Posts
This page aims to contain technical tutorials written by Yilun (and collaborators) and some personal thoughts.
Some of them were done as a part of course project, others were done by pure personal interest.
Good Papers
Criteria: papers that I found motivating and useful such that I will review from time-to-time; many of them are pleasing to read; most of them discovered some fundamental truth that are neat and powerful.
Disclaimer: purely by personal taste; by no means a complete list in any subfield
[1922 Phil. Trans.] On the Mathematical Foundations of Theoretical Statistics
Comment: mind-blowing paper; set the tone for statistics
[1977 Scientific American] Stein’s Paradox in Statistics
Comment: clear, approachable, feels like reading a detective novel
[2008 KDD] Learning Classifiers from Only Positive and Unlabeled Data
Comment: seminal paper in Positive-Unlabeled learning
Inspiring point: Lemma 1 (which is surprising easy)
[2010 JMLR] Semi-Supervised Novelty Detection
Comment: a very tough (yet informative) paper to read
Inspiring point: connection to Neyman-Pearson classification
[2017 CVPR] Making Deep Neural Networks Robust to Label Noise: A Loss Correction Approach
Comment: clear (good intro of concepts), motivating as well as genuine
Inspiring point: a practical application designed (exactly) following the theory; extend binary to multi-class (non-trivial)
[2019 ICML] On Symmetric Losses for Learning from Corrupted Labels
Comment: good discussion and explanation; connects to "traditional examples" (Table 1)
Image of Prof. Alan V. Oppenheim, screen captured from the course lecture.
2020. 8 Recitation Class Slides for Signals & Systems Course
A distinguishing characteristic of Signal & System course is that it illustrates the strong connection between mathematics and the real world. The process of extracting useful information from seeming disordered signals, either via carefully-designed hardwares (e.g., envelope detector in AM radio), or algorithm based on concrete mathematical derivation (e.g., Nyquist-Shannon sampling theorem), arouses my interest to this course and the field of signal processing to the greatest extent.
I was very motivated by this course and started doing research thereafter. I become teaching assistant of this course for three times. Each time I review the course content, I feel the field of signal processing attracts me more.
I hold weekly recitation classes. Time after time, my notes got polished based on feedback from students - what's the transfer function :-) ? [source code of the notes]
2021.12 Compressive Sensing — RIP for Random Matrices
Compressive sensing is everywhere: as long as the number measurements is (much) smaller than the number of parameters we want to estimate. For example, in my own research on imaging for nuclear sources, the goal is to recover a high-resolution image from limited number of measurements: the number of pixels to recover is much larger than the number of measurements.
Gaussian random matrix is also used a lot in various fields of signal processing and computer science, far beyond the scope of compressive sensing.
In the EECS598 Randomized Numerical Linear Algebra course, I got a chance to study the fundamental theory on why (gaussian) random matrix is preferred in compressive sensing and why this randomized design of sensing matrix has better theoretical guarantee than **any** deterministic design.
(Notice that after we generate a realization from gaussian distribution, the matrix becomes deterministic, but the generating process is of random nature.)