CCIMI Short Course: Mathematics of Data - From Theory to Computation

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This short course is organised by the CCIMI , and open to all. Lectures run 2-5pm, with two 15 minute breaks, Tuesday 13th March – Thursday 16th.

Instructor: Volkan Cevher (Laboratory For Information And Inference Systems, LIONS )

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.

It is useful for students to have a laptop/tablet (or even a smartphone) for some of the more practical examples, but this is not necessary. Those without computer access can follow a demo shown by the instructor.