Patrick R. Johnstone
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View article: Problem-dependent convergence bounds for randomized linear gradient compression
Problem-dependent convergence bounds for randomized linear gradient compression Open
In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss, co…
View article: Pathway-based analyses of gene expression profiles at low doses of ionizing radiation
Pathway-based analyses of gene expression profiles at low doses of ionizing radiation Open
Radiation exposure poses a significant threat to human health. Emerging research indicates that even low-dose radiation once believed to be safe, may have harmful effects. This perception has spurred a growing interest in investigating the…
View article: Density estimation via measure transport: Outlook for applications in the biological sciences
Density estimation via measure transport: Outlook for applications in the biological sciences Open
One among several advantages of measure transport methods is that they allow or a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results …
View article: Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciences
Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciences Open
One among several advantages of measure transport methods is that they allow for a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results…
View article: Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers
Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers Open
We present a new, stochastic variant of the projective splitting (PS) family of algorithms for monotone inclusion problems. It can solve min-max and noncooperative game formulations arising in applications such as robust ML without the con…
View article: Convergence Rates for Projective Splitting
Convergence Rates for Projective Splitting Open
Projective splitting is a family of methods for solving inclusions involving\nsums of maximal monotone operators. First introduced by Eckstein and Svaiter in\n2008, these methods have enjoyed significant innovation in recent years,\nbecomi…
View article: Projective Splitting with Forward Steps: Asynchronous and Block-Iterative Operator Splitting
Projective Splitting with Forward Steps: Asynchronous and Block-Iterative Operator Splitting Open
This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental subprobl…
View article: Accelerated first-order optimization methods using inertia and error bounds
Accelerated first-order optimization methods using inertia and error bounds Open
Optimization is an important discipline of applied mathematics with far-reaching applications. Optimization algorithms often form the backbone of practical systems in machine learning, image processing, signal processing, computer vision, …
View article: Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite\n Optimization
Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite\n Optimization Open
We study the convergence properties of a general inertial first-order\nproximal splitting algorithm for solving nonconvex nonsmooth optimization\nproblems. Using the Kurdyka--\\L ojaziewicz (KL) inequality we establish new\nconvergence rat…
View article: Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite Optimization
Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite Optimization Open
We study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka--Łojaziewicz (KL) inequality we establish new convergence rates whi…