Fast and robust bootstrap for multivariate inference: the R package FRB

We present the FRB package for R, which implements the fast and robust bootstrap. This method constitutes an alternative to ordinary bootstrap or asymptotic inference procedures when using robust estimators such as S-, MM- or GS-estimators. The package considers three multivariate settings: principal components analysis, Hotelling tests and multivariate regression. It provides both the robust point estimates and uncertainty measures based on the fast and robust bootstrap. In this paper we give some background on the method, discuss the implementation and provide various examples

Measuring Cluster Stability for Bayesian Nonparametrics Using the Linear Bootstrap

Clustering procedures typically estimate which data points are clustered together, a quantity of primary importance in many analyses. Often used as a preliminary step for dimensionality reduction or to facilitate interpretation, finding robust and stable clusters is often crucial for appropriate for downstream analysis. In the present work, we consider Bayesian nonparametric (BNP) models, a particularly popular set of Bayesian models for clustering due to their flexibility. Because of its complexity, the Bayesian posterior often cannot be computed exactly, and approximations must be employed. Mean-field variational Bayes forms a posterior approximation by solving an optimization problem and is widely used due to its speed. An exact BNP posterior might vary dramatically when presented with different data. As such, stability and robustness of the clustering should be assessed. A popular mean to assess stability is to apply the bootstrap by resampling the data, and rerun the clustering for each simulated data set. The time cost is thus often very expensive, especially for the sort of exploratory analysis where clustering is typically used. We propose to use a fast and automatic approximation to the full bootstrap called the "linear bootstrap", which can be seen by local data perturbation. In this work, we demonstrate how to apply this idea to a data analysis pipeline, consisting of an MFVB approximation to a BNP clustering posterior of time course gene expression data. We show that using auto-differentiation tools, the necessary calculations can be done automatically, and that the linear bootstrap is a fast but approximate alternative to the bootstrap.Comment: 9 pages, NIPS 2017 Advances in Approximate Bayesian Inference Worksho

Fast robust estimation of prediction error based on resampling

A

Robust bootstrap procedures for the chain-ladder method

Insurers are faced with the challenge of estimating the future reserves needed to handle historic and outstanding claims that are not fully settled. A well-known and widely used technique is the chain-ladder method, which is a deterministic algorithm. To include a stochastic component one may apply generalized linear models to the run-off triangles based on past claims data. Analytical expressions for the standard deviation of the resulting reserve estimates are typically difficult to derive. A popular alternative approach to obtain inference is to use the bootstrap technique. However, the standard procedures are very sensitive to the possible presence of outliers. These atypical observations, deviating from the pattern of the majority of the data, may both inflate or deflate traditional reserve estimates and corresponding inference such as their standard errors. Even when paired with a robust chain-ladder method, classical bootstrap inference may break down. Therefore, we discuss and implement several robust bootstrap procedures in the claims reserving framework and we investigate and compare their performance on both simulated and real data. We also illustrate their use for obtaining the distribution of one year risk measures

tRNA functional signatures classify plastids as late-branching cyanobacteria.

BackgroundEukaryotes acquired the trait of oxygenic photosynthesis through endosymbiosis of the cyanobacterial progenitor of plastid organelles. Despite recent advances in the phylogenomics of Cyanobacteria, the phylogenetic root of plastids remains controversial. Although a single origin of plastids by endosymbiosis is broadly supported, recent phylogenomic studies are contradictory on whether plastids branch early or late within Cyanobacteria. One underlying cause may be poor fit of evolutionary models to complex phylogenomic data.ResultsUsing Posterior Predictive Analysis, we show that recently applied evolutionary models poorly fit three phylogenomic datasets curated from cyanobacteria and plastid genomes because of heterogeneities in both substitution processes across sites and of compositions across lineages. To circumvent these sources of bias, we developed CYANO-MLP, a machine learning algorithm that consistently and accurately phylogenetically classifies ("phyloclassifies") cyanobacterial genomes to their clade of origin based on bioinformatically predicted function-informative features in tRNA gene complements. Classification of cyanobacterial genomes with CYANO-MLP is accurate and robust to deletion of clades, unbalanced sampling, and compositional heterogeneity in input tRNA data. CYANO-MLP consistently classifies plastid genomes into a late-branching cyanobacterial sub-clade containing single-cell, starch-producing, nitrogen-fixing ecotypes, consistent with metabolic and gene transfer data.ConclusionsPhylogenomic data of cyanobacteria and plastids exhibit both site-process heterogeneities and compositional heterogeneities across lineages. These aspects of the data require careful modeling to avoid bias in phylogenomic estimation. Furthermore, we show that amino acid recoding strategies may be insufficient to mitigate bias from compositional heterogeneities. However, the combination of our novel tRNA-specific strategy with machine learning in CYANO-MLP appears robust to these sources of bias with high accuracy in phyloclassification of cyanobacterial genomes. CYANO-MLP consistently classifies plastids as late-branching Cyanobacteria, consistent with independent evidence from signature-based approaches and some previous phylogenetic studies

Multivariate generalized S-estimators.

In this paper we introduce generalized S-estimators for the multivariate regression model. This class of estimators combines high robustness and high efficiency. They are defined by minimizing the determinant of a robust estimator of the scatter matrix of differences of residuals. In the special case of a multivariate location model, the generalized S-estimator has the important independency property, and can be used for high breakdown estimation in independent component analysis. Robustness properties of the estimators are investigated by deriving their breakdown point and the influence function. We also study the efficiency of the estimators, both a symptotically and a finite samples. To obtain inference for the regression parameters, we discuss the fast and robust boot strap for multivariate generalized S-estimators. The method is illustrated on several real data examples.bootstrap; efficiency; multivariate regression; robustness;