Mathematical Modeling of Cognition
Wed. 10-12:30, Muen E317
Office hours: MW afternoons, TR mornings, some F afternoons. Drop in or email to set a time to meet.
Class time will be divided between tutorial-style lecture and group discussion of modeling articles. Tutorials will aim to convey the basic mathematical ideas, and articles will allow us to see how they are applied. Because this is a small and advanced group, even the tutorials should be significantly interactive; it is important that everyone keeps up and asks frequent questions. The goals of the article discussions will to understand the details of how each model was implemented, fitted, and tested; to consider alternative modeling approaches; and to critically analyze what explanatory work the model contributes to the research.
Exercises. Homework exercises will range from running code I provide and exploring minor modifications, to analyzing more complex properties of models or coding extensions. Students can choose how ambitious to be with these exercises depending on their level of experience.
Modeling project. Each student will develop and implement a model based on one (or more) of the frameworks we study. Ideally, you will apply the model to data of your own, possibly to some aspect of the data that you would not have otherwise considered. If this is not feasible, I can provide data for you to work with. A primary goal is for the project to be useful to your own research, rather than being a dead-end exercise. As with the class as a whole, the idea is to extend the range of tools you use to address your research questions. In keeping with this goal, writeups need not include extensive background theory or data-collection methods. Just focus on how the model was conceived, implemented, and evaluated. Conclusions should describe what the model tells you about your data (and the underlying psychological processes), and in particular how the model tells you more than you could learn from basic statistics or qualitative analysis.
Project timeline: Everyone should send me initial ideas on their projects by the end of September. If you’re unsure or would like suggestions, email me and we’ll plan a time to meet (also by the end of September). Everyone should have a concrete plan for their project by the end of October. The writeup will be due December 15.
All code used in class will be written in Matlab. See CU’s overview page and installation instructions for students or faculty (you can access only one or the other).
Class participation: 25%
Weekly exercises: 25%
Modeling project: 50%
A prioritization of modeling domains and frameworks will be decided by the class in the first week. Some options:
This will be updated as we go.
8/30: Introduction - Reinforcement learning and Rescorla-Wagner
9/6: Full Reinforcement Learning
9/13: Bayesian Inference
9/20: Bayesian Models
9/27: Bayes nets and MCMC
10/11: Fitting diffusion models
10/25: Hopfield networks
11/1: Boltzmann machines
11/8: More Boltzmann machines
11/29: Categorization and model translation
12/6: Reproducing-kernel Hilbert space
12/13: Function learning
University Policies (standard on all course syllabi)
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If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services in a timely manner so that your needs be addressed. Disability Services determines accommodations based on documented disabilities. Contact: 303-492-8671, Willard 322, and www.Colorado.EDU/disabilityservices
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Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender, gender variance, and nationalities. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. See policies at
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All students of the University of Colorado at Boulder are responsible for knowing and adhering to the academic integrity policy of this institution. Violations of this policy may include: cheating, plagiarism, aid of academic dishonesty, fabrication, lying, bribery, and threatening behavior. All incidents of academic misconduct shall be reported to the Honor Code Council (email@example.com; 303-725-2273). Students who are found to be in violation of the academic integrity policy will be subject to both academic sanctions from the faculty member and non-academic sanctions (including but not limited to university probation, suspension, or expulsion). Other information on the Honor Code can be found at