The 290 courses cover current topics of research interest in electrical engineering. The course content may vary from semester to semester.

This 3-unit graduate level course introduces basic geometric and statistical concepts and principles of low-dimensional models for high-dimensional signal and data analysis, spanning basic theory, efficient algorithms, and diverse applications. We will discuss recovery theory, based on highdimensional geometry and non-asymptotic statistics, for sparse, low-rank, and low-dimensional models – including compressed sensing theory, matrix completion, robust principal component analysis, and dictionary learning etc. We will introduce principled methods for developing efficient optimization algorithms for recovering low-dimensional structures, with an emphasis on scalable and efficient first-order methods, for solving the associated convex and nonconvex problems. We will illustrate the theory and algorithms with numerous application examples, drawn from computer vision, image processing, audio processing, communications, scientific imaging, bioinformatics, information retrieval etc. The course will provide ample mathematical and programming exercises with supporting algorithms, codes, and data. A final course project will give students additional hands-on experience with an application area of their choosing. Throughout the course, we will discuss strong conceptual, algorithmic, and theoretical connections between low-dimensional models with other popular data-driven methods such as deep neural networks (DNNs), providing new perspectives to understand deep learning. Prerequisites: Linear algebra and probability. Background in signal processing, optimization, and statistics may allow you to appreciate better certain aspects of the course material, but not necessary all at once. If you’re curious about whether you would benefit from this course, contact the instructor for details. The course is open to senior undergraduates, with consent from the instructor.

MENG students are blocked from enrolling in this class because they will be enrolled by their advisor. Please contact your advisor for more information.

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