Statistics Seminar: Cao

Our next statistics seminar is presented by Professor Jiguo Cao, who is visiting Sydney from Simon Fraser University, Vancouver, Canada. Please note this seminar is not held in our regular time.

Title: Functional Nonlinear Learning
Speaker: Prof. Jiguo Cao (Simon Fraser University)
Time and location : 11am-12pm on Wednesday, 25 Sep at Seminar Room 107 Law Annex, F10A.01.107.Law or Zoom

Abstract : Functional Data Analysis (FDA) is an emerging field in statistics that focuses on the analysis of curves, images, and multidimensional functions. A key feature of FDA is the treatment of each random function as an individual sample element. This type of data is common in areas such as longitudinal studies and brain imaging. Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual curves. The existing representation learning approaches in functional data analysis usually use linear mapping in parallel to those from multivariate analysis, e.g., functional principal component analysis (FPCA). However, functions, as infinite-dimensional objects, sometimes have nonlinear structures that cannot be uncovered by linear mapping. Linear methods will be more overwhelmed by multivariate functional data. In this talk, I will introduce two functional nonlinear learning (FunNoL) methods to sufficiently represent multivariate functional data in a lower-dimensional feature space. Furthermore, we merge a classification model for enriching the ability of representations in predicting curve labels. Hence, representations from FunNoL can be used for both curve reconstruction and classification. Additionally, we have endowed the proposed model with the ability to address the missing observation problem as well as to further denoise observations. The resulting representations are robust to observations that are locally disturbed by uncontrollable random noises. We apply the proposed FunNoL methods to several real data sets and show that FunNoL can achieve better classifications than FPCA, especially in the multivariate functional data setting. Simulation studies have shown that FunNoL provides satisfactory curve classification and reconstruction regardless of data sparsity.

Short Bio : Dr. Jiguo Cao holds the prestigious position of Canada Research Chair in Data Science and is a Professor in the Department of Statistics and Actuarial Science at Simon Fraser University, Burnaby, BC, Canada. His research areas focus on functional data analysis (FDA) and machine learning. In recognition of his outstanding contributions, Dr. Cao received the CRM-SSC Award in 2021, jointly conferred by the Statistical Society of Canada (SSC) and the Centre de recherches mathématiques (CRM).