arXiv subjects

Ali Saab

Publications and source records attributed to Ali Saab.

3 recordsLinked to original sources

arXiv2021

Impact of Airways Geometry on Transport of Gases to Blood

Topological structure of bronchial trees affects transport of gases and aerosols in the respiratory system. We start by providing a quantitative assessment of the ability of the alternative tree representations to predict observable geometric and mechanistic characteristics, such as network resistance, dead space volume, and path length. Then we present a model of dynamic transport of oxygen and carbon dioxide along the airways, in the alveoli, across the alveolar membrane, and along the pulmonary blood capillaries. The model also accounts for the exchange of these two gases with blood in the capillaries, as well as for age, gender and other in-species characteristics. Our model's predictions are compared with corresponding observations, providing an additional venue to assess the validity of the existing representations of the lung's bronchial tree.

physics.med-ph↗

arXiv2020

Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization

We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key importance in many high-dimensional statistical settings. However, exact computation of these estimators remains a major challenge. Indeed, modern exact methods, based on mixed integer programming (MIP), face difficulties when the number of features $p \sim 10^4$. In this work, we present a new exact MIP framework for $\ell_0\ell_2$-regularized regression that can scale to $p \sim 10^7$, achieving speedups of at least $5000$x, compared to state-of-the-art exact methods. Unlike recent work, which relies on modern commercial MIP solvers, we design a specialized nonlinear branch-and-bound (BnB) framework, by critically exploiting the problem structure. A key distinguishing component in our framework lies in efficiently solving the node relaxations using a specialized first-order method, based on coordinate descent (CD). Our CD-based method effectively leverages information across the BnB nodes, through using warm starts, active sets, and gradient screening. In addition, we design a novel method for obtaining dual bounds from primal CD solutions, which certifiably works in high dimensions. Experiments on synthetic and real high-dimensional datasets demonstrate that our framework is not only significantly faster than the state of the art, but can also deliver certifiably optimal solutions to statistically challenging instances that cannot be handled with existing methods. We open source the implementation through our toolkit L0BnB.

stat.CO↗

arXiv2018

Robust Designs via Geometric Programming

An approximate formulation of a robust geometric program (RGP) as a convex program is proposed. Interest in using geometric programs (GPs) to model complex engineering systems has been growing, and this has motivated explicitly modeling the uncertainties fundamental to engineering design optimization. RGPs provide a framework for modeling and solving GPs while representing their uncertainties as belonging to an uncertainty set. The RGP methodologies presented here are based on reformulating the GP and then robustifying it with methods from robust linear programming. These new methodologies, along with previous ones from the literature, are used to robustify two aircraft design problems, and the results of these different methodologies are compared and discussed.

math.OC↗