This course will cover advanced topics at the intersection of probabilistic modeling, neural computation, and artificial intelligence, with an emphasis on approaches using generative models. Students will develop a deep understanding of how probability theory provides a unified framework for understanding the human brain and intelligence more broadly. Topics include fundamental concepts in probability theory and philosophical foundations of uncertainty, methods for learning and inference in probabilistic models, and probabilistic methods in machine learning like VAEs. The course will cover how probabilistic models have contributed to our understanding of learning, perception, and decision-making. The course will emphasize both theoretical foundations and practical implementations, preparing students to engage with current research in computational neuroscience and AI. Prior exposure to linear algebra, multivariable calculus, machine learning, and probability theory are all recommended.

This course will introduce students to foundational concepts in numerical computation that are useful for engineering and the mathematical, computational, and physical sciences. Topics will include floating-point arithmetic, error analysis, linear and nonlinear equations, numerical solution of systems of algebraic equations, constrained and unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, and basic methods for sampling stochastic processes. Implementation of various numerical methods and solvers will be done in Python, MATLAB, and R. Connections to computational modeling of cognition will be made throughout the course as motivating examples for various key concepts and tools.

This course will cover advanced topics at the intersection of probabilistic modeling, neural computation, and artificial intelligence, with an emphasis on approaches using generative models. Students will develop a deep understanding of how probability theory provides a unified framework for understanding the human brain and intelligence more broadly. Topics include fundamental concepts in probability theory and philosophical foundations of uncertainty, methods for learning and inference in probabilistic models, and probabilistic methods in machine learning like VAEs. The course will cover how probabilistic models have contributed to our understanding of learning, perception, and decision-making. The course will emphasize both theoretical foundations and practical implementations, preparing students to engage with current research in computational neuroscience and AI. Prior exposure to linear algebra, multivariable calculus, machine learning, and probability theory are all recommended.

This course is to fulfill the work plan agreed by the student and the dissertation adviser. The guiding principle of the Dissertation Research course is to complete the doctoral dissertation research proposed by the doctoral candidate and approved by the candidate’s dissertation committee. The course consists of carrying out the thesis research, including collection and analysis of data, and completion and public defense of the dissertation document for partial fulfillment of the requirements of the PhD degree in Cognitive Science. This course can only be taken after successful completion of COGS-800 Cognitive Science Qualifying Examination.

An introduction to the underlying concepts of computer vision and image understanding. The course will consider fundamental topics, including image formation, edge detection, texture analysis, color, segmentation, shape analysis, detection of objects in images and high level image representation. Depending on the interest of the class, more advanced topics will be covered, such as image database retrieval or robotic vision. Programming assignments are an integral part of the course. Note: students who complete CSCI-431 may not take CSCI-631 for credit.