Talk Abstracts

Michael Friedlander, University of British Columbia

Time: 8:50 - 9:30
Title: Polar duality and atomic alignment.
Abstract: The aim of structured optimization is to assemble a solution, using a given set of atoms, to fit a model to data. Polarity, which generalizes the notion of orthogonality from linear sets to general convex sets, plays a special role in a simple and geometric form of convex duality. The atoms and their implicit “duals” share a special relationship, and their participation in the solution assembly depends on a notion of alignment. This geometric perspective leads to practical algorithms for large-scale problems.

Nathan Kutz, University of Washington

Time: 9:30 - 10:10
Title: Sparse regression for the discovery of governing equations in the physical and engineering sciences.
Abstract: A major challenge in the study of dynamical systems is that of model discovery: turning data into models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. This problem is made more difficult by the fact that many systems of interest exhibit parametric dependencies and diverse behaviors across multiple time scales. We introduce a number of data-driven strategies for discovering nonlinear dynamical systems and their embeddings from data. We consider two canonical cases: (i) systems for which we have full measurements of the governing variables, and (ii) systems for which we have incomplete measurements. For systems with full state measurements, we show that the recent sparse identification of nonlinear dynamical systems (SINDy) method can discover governing equations with relatively little data and introduce a sampling method that allows SINDy to scale efficiently to problems with multiple time scales and parametric dependencies. Specifically, we can discover distinct governing equations at slow and fast scales. For systems with incomplete observations, we show that using time-delay embedding coordinates can be used to obtain a linear model and Koopman invariant measurement system that nearly perfectly captures the dynamics of nonlinear quasiperiodic systems. Together, our approaches provide a suite of mathematical strategies for reducing the data required to discover and model nonlinear systems.

Heinz Bauschke, University of British Columbia

Time: 10:20 - 11:00
Title: Monotone operator theory, rugged Banach spaces, and the Gossez operator.
Abstract: The talk is organized in two parts. In the first half, I will make a case for the beauty of monotone operator theory and its usefulness in optimization. The second half concerns Stephen Simons’s recent work on the Gossez operator and the lack of convexity of a certain associated maximally monotone operator. Based on joint works with Walaa Moursi and Shawn Wang.

Minsun Kim, University of Washington

Time: 11:00 - 11:40
Title: Radiotherapy planning optimization using multiple modalities.
Abstract: Radiotherapy is currently one of the three major modalities to treat cancer patients along with surgery and chemotherapy. High-energy, ionizing radiation is used to kill cancerous cells; however, it also damages normal cells along its path. Therefore, the therapeutic effect of radiation is often limited by the normal tissue toxicity, and the goal of radiotherapy planning is to maximize the radiobiological damage to the tumor while keeping the normal tissue toxicity under its tolerable level. Photons are the most widely used radiation type in current practice. In the mid 1990’s, radiotherapy planning with photons achieved a big milestone with the introduction of an inverse planning technique, where the beam parameters are optimized to deliver desirable radiation dose distributions. More recently, there are emerging interests in using different types of radiation than photons to exploit their unique characteristics in dosimetry and radiobiological responses. It is currently unknown which modality is optimal and such investigation is mostly empirical. In this talk, we start discussing a brief history of inverse planning in radiotherapy and propose a first-ever optimization framework for multi-modality radiotherapy inverse planning, where two or more modalities are simultaneously optimized to maximize the therapeutic effect. Using the linear-quadratic cell survival model, this leads to non-convex QCQP. We present the algorithms to efficiently solve the problem using a proximal operator and the projection onto the constraint set. In addition, the radiation dose is typically delivered in many fractions to exploit the differential in the recovery time from radiation damage among different tissue types. We present a novel approach to optimize the number of fractions in the multi-modality setup, which can be easily specialized to a single-modality setup. We demonstrate the feasibility and potential benefits of our proposed framework using a simple, phantom case.

Hilal Asi, Stanford University

Time: 1:10 - 1:50
Title: The importance of better models in stochastic optimization.
Abstract: Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate models for stochastic minimization and learning problems that exhibit better robustness to problem families and algorithmic parameters. With appropriately accurate models, which we call the aProx family, stochastic methods can be made stable, provably convergent and asymptotically optimal; even modeling that the objective is nonnegative is sufficient for this stability. We extend these results beyond convexity to weakly convex objectives, which include compositions of convex losses with smooth functions common in modern machine learning applications. We highlight the importance of robustness and accurate modeling with a careful experimental evaluation of convergence time and algorithm sensitivity.

Daniel Shapero, University of Washington

Time: 1:50 - 2:30
Title: Two optimization problems in glacier physics.
Abstract: In this talk I’ll describe some of my work on modeling glacier flow and how optimization is used in this field. First, the conservation law that determines the velocity of a glacier can be described through a convex variational principle. Variational principles are a powerful tool for designing effective numerical solvers. Second, the ice temperature, bed friction, and bed topography are not directly observable at large scales via remote sensing. Estimating these fields from satellite measurements of ice velocity and surface elevation can be formulated as a constrained optimization problem. I’ve developed a set of tools for solving these (and other) problems in glacier physics called icepack, available at icepack.github.io. Finally, I’ll talk about some of my experiences working with physical scientists.

Anne Greenbaum, University of Washington

Time: 2:40 - 3:20
Title: Roundoff Error in High Performance Implementations of the Conjugate Gradient Algorithm.
Abstract: The conjugate gradient algorithm (CG) is a widely used iterative method for solving large symmetric positive definite linear systems Ax = b. It is unusual in that it does not behave the way exact arithmetic theory predicts, when implemented with standard floating point arithmetic. Consequently, a good deal of research dating back to the 1970’s has been aimed at explaining why practical implementations of the algorithm converge as well as they do, or why they converge at all. With the advent of parallel computing, different variants of the CG algorithm have been proposed to take better advantage of parallelism. With lower precision arithmetic now being used on many machines, what will be the effect on CG and related iterative methods? I will discuss these issues and what insight might be gained from the early analysis in order to devise stable and efficient CG implementations.

Peng Zheng, University of Washington

Time: 3:20 - 4:00
Title: Robust linear mixed effects models, with applications to meta-analysis of global health data.
Abstract: Meta-analysis synthesizes knowledge from all available studies to address scientific questions. In particular, meta-analyses guide global health policy and recommendations. However, studies and their estimates vary widely (study design, controlling for confounders, etc.) and there is currently no rigorous way to adjust for this variation in meta-analysis. To get a robust evidence score, we propose a mixed effects model that incorporates information about study design, and develop a robust extension for fitting general mixed effects models. With this model, we can estimate effects of inter-study variables on bias and heterogeneity, while eliminating the effect of outliers. The full approach requires multiple extensions, including constraints, priors, and spline modeling to accommodate dose-response relationships. We discuss the formulation and technical aspects of the fitting algorithm, and illustrate its impact on a range of examples in global health. This work is joint with Sasha Aravkin, Chris Murray, and the research team at the Institute for Health and Metrics Evaluations (IHME).