• • Jun Song (2019)

    On sufficient dimension reduction for functional data: Inverse moments based methods

    WIREs: Computational Statistics, In PRESS.

    In this article, we present methods of sufficient dimension reduction (SDR) for functional data and organize them in a unified framework. The current existing methods for multivariate, functional data, functional response, and nonlinear SDR for functional data are illustrated in a way that they are naturally generalized. If a covariance operator is defined on an infinite‐dimensional space, the inverse of it is not bounded. Thus it is difficult to estimate and even impossible to apply the conventional results. We present solutions to resolve the inverse issue for the methods of functional SDR. Then we explain the functional SDR methods in three different scenarios: scalar‐on‐function, function‐on‐function, nonlinear SDR for function‐on‐function problem.      
  • • Holly Holt, Gabriel Villar, Weiyi Cheng, Jun Song, and Christina Grozinger (2018)

    Molecular, physiological and behavioral responses of honey bee (Apis mellifera) drones to infection with microsporidian parasites

    Journal of Invertebrate Pathology, 155, 14--24.

    Susceptibility to pathogens and parasites often varies between sexes due to differences in life history traits and selective pressures. Nosema apis and Nosema ceranae are damaging intestinal pathogens of European honey bees (Apis mellifera). Nosema pathology has primarily been characterized in female workers where infection is energetically costly and accelerates worker behavioral maturation. Few studies, however, have examined infection costs in male honey bees (drones) to determine if Nosema similarly affects male energetic status and sexual maturation. We infected newly emerged adult drones with Nosema spores and conducted a series of molecular, physiological, and behavioral assays to characterize Nosema etiology in drones. We found that infected drones starved faster than controls and exhibited altered patterns of flight activity in the field, consistent with energetic distress or altered rates of sexual maturation. Moreover, expression of candidate genes with metabolic and/or hormonal functions, including members of the insulin signaling pathway, differed by infection status. Of note, while drone molecular responses generally tracked predictions based on worker studies, several aspects of infected drone flight behavior contrasted with previous observations of infected workers. While Nosema infection clearly imposed energetic costs in males, infection had no impact on drone sperm numbers and had only limited effects on antennal responsiveness to a major queen sex pheromone component (9-ODA). We compare Nosema pathology in drones with previous studies describing symptoms in workers and discuss ramifications for drone and colony fitness.      
  • • Bing Li and Jun Song (2017)

    Nonlinear sufficient dimension reduction for functional data

    The Annals of Statistics, 45, 1059--1095.

    We propose a general theory and the estimation procedures for nonlinear sufficient dimension reduction where both the predictor and the response may be random functions. The relation between the response and predictor can be arbitrary and the sets of observed time points can vary from subject to subject. The functional and nonlinear nature of the problem leads to construction of two functional spaces: the first representing the functional data, assumed to be a Hilbert space, and the second characterizing nonlinearity, assumed to be a reproducing kernel Hilbert space. A particularly attractive feature of our construction is that the two spaces are nested, in the sense that the kernel for the second space is determined by the inner product of the first. We propose two estimators for this general dimension reduction problem, and establish the consistency and convergence rate for one of them. These asymptotic results are flexible enough to accommodate both fully and partially observed functional data. We investigate the performances of our estimators by simulations, and applied them to data sets about speech recognition and handwritten symbols.      
  • • *Paul H. Jung and Jun Song(2019+)

    Multivariate Neighborhood Trajectory Analysis: A Critique and Propose of Functional Data Analysis Approach


  • • Jun Song and Bing Li (2018+)

    Nonlinear and additive principal component analysis for functional data


  • • Bing Li and Jun Song (2017+)

    Dimension reduction for functional data based on weak conditional moments


  • • Jun Song, Naomi S. Altman, and Kalyan Das (2018+)

    Self-modeling Nonlinear Poisson regression model

  • • Jun Song, Bing Li, and Hannu Oja (2018+)

    On functional Spearman's correlation and the related canonical correlation analysis

  • • Jun Song and Won Chang (2018+)

    Calibration of High-dimensional Spatial Data via nonlinear sufficient dimension reduction

  • • Jun Song, Kyongwon Kim, and Bing Li (2018+)

    Functional Sparse PCA

  • • Bing Li and Jun Song (2018+)

    Sufficient dimension reduction for general tensor product