Functional and Object-Oriented Data Analysis

Speakers

• Peter Hall (University of Melbourne, Australia; University of California, Davis)
• J. S. Marron (University of North Carolina, Chapel Hill)
• Hulin Wu (University of Rochester)
• Harrison Zhou (Yale University)

Description

This session focuses on analysis of functional data and object oriented data. The emerging field of object oriented data extends the very active research area of Functional Data Analysis and generalizes the fundamental FDA concept of curves as data points, to the more general concept of objects as data points. Examples include images, shapes of objects in 3D, points on a manifold, tree structured objects, and various types of movies. Five experts in these two areas will present both theoretical and applied work in both functional and object oriented data analysis. 

Schedule

Fri, June 22 - Location: STEW 206

Time	Speaker	Title
8:30-9:10AM	Peter Hall	Classification using Function Scraps
	Abstract: Function scraps are fragments of "whole" curves that are, at least conceptually, conventional random functions defined over a common domain. In particular, a function scrap is observed only over a subinterval of the common domain, and the subintervals are generally different for different scraps. Functional data of this type are increasingly common. We shall suggest new methods for reconstructing the whole functions, and for classifying function scraps.
9:15-9:55AM	J. S. Marron	Object Oriented Data Analysis: HDLSS Asymptotics
	Abstract: Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. On overview of insightful mathematical statistics for object data is given, based on High Dimension Low Sample Size asymptotics, where the dimension grows, but the sample size is fixed.
10:00-10:30AM	Break
10:30-11:10AM	Hulin Wu	Variable Selection for High-Dimensional Differential Equation Models with Applications to Systems Biology Research
	Abstract: Gene regulation is a complicated process. The interaction of many genes and their products forms an intricate biological network. Identification of this dynamic network will help us understand the biological process in a systematic way. However, the construction of such a dynamic network is very challenging for a high-dimensional system. We propose to use a set of ordinary differential equations (ODE), coupled with dimensional reduction by clustering and mixed-effects modeling techniques, to model the dynamic gene regulatory network (GRN). The ODE models allow us to quantify both positive and negative gene regulations as well as feedback effects of one set of genes in a functional module on the dynamic expression changes of the genes in another functional module, which results in a directed graph network. A six-step procedure, Screening, Clustering, Smoothing, regulation Identification, parameter Estimates refining and Function enrichment analysis (SCSIEF) is developed to identify the ODE-based dynamic GRN. In the proposed CSIEF procedure, a series of cutting-edge statistical methods and techniques are employed. We apply the proposed method to identify the dynamic GRN for yeast cell cycle progression data and immune response to influenza infection. We are able to annotate the identified modules through function enrichment analyses. Some interesting biological findings are discussed. The proposed procedure is a promising tool for constructing a general dynamic GRN and more complicated dynamic networks.
11:15-11:55	Harrison Zhou	Parameters Estimation for Differential Equations
	Abstract: Parameters estimation for differential equations arises in many fields of science and engineering with applications ranging from small scale industrial processes to the future global climate evolution. Traditional methods are often either computationally intensive or inaccurate for statistical inference. Recently, Ramsay, et. al. (2007, JRSSB) proposed a generalized profiling approach which sparked a lot of interesting discussions. However, statistical properties of this approach including consistency are largely unknown. In this talk, we will try to give a rigorous justification for their methodology, and as a consequence some theoretical guidelines are provided for selecting tuning parameters in their procedure.