First workshop at the ECSSC 2021.
Optimization plays an important role in fitting many statistical models. Some examples include least squares, ridge and lasso regression, Huber regression, and support vector machines. CVXR is an R package that provides an object-oriented modeling language for convex optimization. It allows the user to formulate convex optimization problems in a natural mathematical syntax rather than the standard form required by most solvers. Moreover, problems can be easily modified and re-solved, making the package ideal for prototyping new statistical methods. First, the user specifies an objective and set of constraints by combining constants, variables, and parameters using a library of functions with known mathematical properties. CVXR then applies disciplined convex programming (DCP) to verify the problem's convexity. Once verified, the problem is automatically converted into quadratic or conic form and passed to a solver like OSQP, MOSEK, or GUROBI. We demonstrate CVXR's modeling framework with several applications in statistics and machine learning.
We will begin with a gentle introduction to convex optimization using examples from ordinary least squares and penalized regression. This will be followed by a high-level description of CVXR, how it differs from other packages, and a discussion of the domain specific language that CVXR implements. We will show how CVXR works on different classes of problems, such as linear programs, quadratic programs, and semidefinite programs, and demonstrate its usage with a variety of examples. Finally, we will have a segment for potential developers in which we go over the nuts and bolts of adding new functions to CVXR’s library.
About the presenter: Anqi Fu is a Ph.D candidate in the Electrical Engineering department at Stanford University. Her research focuses on developing algorithms and software for large-scale optimization with applications to data science. One of her recent projects leverages methods from optimal control to design treatment plans for cancer radiation therapy. Prior to starting her Ph.D, Anqi worked as a machine learning scientist at H2O.ai. She received an M.S. in Statistics from Stanford University, and a B.S. in Electrical Engineering and a B.A. in Economics from the University of Maryland, College Park.
Prerequisites: A working knowledge of statistics and linear algebra, and basic experience with a scripting language like R. We also invite attendees to bring problems of interest, which we will do our best to formulate and solve in CVXR.
Prior to the course, please follow the instructions under “Preparatory Steps” at this link. At a minimum, you will need to install the latest stable version of R and CVXR.
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