Differentiating the multipoint Expected Improvement for optimal batch design

This work deals with parallel optimization of expensive objective functions which are modeled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis' formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batch-sequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization

Some properties of the unified skew-normal distribution

For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia's measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, and closure with respect to conditioning on intervals

Habitat corridors facilitate genetic resilience irrespective of species dispersal abilities or population sizes

Corridors are frequently proposed to connect patches of habitat that have become isolated due to human‐mediated alterations to the landscape. While it is understood that corridors can facilitate dispersal between patches, it remains unknown whether corridors can mitigate the negative genetic effects for entire communities modified by habitat fragmentation. These negative genetic effects, which include reduced genetic diversity, limit the potential for populations to respond to selective agents such as disease epidemics and global climate change. We provide clear evidence from a forward‐time, agent‐based model (ABM) that corridors can facilitate genetic resilience in fragmented habitats across a broad range of species dispersal abilities and population sizes. Our results demonstrate that even modest increases in corridor width decreased the genetic differentiation between patches and increased the genetic diversity and effective population size within patches. Furthermore, we document a trade‐off between corridor quality and corridor design whereby populations connected by high‐quality habitat (i.e., low corridor mortality) are more resilient to suboptimal corridor design (e.g., long and narrow corridors). The ABM also revealed that species interactions can play a greater role than corridor design in shaping the genetic responses of populations to corridors. These results demonstrate how corridors can provide long‐term conservation benefits that extend beyond targeted taxa and scale up to entire communities irrespective of species dispersal abilities or population sizes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111750/1/eva12255.pd

A robust imputation method for missing responses and covariates in sample selection models

Sample selection arises when the outcome of interest is partially observed in a study. Although sophisticated statistical methods in the parametric and non-parametric framework have been proposed to solve this problem, it is yet unclear how to deal with selectively missing covariate data using simple multiple imputation techniques, especially in the absence of exclusion restrictions and deviation from normality. Motivated by the 2003-2004 NHANES data, where previous authors have studied the effect of socio-economic status on blood pressure with missing data on income variable, we proposed the use of a robust imputation technique based on the selection-t sample selection model. The imputation method, which is developed within the frequentist framework, is compared with competing alternatives in a simulation study. The results indicate that the robust alternative is not susceptible to the absence of exclusion restriction- a property inherited from the parent selection-t model- and performs better than models based on the normal assumption even when the data is generated from the normal distribution. Applications to missing outcome and covariate data further corroborate the robustness properties of the pro-posed method. We implemented the proposed approach within the MICE environment in R Statistical Software