Functional Data Analysis STAN 46 (7.5p)

Course description:
In many practical problems originating from areas like geophysical sciences, astronomy, medicine, etc., the observations often correspond to measurements of a continuous process, which is a function of time and/or space. With rapid advances in technology, such measurements are becoming more and more frequent, thus pushing the boundaries of highdimensional data analysis. In data science, high dimensional problems are often approached through dimension free analysis by treating an observation as a function. This is one way to circumvent the technical aspects identified with analyzing highdimensional data, and thus avoiding the curse of dimensionality. This course is meant to introduce the students to various aspects of dimension free analysis, which obviates the technical and computational hurdles associated with high dimensional data. This way of dealing with high dimensional data is an emerging and rapidly developing field that requires understanding both established methods and newly adopted techniques. The primary objective of this course will be to focus on the application of functional data analysis techniques to real world problems, and thus, mathematical rigor is often traded for adaptability to applications.
Beginning with the basics of the analysis of data that may be considered to be ``functions'', this course will discuss various visualization and data exploration techniques. Specifically, the course will extensively deal with nonparametric spline smoothing, functional linear models, functional PCA, regularization methods, analysis involving derivatives, registration and nonlinear smoothing.
Students are required to work on projects to apply the techniques on real world problems. The preferred software for this course will be `R' and/or Python, however, the students are permitted to use any mathematical software of their liking that have facilities to perform all task in the course (Matlab being one example). Project discussions will enable students to share and compare ideas with each other and to receive specific guidance from the instructors. Efforts will be made to help students to embed realworld problems into mathematical models so that suitable algorithms can be applied with consideration of computational constraints. By surveying special topics, students will be exposed growing range of new methodologies.
Learning outcomes:
Textbooks:
Supporting computer package:
All projects and exercises can be completed using
Week #  Day  Time and Location  Lecture/Lab/Discussion #  Material  Handouts/Reading material 

17  Monday, 23/04/2018  09:1511:00, E1:369 (Blue Room)  Lecture 1: : The concept of functional data and examples  Overview ,  
13:1515:00 E1:369 (Blue Room)  Lecture 2: Representing functional data in functional bases  Orthonormal bases  
Wednesday, 25/04/2018  09:1511:00 E1:369 (Blue Room)  Discussion 1: Basis decomposition of a function.  Assignment 1  
18  Wednesday, 02/05/2018  09:1511:00 E1:369 (Blue Room)  Lecture 3: Locality and smoothing: wavelets and splines  Wavelets and splines,  Code to be used in Lab 1 
15:1517:00, Alfa1:0043  Lab 1: Introduction to fda package, working with functional bases and regularization  Topics for Lab 1  
Friday, 04/05/2018  09:1511:00 E1:369 (Blue Room)  Discussion 2: Splines and regularization  Assignment 2  
19  Monday, 07/05/2018  09:1511:00 E1:369 (Blue Room)  Lecture 4: Exploratory data analysis of functional data  Descriptive functional statisitcs  
13:1515:00 E1:369 (Blue Room)  Lecture 5: Mathematical model of functional data  FDA model  
Wednesday, 09/05/2018  09:1511:00 E1:369 (Blue Room)  Discussion 3: Eigenfunctions  Assignment 3  
20  Monday, 14/05/2018  09:1511:00 E1:369 (Blue Room)  Lecture 6: Inference for functional data  Statistical Inference  Code to be used in Lab 2 
13:1515:00 E1:369 (Blue Room)  Lecture 7: Functional principal component analysis  FPCA  
Wednesday, 16/05/2018  09:1511:00  Lab 2: Smoothing and PCA  Lab 2  
21  Monday, 21/05/2018  10:1512:00 E1:369 (Blue Room)  Lecture 8: Functional linear models  Linear models  
13:1515:00 E1:369 (Blue Room)  Discussion 4: Functional regression  properties  Functional Regression  
Wednesday, 23/05/2018  09:1511:00  Lab 3: Data Analysis for linear models  
22  Monday, 28/05/2018  09:1511:00 E1:369 (Blue Room)  Lecture 9: Functional autoregressive models  
13:1515:00 E1:369 (Blue Room)  Discussion 5: Functional autoregression  
Wednesday, 30/05/2018  09:1511:00  Lab 4: Example with autoregressive functional data  
Friday, 01/06/2018  09:1511:00 E1:369 (Blue Room)  Lecture 10: Dynamical functional model  
09:1511:00  Lab 5: Example with dynamical functional data 
Comprehensive Exam: The work throughout the course will be compounded into one comprehensive examination paper. It will comprise three parts:
The final grades will be assigned according to the following table:
Percentage  Grade 

49  0  F 
54  50  E 
64  55  D 
74  65  C 
84  75  B 
100  85  A 