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Principal components analysis (PCA) is a well-known technique for approximating a data set represented by a matrix by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in data analysis, such as… (More)

This paper describes Convex, a convex optimization modeling framework in Julia. Convex translates problems from a user-friendly functional language into an abstract syntax tree describing the problem. This concise representation of the global structure of the problem allows Convex to infer whether the problem complies with the rules of disciplined convex… (More)

The problem of maximizing a sum of sigmoidal functions over a convex constraint set arises in many application areas. This objective captures the idea of decreasing marginal returns to investment, and has applications in mathematical marketing, network bandwidth allocation, revenue optimization, optimal bidding, and lottery design. We define the sigmoidal… (More)

Doctors prescribe drugs for indications that are not FDA approved. Research indicates that 21% of prescriptions filled are for off-label indications. Of those, more than 73% lack supporting scientific evidence. Traditional drug safety alerts may not cover usages that are not FDA approved. Therefore, analyzing patterns of off-label drug usage in the clinical… (More)

- Madeleine Udell
- 2014

We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convex-ified version of the problem, in which each function in the objective is replaced by its convex envelope. We propose a randomized algorithm to solve the… (More)

We present matrix factorization as an enabling technique for analog-to-digital matrix multiplication (AD-MM). We show that factorization in the analog domain increases the total precision of AD-MM in precision-limited analog multiplication, reduces the number of analog-to-digital (A/D) conversions needed for overcomplete matrices, and avoids unneeded… (More)

We introduce the Stochastic Asynchronous Proximal Alternating Linearized Minimization (SAPALM) method, a block coordinate stochastic proximal-gradient method for solving nonconvex, nonsmooth optimization problems. SAPALM is the first asynchronous parallel optimization method that provably converges on a large class of nonconvex, nonsmooth problems. We prove… (More)

We present two modifications of the flux balance analysis (FBA) metabolic modeling framework which relax implicit assumptions of the biomass reaction. Our flexible flux balance analysis (flexFBA) objective removes the fixed proportion between reactants, and can therefore produce a subset of biomass reactants. Our time-linked flux balance analysis (tFBA)… (More)

This paper develops a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple,… (More)

—Broadband internet service providers (ISPs) are for-profit companies: they provide high speed internet service to customers in order to maximize revenue. Their revenue depends on prices they are able to charge the customers, which in turn depends on the data rates provided. This paper defines the revenue capacity of a communication channel as the maximum… (More)