Instructor
Prof. Volkan Cevher
Description
Convex optimization offers a unified framework in obtaining numerical solutions to data analytics problems with provable statistical guarantees of correctness at well-understood computational costs.
To this end, this course reviews recent advances in convex optimization and statistical analysis in the wake of Big Data. We provide an overview of the emerging convex data models and their statistical guarantees, describe scalable numerical solution techniques such as stochastic, first-order and primal-dual methods. Throughout the course, we put the mathematical concepts into action with large-scale applications from machine learning, signal processing, and statistics.
Throughout the course, we put the mathematical concepts into action with large-scale applications from machine learning, signal processing, and statistics.
Learning outcomes
By the end of the course, the students are expected to understand the so-called time-data tradeoffs in data analytics. In particular, the students must be able to
- Choose an appropriate convex formulation for a data analytics problem at hand
- Estimate the underlying data size requirements for the correctness of its solution
- Implement an appropriate convex optimization algorithm based on the available computational platform
- Decide on a meaningful level of optimization accuracy for stopping the algorithm
- Characterize the time required for their algorithm to obtain a numerical solution with the chosen accuracy
Prerequisites
Previous coursework in calculus, linear algebra, and probability is required. Familiarity with optimization is useful.