Date 
Topic 
Instructor 
Scriber 
02/23/2016, Tue 
Lecture 00: Introduction to Course Syllabus [pdf]

Yuan Yao 

03/01/2016, Tue 
Lecture 01: Maximum Likelihood Estimate and Stein's Phenomenon [pdf]
[Homework 1]:
 Homework 1 [pdf]. Deadline: 3/08/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 

03/08/2016, Tue 
Lecture 02: Random Matrix Theory and Phase Transitions in PCA [pdf]
[Homework 2]:
 Homework 2 [pdf]. Deadline: 3/15/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 

03/15/2016, Tue 
Lecture 03: Geometry of PCA and MDS [pdf]
[Homework 3]:
 Homework 3 [pdf]. Deadline: 3/22/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 

03/22/2016, Tue 
Lecture 04: MDS and Random Projections [pdf]
[Homework 4]:
 Homework 4 [pdf]. Deadline: 3/29/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 
Zhu, Weizhi 
03/29/2016, Tue 
Lecture 05: Introduction to Compressed Sensing and High Dimensional Statistics: OMP, BP, LASSO, and ISS [pdf]
[Homework]: Enjoy the holiday break!

Yuan Yao 
Zhan, Ruohan Zhu, Weizhi 
04/05/2016, Tue 
Lecture 06: Robust PCA and Sparse PCA: SDP approach[pdf]
[Homework 5]:
 Homework 5 [pdf]. Deadline: 4/12/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 

04/12/2016, Tue 
Lecture 07: Generalized MDS (Sensor Network Localization): SDP approach[pdf]
[Homework 6]:
 Homework 6 [pdf]. Deadline: 4/19/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 

04/19/2016, Tue 
Lecture 08: Manifold Learning I: ISOMAP and LLE[pdf]
[Homework 7]:
 Homework 7 [pdf]. Deadline: 4/26/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 

04/26/2016, Tue 
Lecture 09: Manifold Learning II: generalized LLE  Laplacian, Hessian, Diffusion, LTSA, and VDM [pdf]
[Homework 8]:
 Homework 8 [pdf]. Deadline: 5/3/2016, Tuesday. Mark on the head of your homework: Name  Student ID.
[Project 1]:
 Mini Project 1 [pdf]. Deadline: 5/17/2016, Tuesday. Mark on the head of your homework: Name  Student ID.

Yuan Yao 

05/03/2016, Tue 
Lecture 10: PerronFrobenius Theory vs. PageRank and Fiedler/Cheeger Cut vs. Spectral Bipartition

Yuan Yao 

05/10/2016, Tue 
Lecture 11: Lumpable Markov Chains vs. Multiple Spectral Clustering and Transition Path Theory vs. Semisupervised Learning

Yuan Yao 

05/17/2016, Tue 
Lecture 12: An Introduction to Topological Data Analysis [pdf]
[Seminar]:
 Speaker: Dr. Ke Ye, Department of Statistics, University of Chicago
 Title: The distance between linear subspaces of different dimensions
 Abstract: The distance between linear subspaces of the same dimension is well known. Such a distance can be easily computed by singular value decomposition (SVD). In this talk, we first review classical results then we will discuss how to generalize the notion of the distance between linear subspaces of different dimensions, from the geometric point of view. Our results are based on the observation that for linear subspaces A, B of different dimensions, there are two natural candidates for the distance between A and B. It turns out that the two candidates actually coincide. With this observation, we are able to derive distances on the Sato grassmannian, which is defined as the union of all grassmannians. Such a distance can also be easily computed by SVD. If time permits, we also explain how to generalize our results to affine linear subspaces of different dimensions. This is a join work with LekHeng Lim.
 Reference: Ke Ye and LekHeng Lim Schubert varieties and distances between subspaces of different dimensions.

Yuan Yao 

05/18/2016, Tue 
Seminar: The Cohomology of the CryoEM problem
 Speaker: Dr. Ke Ye, Department of Statistics, University of Chicago
 Abstract: Cryoelectron microscopy (CryoEM) is a device to study the 3D structure of molecules. For a given type of molecule, we freeze samples rapidly in a thin layer of ice (without crystals). We take tomographic images of each sample to obtain a large collection of 2D images. The goal of the CryoEM problem is to reconstruct the 3D structure of the molecule from those 2D images. In this talk, we first present the Hadani  Singer model for the CryoEM problem and then we review necessary results from algebraic topology. Lastly, we relate the data obtained from 2D projection images to the cohomology of a two dimensional simplicial complex with coefficient in SO(2). This is a joint work with LekHeng Lim.

Yuan Yao 

05/24/2016, Tue 
Lecture 13: Applied Hodge Theory[pdf]
[Reference]:
 Xiaoye Jiang, LekHeng Lim, Yuan Yao, and Yinyu Ye. Statistical ranking and combinatorial Hodge theory. Mathematical Programming, Volume 127, Number 1, Pages 203244, 2011. http://arxiv.org/abs/0811.1067.
 O. Candogan, I. Menache, A. Ozdaglar and P. A. Parrilo. Flows and Decompositions of Games: Harmonic and Potential Games . Mathematics of Operations Research, Vol. 36, No. 3, 2011, pp. 474503. http://arxiv.org/abs/1005.2405.
 Qianqian Xu, Qingming Huang, Tingting Jiang, Bowei Yan, Weisi Lin, and Yuan Yao. HodgeRank on Random Graphs for Subjective Video Quality Assessment. IEEE Transactions on Multimedia, 14(3):844857, 2012.
 Qianqian Xu, Jiechao Xiong, Qingming Huang, and Yuan Yao. Online HodgeRank on Random Graphs for Crowdsourceable QoE Evaluation.
IEEE Transactions on Multimedia, 16(2):373386, Feb. 2014.
 Qianqian Xu, Jiechao Xiong, Qingming Huang, and Yuan Yao. Robust Evaluation for Quality of Experience in Crowdsourcing. ACM Multimedia 2013.
 Yanwei Fu, Timothy M. Hospedales, Tao Xiang, Jiechao Xiong, Shaogang Gong, Yizhou Wang, and Yuan Yao.
Robust Subjective Visual Property Prediction from Crowdsourced Pairwise Labels. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), vol.38, no.3, pp. 563577, March 2016.
 IMA Workshop on Modern Applications of Homology and Cohomology, 2013

Yuan Yao 

05/31/2016, Tue 
Lecture 14: Final Project [pdf]

Yuan Yao 
