arXiv subjects

Noah Simon

Publications and source records attributed to Noah Simon.

40 records · Page 3Linked to original sources

arXiv2013

On Estimating Many Means, Selection Bias, and the Bootstrap

With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated to be most extreme. Unfortunately naive estimates of these effect-sizes (even after potentially accounting for multiplicity in a testing procedure) can be severely biased. In this manuscript we explore this bias from a frequentist perspective: we give a formal definition, and show that an oracle estimator using this bias dominates the naive maximum likelihood estimate. We give a resampling estimator to approximate this oracle, and show that it works well on simulated data. We also connect this to ideas in empirical Bayes.

stat.ML↗

arXiv2012

A Permutation Approach to Testing Interactions in Many Dimensions

To date, testing interactions in high dimensions has been a challenging task. Existing methods often have issues with sensitivity to modeling assumptions and heavily asymptotic nominal p-values. To help alleviate these issues, we propose a permutation-based method for testing marginal interactions with a binary response. Our method searches for pairwise correlations which differ between classes. In this manuscript, we compare our method on real and simulated data to the standard approach of running many pairwise logistic models. On simulated data our method finds more significant interactions at a lower false discovery rate (especially in the presence of main effects). On real genomic data, although there is no gold standard, our method finds apparent signal and tells a believable story, while logistic regression does not. We also give asymptotic consistency results under not too restrictive assumptions.

stat.ML↗

arXiv2011

Discriminant Analysis with Adaptively Pooled Covariance

Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and classify using Bayes theorem. With LDA, we estimate a single, pooled covariance matrix, while for QDA we estimate a separate covariance matrix for each group. Rarely do we believe in a homogeneous covariance structure between groups, but often there is insufficient data to separately estimate covariance matrices. We propose L1- PDA, a regularized model which adaptively pools elements of the precision matrices. Adaptively pooling these matrices decreases the variance of our estimates (as in LDA), without overly biasing them. In this paper, we propose and discuss this method, give an efficient algorithm to fit it for moderate sized problems, and show its efficacy on real and simulated datasets.

stat.ML↗

arXiv2010

Strong rules for discarding predictors in lasso-type problems

We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui et al (2010) propose "SAFE" rules that guarantee that a coefficient will be zero in the solution, based on the inner products of each predictor with the outcome. In this paper we propose strong rules that are not foolproof but rarely fail in practice. These can be complemented with simple checks of the Karush- Kuhn-Tucker (KKT) conditions to provide safe rules that offer substantial speed and space savings in a variety of statistical convex optimization problems.

math.ST↗