With increasingly "big" data available in biomedical research, deriving accurate and reproducible biology knowledge from such big data imposes enormous computational challenges. In this paper, motivated by recently developed stochastic block coordinate algorithms, we propose a highly scalable randomized block coordinate Frank-Wolfe algorithm for convex optimization with general compact convex c...

Influencer marketing has become a thriving industry with global market value expected to reach 15 billion dollars by 2022. The advertising problem that such agencies face is the following: given monetary budget find set of appropriate influencers can create and publish posts various types (e.g. text, image, video) for promotion target product. campaign's objective maximize across one or multipl...

We study a first-order method to find the minimum cross-sectional area ellipsoidal cylinder containing a finite set of points. This problem arises in optimal design in statistics when one is interested in a subset of the parameters. We provide convex formulations of this problem and its dual, and analyze a method based on the Frank-Wolfe algorithm for their solution. Under suitable conditions o...

In many signal processing applications, the aim is to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as “atoms” allow us to define “atomic norms” that can be used to formulate convex regularizations for the reconstruction problem. Efficient algorithms are available to solve these formulations in certain spe...

An important task in computational statistics and machine learning is to approximate a posterior distribution p(x) with an empirical measure supported on a set of representative points {xi}i=1. This paper focuses on methods where the selection of points is essentially deterministic, with an emphasis on achieving accurate approximation when n is small. To this end, we present Stein Points. The i...

This paper presents new consistent algorithms for multiclass learning with complex performance measures, defined by arbitrary functions of the confusion matrix. This setting includes as a special case all loss-based performance measures, which are simply linear functions of the confusion matrix, but also includes more complex performance measures such as the multiclass G-mean and micro F1 measu...

This paper considers a general class of iterative optimization algorithms, referred to as linearoptimization-based convex programming (LCP) methods, for solving large-scale convex programming (CP) problems. The LCP methods, covering the classic conditional gradient (CndG) method (a.k.a., Frank-Wolfe method) as a special case, can only solve a linear optimization subproblem at each iteration. In...

We consider the problem of finding a point in the intersection of an affine set with a compact convex set, called a convex linear system (CLS). The conditional gradient method is known to exhibit a sublinear rate of convergence. Exploiting the special structure of (CLS), we prove that the conditional gradient method applied to the equivalent minimization formulation of (CLS), converges to a sol...