Description
The goal of this course is to provide necessary mathematical tools necessary to
perform research in not only computer perception, but also machine
learning, robotics, and probably any other continuous-math
intensive branch of Artificial Intelligence.
Instructor
CCB 241
(404)894-8591 (never pick it up - email much better...)
Office Hours: For now, drop by or send email to schedule an appointment.
Teaching Assistant
Raffay Hamid
raffay@cc.gatech.edu
Office hours: TBD
Course Administrator
Wanda Abbott
GVU Office, CCB 244 CCB
(404)894-0075
This course will cover a variety of intermediate to advanced mathematical theories and practices with the intent of making students more comfortable when taking a variety of numerically oriented AI courses such as Pattern Recognition, Machine Learning, Computational Perception or any of the robotics offerings.
As this is a survey of relevant topics there will be no specific text. Rather, we will make available chapters of various textbooks which in there totality will hopefully provide a good coverage. Copies will be handed out in class; if you miss them there they will be available in the GVU office from Wanda.
Texts that material will be drawn from:
·
Duda, Hart, and Stork, Pattern Classification 2nd
Edition, Wiley-Interscience
·
Gelb, Applied Optimal Estimation, MIT Press
·
Strang, Introduction to Applied Mathematics,
·
Press, Numerical Recipes in C,
·
Strang, Linear Algebra
·
Matlab Manuals (yes, these are often
unbelievably good sources of math background)
and more as we get to them.
The grades will be assessed as follows:
|
Problem Sets (not all PS are created equal) |
70% |
|
Final |
25% |
|
Class Participation |
5% |
There will be 5 or so bi-weekly problem sets that will involve some Matlab, sometimes plain old writing, and hopefully some thinking. Collaboration on problem sets is encouraged at the "white board interaction" level. That is, share ideas and technical conversation, but write your own code. All problem sets should be in on time. One late problem set is accepted late (but before the next one is due) without excuse. After that, get prior permission.
As this is a math class there will be a final, but as you can see from the grading it is not intended to be the dominant part of your grade.
This course is designed to be a first year or second year grad course. The syllabus is being designed (notice I did not say has been designed – this is a work in progress) in consultation with the other numerical-AI professors and will attempt to hit concepts seen as relevant to them. There are approximately 44 lectures this semester. Break down should be about the following:
|
Topics |
Lectures |
|
Matrices
and Lin Alg: positive definiteness, eigen everything, SVD, rank, conditioning, null spaces |
9 |
|
Probability:
discrete vs continuous, lots of Gaussians, other useful densities
KL-divergence, entropy, |
9 |
|
E/M
algorithms |
3 |
|
Minimization
Methods: various gradient methods, stochastic approaches, numerical issues |
6 |
|
Basic
Signal Manipulation: convolution, filter theory, Fourier/spectral
decomposition |
6 |
|
State-based
systems: recursive prediction and estimation, Kalman filtering, non-linear
filtering |
4 |
|
Coordinate
systems: Homogeneous,
transformations, quaternions |
2 |
|
Geometry:
perspective, homographies, projective, |
2 |
When possible we will use examples from computer vision, something close to my heart.
|
Date |
Title |
Assignments |
Handouts |
|
August 18 |
Intro |
Read Chapter 1, Strang Applied Math |
Syllabus (on line); Chapter 1, Strang
Applied Math |
|
20 |
Rows, Cols, and Pivots |
|
|
|
22 |
Pos Def Matrices |
|
|
|
25 |
Least Squares |
|
|
PS 1: Available: Aug 26. Due Sept 3. PDF is here. No matlab yet – just pencil.
PS 2: Available: Sept 12. Due Sept 19. PDF is here.
PS 3: Available: Sept 26. Due Oct 3. PDF is here.
PS 4: Available: Oct 14. Due Oct 22. PDF is here.
PS 5: Available: Nov 4th. Due *** NEW DATE*** Nov 14. PDF is here. The energy function data are available as either a MAT file or as ASCII. Both create the variables e1, e2, and e3.
You were so smart you didn’t need one…..