Mathematical Algorithms for Artificial Intelligence and Big Data Analysis (Spring 2017)

Shuyang Ling E-mail: syling@math.ucdavis.edu
Office: MSB 2127, Office hours: F 12pm-1pm.

Course Objective:

Experiments, observations, and numerical simulations in many areas of science nowadays generate massive amounts of data. This rapid growth heralds an era of "data-centric science," which requires new paradigms addressing how data are acquired, processed, distributed, and analyzed. This course will cover mathematical concepts and algorithms that can deal with some of the challenges posed by Artificial Intelligence and Big Data. The course may be of interest to all those students dreaming of becoming a billionaire by starting the next Google--or if you simply want to get a job at Google, Facebook, Twitter, one of the hundreds of startups in AI, ... .

Linear algebra as well as basic experience in programming (preferably Matlab) will be required. Some basic knowledge in probability and optimization is helpful but not required. This class targets seniors or advanced juniors with knowledge how to write proofs, say at the level of MAT 125A.

• Brief overview of the aims of Artificial Intelligence and Machine Learning
• Principal Component Analysis, Singular Value Decomposition.
• Curse and Blessings of dimensionality. Strange phenomena in high dimensions
• Data clustering, k-means
• Dimension reduction. Johnson-Lindenstrauss, sketching, random projections.
• Graph Laplacian, spectral clustering, nonlinear dimension reduction.
• Diffusion maps, manifold learning, intrinsic geometry of massive data sets.
• Basic concepts of Deep Learning

There is no required textbook. The following books contains some material on these topics. But there is definitely no need to buy these books.


• C. Bishop. Pattern Recognition and Machine Learning.
• F. Cucker, D. X. Zho. Learning Theory: an approximation theory viewpoint.
• T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction.
• Yoshua Bengio. Learning Deep Architectures for AI.

See here for lecture notes.

Grading Scheme:

• 50% Homework
• 50% Final Project

I will assign homework about every other week. A subset of these problems will be graded. The homework will be announced at the homework page. Late homework will not be accepted.

For the Final Project you need to write a report on one of the following topics:
• Find a practical application yourself (not copying from papers/books) using the methods you learned in this course; describe how to use them; describe the importance of that application; what impact would you expect if you are successful?
• A report describing a thorough numerical comparison of existing algorithms related to one of the topics of this couse for a specific application or problem.