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Aleksandr Aravkin, UW
Meta-analysis with applications to global health
We present new developments for meta-analysis with applications to global health. For this talk, we confine the scientific context to effects of red meat consumption on heart disease and common cancers. Understanding these effects and their associated uncertainties is complicated by the nonlinear dose response mechanism, a complex relationship of reported outcomes to quantities of interest, and by between-study heterogeneity (disagreement).
We present new models that address these issues, highlight the underlying optimization problem, and present recent results on red meat that include all relevant studies. This talk is based on joint work with Peng Zheng, Chris Murray, and a large team of researchers and data analysts at the Institute for Health Metrics and Evaluation (IHME).
- Eldad Haber, Earth, Ocean and Atmospheric Science, UBCV
Optimization problems in deep neural networks
In this talk we will introduce the field of deep neural networks and discuss some optimization
algorithms and open problems in the field.
We will explore the reason that stochastic gradient descent has been so successful for the problem
as well as try to suggest new approaches to improve upon the technique.
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Tim Hoheisel, McGill University
Convex convex-composite functions
We study convex-composite functions that are fully convex.
In particular, we derive formulas for the conjugate and subdifferential of such functions.
Applications to conic programming, variational Gram functions and the matrix-fractional function are established.
- Bahbru Joshi, UBCV
Global Guarantees for Blind Demodulation with Generative Priors
In this talk, we will consider a deep learning inspired formulation for the blind demodulation problem, which is the task of recovering two unknown vectors from their entrywise multiplication. We consider the case where the unknown vectors are in the range of known deep generative models. In the case where the networks corresponding to the generative models are expansive and the weight matrices are random, we show that the empirical risk objective has a favorable landscape. That is, the objective function has a descent direction at every point outside of a small neighborhood around four hyperbolic curves. We also implement a gradient descent scheme inspired by the geometry of the objective function. We show that this gradient descent scheme can effectively remove distortions synthetically introduced to the MNIST dataset.
- Bala Krishnamoorthy, Math, WSU
Robust Feasibility Using Topological Degree Theory
We consider the problem of measuring the margin of robust feasibility of solutions to a system of nonlinear equations. We study the special case of a system of quadratic equations, which shows up in many practical applications such as the power grid and other infrastructure networks. This problem is a generalization of quadratically constrained quadratic programming (QCQP), which is NP-Hard in general. We develop approaches based on topological degree theory to estimate bounds on the robustness margin of such systems. We cast the problem of checking the conditions for robust feasibility as a nonlinear optimization problem. We then develop inner and outer bound procedures for this optimization problem, which could be solved efficiently to derive lower and upper bounds, respectively, for the margin of robust feasibility. We evaluate our approach numerically on instances taken from the MATPOWER database of AC power flow equations.
A preprint is available at https://arxiv.org/abs/1907.12206.
- Dominique Monnet, UBCO
Fast feasibility check of the multi-material vertical alignment problem in road design
When building a road, it is critical to select a vertical alignment which ensures design and safety constraints. Finding such a vertical alignment is not necessarily a feasible problem, and the models describing it generally involve a large number of variables and constraints. This talk presents a way to rapidly proving the feasibility or the infeasibility of a Mixed Integer Linear Program (MILP) modeling the vertical alignment problem. To do so, we take advantage of the particular structure of the MILP, and we prove that only a few of the MILP's constraints determine the feasibility of the problem. In addition, we propose a method to build a feasible solution to the MILP that does not involve integer variables.
- Hui Ouyang, UBCO
Convergence of Circumcentered isometry methods
This talk is mainly based on the recent work on circumcentered isometry methods by
Bauschke, Wang and Ouyang. The circumcentered isometry method is a generalization
of the circumcentered Douglas–Rachford method recently introduced by Behling, Bello
Cruz and Santos to accelerate the Douglas–Rachford method.
In this talk, we first present the properness of the circumcenter mapping induced by
isometries, which makes the circumcentered isometry method well-defined. Then by the
demiclosedness principle for circumcenter mapping, we show weak convergence results
for circumcentered isometry methods, which include the Douglas–Rachford method and
circumcentered reflection methods as special instances. We also provide sufficient conditions
for the linear convergence of circumcentered isometry methods.
At last, we display pictures on the performance of four circumcentered reflection methods,
Shadow Douglas–Rachford method and method of alternating projections for finding the best approximation
to the intersection of linear subspaces.
- Pooya Ronagh, 1QBit
Optimization techniques in quantum information processing
This talk is an introduction to the synergy between classical optimization and quantum information processing. On one hand, we discuss how optimization and control is used today for implementation of quantum information processing platforms. On the other hand, we will see how quantum algorithms, run on processors built as such, will provide quantum speed-up over classical algorithms for real-world applications. Through this presentation we will report on our recent results and several open areas in which optimization theorists can contribute to state-of-the-art in quantum computing.
- Vincent Roulet, UW
Restarts of accelerated gradient methods: theoretical speed-up and statistical interpretations
We present how restarts of universal fast gradient methods speed-up convergence under the additional generic assumption that the convex problem satisfy a Holderien error bound. This speed-up is obtained for all range of smoothness: from non-smooth to smooth passing by smoothable. The bounds are continuous with respect to unknown parameters allowing to build nearly optimal adaptive schemes by log-scale grid-search. We then present how sharp error bounds are derived from statistical properties in sparse recovery problems which enables to link computational complexity and statistical performance.
- Bruce Shepherd, CS, UBCV
Greedy Algorithms on Downwards-Closed Polytopes
Matroids are set systems which have been at the heart of many developments
in combinatorial optimization. Tom Jenkyns generalized this notion to set families he called p-systems
which include much more general families, such as intersections of p matroids. Jenkyn's Theorem
says that the greedy algorithm yields a factor-p approximation for maximizing
a modular objective over these families. We discuss a generalized version of his theorem which becomes
cleaner and simpler by thinking of linear optimization over downwards-closed polytopes.
