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Statistics Seminar - Dr. Bin Yu, University of California Berkeley: "Stability"

Event Type
Department of Statistics
Noyes Lab Room 165
Dec 2, 2013   12:00 - 1:15 pm  
Bin Yu (University of California at Berkeley)

Reproducibility is imperative for any scientific discovery. More 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 talk, 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 statis- tical 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 performane across over 2,000 voxels. Last, a novel “stability”

argument is seen to drive new results that shed light on the intriquing

interactions between sample to sample varibility 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.

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