ORIE Colloquium, 2014-05-05 - Suvrit Sra: Inexactness, Geometry, and Optimization: Recurrent Themes in Modern Data Analysis
From E. Cornelius
Monday, May 5 3 p.m. – Presentation – 253 Rhodes Hall Suvrit Sra Inexactness, geometry, and optimization: recurrent themes in modern data analysis The current data-age is witnessing an unprecedented confluence of disciplines, blurring traditional domain boundaries. But what aspects of data are driving this rich interaction? We can single out at least two: size and geometry. Today, I will talk about both size and geometry of data. In particular, I will demonstrate how a large number of machine learning problems (for instance regularized risk minimization, dictionary learning and matrix factorization) fall into a generic framework for scalable nonconvex optimization. I will highlight a few applications that have benefited from this framework, while commenting on ongoing and future work that strives for even greater scalability. Beyond size, I shall talk about "geometry", specifically geometric structure of data. My motivation lies in a number of applications of machine learning and statistics to data that are not just vectors, but richer objects such as matrices, strings, functions, graphs, trees, etc. Processing such data in their "intrinsic representation" can be of great value. Notably, we'll see examples where exploiting the data geometry allows us to efficiently minimize several nonconvex cost functions, not to local, but to global optimality! Time permitting, I will also mention some surprising connections of our work to areas well beyond machine learning and data analysis.