Estimating Mixture of Gaussian Processes by Kernel Smoothing

Water limitation regulates positive feedback of increased ecosystem respiration

Terrestrial ecosystem respiration increases exponentially with temperature, constituting a positive feedback loop accelerating global warming. However, the response of ecosystem respiration to temperature strongly depends on water availability, yet where and when the water effects are important, is presently poorly constrained, introducing uncertainties in climate-carbon cycle feedback projections. Here, we disentangle the effects of temperature and precipitation (a proxy for water availability) on ecosystem respiration by analysing eddy covariance CO2 flux measurements across 212 globally distributed sites. We reveal a threshold precipitation function, determined by the balance between precipitation and ecosystem water demand, which separates temperature-limited and water-limited respiration. Respiration is temperature limited for precipitation above that threshold function, whereas in drier areas water limitation reduces the temperature sensitivity of respiration and its positive feedback to global warming. If the trend of expansion of water-limited areas with warming climate over the last decades continues, the positive feedback of ecosystem respiration is likely to be weakened and counteracted by the increasing water limitation.

When Gaussian Process Meets Big Data: A Review of Scalable GPs

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process regression (GPR), a well-known nonparametric, and interpretable Bayesian model, which suffers from cubic complexity to data size. To improve the scalability while retaining desirable prediction quality, a variety of scalable GPs have been presented. However, they have not yet been comprehensively reviewed and analyzed to be well understood by both academia and industry. The review of scalable GPs in the GP community is timely and important due to the explosion of data size. To this end, this article is devoted to reviewing state-of-the-art scalable GPs involving two main categories: global approximations that distillate the entire data and local approximations that divide the data for subspace learning. Particularly, for global approximations, we mainly focus on sparse approximations comprising prior approximations that modify the prior but perform exact inference, posterior approximations that retain exact prior but perform approximate inference, and structured sparse approximations that exploit specific structures in kernel matrix; for local approximations, we highlight the mixture/product of experts that conducts model averaging from multiple local experts to boost predictions. To present a complete review, recent advances for improving the scalability and capability of scalable GPs are reviewed. Finally, the extensions and open issues of scalable GPs in various scenarios are reviewed and discussed to inspire novel ideas for future research avenues.

Mapping morphological shape as a high-dimensional functional curve

Detecting how genes regulate biological shape has become a multidisciplinary research interest because of its wide application in many disciplines. Despite its fundamental importance, the challenges of accurately extracting information from an image, statistically modeling the high-dimensional shape and meticulously locating shape quantitative trait loci (QTL) affect the progress of this research. In this article, we propose a novel integrated framework that incorporates shape analysis, statistical curve modeling and genetic mapping to detect significant QTLs regulating variation of biological shape traits. After quantifying morphological shape via a radius centroid contour approach, each shape, as a phenotype, was characterized as a high-dimensional curve, varying as angle θ runs clockwise with the first point starting from angle zero. We then modeled the dynamic trajectories of three mean curves and variation patterns as functions of θ. Our framework led to the detection of a few significant QTLs regulating the variation of leaf shape collected from a natural population of poplar, Populus szechuanica var tibetica. This population, distributed at altitudes 2000-4500 m above sea level, is an evolutionarily important plant species. This is the first work in the quantitative genetic shape mapping area that emphasizes a sense of 'function' instead of decomposing the shape into a few discrete principal components, as the majority of shape studies do.