Bayesian assessment of dimensionality in reduced rank regression

Stability Approach to Regularization Selection for Reduced-Rank Regression

The reduced-rank regression model is a popular model to deal with multivariate response and multiple predictors, and is widely used in biology, chemometrics, econometrics, engineering, and other fields. In the reduced-rank regression modelling, a central objective is to estimate the rank of the coefficient matrix that represents the number of effective latent factors in predicting the multivariate response. Although theoretical results such as rank estimation consistency have been established for various methods, in practice rank determination still relies on information criterion based methods such as AIC and BIC or subsampling based methods such as cross validation. Unfortunately, the theoretical properties of these practical methods are largely unknown. In this paper, we present a novel method called StARS-RRR that selects the tuning parameter and then estimates the rank of the coefficient matrix for reduced-rank regression based on the stability approach. We prove that StARS-RRR achieves rank estimation consistency, i.e., the rank estimated with the tuning parameter selected by StARS-RRR is consistent to the true rank. Through a simulation study, we show that StARS-RRR outperforms other tuning parameter selection methods including AIC, BIC, and cross validation as it provides the most accurate estimated rank. In addition, when applied to a breast cancer dataset, StARS-RRR discovers a reasonable number of genetic pathways that affect the DNA copy number variations and results in a smaller prediction error than the other methods with a random-splitting process.

Fine- and regional-scale genetic structure of the exotic ascidian Styela clava (Tunicata) in southwest England, 50 years after its introduction

Styela clava, an ascidian native to the northwest Pacific, was first recorded in the Atlantic at Plymouth, southwest England, in 1953. It now ranges in the northeast Atlantic from Portugal to northern Denmark, and has colonized the east coast of North America. Within the region of first introduction, we aimed to characterize current genetic diversity in the species, elucidate the respective roles of human-aided vs. natural dispersal, and assess the extent of larval dispersal by looking for genetic differentiation at very small scales. Eight sites, mostly marinas, were studied along c. 200 km of coast in southwest England encompassing Plymouth. Five microsatellite loci were genotyped in 303 individuals to analyse gene flow at regional (among sites) and fine (within sites) scales. F-statistics and assignment tests were used to investigate regional genetic structure. At the fine scale, deviation from mutation-drift equilibrium was tested, and isolation by distance and genetic clustering analyses were undertaken. Significant genetic differentiation existed between sites, unrelated to geographical separation; migration between geographically distant marinas was inferred, highlighting the likely importance of human-mediated dispersal in range expansion and occupancy by S. clava. Fine-scale population structure was present within at least four sites, which may be explained by the limited dispersal ability of this ascidian and recruitment from differentiated pools of larvae. Populations in enclosed marinas had higher self-recruitment rates than those in open sites. Some marinas might therefore function as reservoirs of propagules for subsequent spread, whereas others might be sinks for migrants.