation are based on perturbations to data, while robust statistics methods deal with perturbations to models. In this article, a case is made for the importance of stability in statistics. Firstly, we motivate the necessity of stability of interpretable encoding models for movie reconstruction from brain fMRI signals. Secondly, we find strong evidence in the literature to demonstrate the central role of stability in statistical inference. Thirdly, a smoothing parameter selector based on estimation stability (ES), ES-CV, is proposed for Lasso, in order to bring stability to bear on cross-validation (CV). ES-CV is then utilized in the encoding models to reduce the number of predictors by 60% with almost no loss (1.3%) of prediction performance across over 2,000 voxels. Last, a novel “stability” argument is seen to drive new results that shed light on the intriguing interactions between sample to sample variability and heavier tail error distribution (e.g. double-exponential) in high dimensional regression models with p predictors and n independent samples. In particular, when p/n → κ ∈ (0.3, 1) and error is double-exponential, OLS is a better estimator than LAD.
Bin Yu is Chancellor's Professor in the Departments of Statistics and of Electrical Engineering & Computer Science at UC Berkeley. She has published over 100 scientific papers in premier journals in Statistics, EECS, remote sensing and neuroscience, in a wide range of research areas including empirical process theory, information theory (MDL), MCMC methods, signal processing, machine learning, high dimensional data inference (boosting and Lasso and sparse modeling in general), and interdisciplinary data problems. She has served on many editorial boards for journals such as Annals of Statistics, Journal of American Statistical Association, and Journal of Machine Learning Research.
She was a 2006 Guggenheim Fellow, co-recipient of the Best Paper Award of IEEE Signal Processing Society in 2006, and the 2012 Tukey Memorial Lecturer of the Bernoulli Society (selected every four years). She is a Fellow of AAAS, IEEE, IMS (Institute of Mathematical Statistics) and ASA (American Statistical Association).
She is currently President-Elect of IMS (Institute of Mathematical Statistics). She is serving on the Scientific Advisory Board of IPAM (Institute for Pure and Applied Mathematics) and on the Board of Mathematical Sciences and Applications of NAS. She was co-chair of the National Scientific Committee of SAMSI (Statistical and Applied Mathematical Sciences Institute), and on the Board of Governors of IEEE-IT Society.