Tue, 3:20-5:00pm, in 60 5th Av, C10
Thu, 6.45- 7.35pm in 60 5th Av, C12
Cristina Savin, csavin@nyu.edu Office hours: Mo, 4-5pm, Room 608
Yiqiu (Artie) Shen, ys1001@nyu.edu Office hours: Thu, 11am-12pm, Room 660
This graduate level course presents fundamental tools for characterizing data with statistical dependencies over time, and using this knowledge for predicting future outcomes. These methods have broad applications from econometrics to neuroscience. The course emphasizes generative models for time series, and inference and learning in such models. We will cover range of approaches including AR(I)MA, Kalman Filtering, HMMs, Gaussian Processes, and their application to several kinds of data.
Note: information presented is tentative, syllabus may be subject to change as the course progresses.
problem sets (35%) + midterm exam (25%) + final project (25%) + participation (15%).
We will use Piazza to answer questions and post announcements about the course. Students' use of Piazza, in particular answering other students' questions well, will contribute to the participation grade.
Lecture videos will be posted to NYU Classes. Class attendance is still required.
| Date | Lecture | Extras | |
|---|---|---|---|
| Jan.23 | Lecture 1: Logistics. Introduction. Basic statistics for characterizing time series. | Shumway Stoffer Ch.1 | |
| Jan.25 | Lab1: Simulating simple stochastic processes. Basic statistics. | ||
| Jan.30 | Lecture 2: AR(I)MA | Shumway Stoffer Ch.3 | |
| Febr.1 | Lab 2: AR(I)MA | Problem set 1, solution, due Febr. 12 | |
| Febr.6 | Lecture 3: LDS; Kalman filtering | kalmanderivations.pdf | Brainstorm project ideas |
| Febr.8 | Lab 3: Basic probability review. LDS inference | Project proposal due Febr. 27 | |
| Febr.13 | EM. Particle filtering | LDSlearning.pdf, particlefiltering.pdf | |
| Febr.15 | Lab LSD: learning | ||
| Febr.20 | Lecture 4: HMMs | hmms.pdf | Problem set 2, due March 2 |
| Febr.22 | Lab 4: HMMs | Problem set 3, due March 22 | |
| Febr.27 | Lecture 5: An unified view of linear models. Beyond linear. | Roweis and Ghahramani, 1999 | |
| March 1 | Lab 5: Revisiting ARIMA, focus on applications | arima.pdf | |
| March 6 | Midterm | ||
| March 8 | No lab | ||
| March 20 | Guest lecture: State space models in the brain, Il Memming Park | ||
| March 22 | No lab | ||
| March 27 | Lecture 6: GP basics | ||
| March 29 | Lab: GP | ||
| April 3 | Guest lecture: RNNs Kyunghyun Cho | ||
| April 5 | Recitation: read discuss RNNs state of the art | ||
| April 10 | Lecture 7 GP advanced topics: overcoming computational limitation; extrapolation SM kernels. | ||
| April 12 | Lab 7: GP | Problem set 4, due April 20 | |
| April 17 | Lecture 8 Spectral methods | ||
| April 19 | Lab 8 | ||
| April 24 | Lecture 9 Spectral methods 2 | ||
| April 26 | Lab 9 | ||
| May 1 | Final projects presentation | Corresponding reports due April 26! |
There is no required textbook. Assigned readings will come from freely-available online material.
- Time series analysis and its applications, by Shumway and Stoffer, 4th edition (freely available pdf)
- Pattern recognition and machine learning, Bishop
- Gaussian processes Rassmussen & Williams, (materials freely available online, including gpml library)
- Review notes from Stanford's machine learning class
- Sam Roweis's probability review
- Carlos Ferndandez's notes on Statistics and Probability for Data Science DS-GA 1002
We expect you to try solving each problem set on your own. However, if stuck you should discuss things with other students in the class, subject to the following rules:
- Brainstorming and verbally discussing the problem with other colleagues ok, going together through possible solutions, but should not involve one student telling another a complete solution.
- Once you solve the homework, you must write up your solutions on your own.
- You must write down the names of any person with whom you discussed it. This will not affect your grade.
- Do not consult other people's solutions from similar courses.
During the full semester you are allowed a total of maximum of 5 days extension on homework assignments. Each day comes with a penalty of 20% off your assignment.