9 papers · ranked by Valyu relevance
Fabian Fröhlich, Peter K. Sorger
Ordinary differential equation (ODE) models are widely used to describe biochemical processes, since they effectively represent mass action kinetics. Optimization-based calibration of ODE models on experimental data can be challenging, even for low-dimensional problems. However, reliable model calibration is a…
Frank Dondelinger, Sach Mukherjee
We consider high-dimensional regression over subgroups of observations. Our work is motivated by biomedical problems, where disease subtypes, for example, may differ with respect to underlying regression models, but sample sizes at the subgroup-level may be limited. We focus on the case in which subgroup-specific…
Kazunori D Yamada
In the deep learning era, a gradient descent method is the most common method to optimize parameters of neural networks. Among various mathematical optimization methods, a gradient descent method is the most naive method. Although controlling a learning rate of the method is necessary for quick convergence, the…
Peter L. Bartlett, Chris Junchi Li, Jingfeng Wu, Bin Yu
In the field of optimization, developing accelerated methods for solving minimax and fixed-point problems remains a fundamental challenge. This paper presents a novel family of dual accelerated algorithms that achieve optimal convergence rates for both minimax and fixed-point problems. By exploring new anchoring…
Paul Stapor, Fabian Fröehlich, Jan Hasenauer
Parameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational efficiency. However, the computational complexity of established methods to evaluate the Hessian scales linearly with…
Leonard Schmiester, Daniel Weindl, Jan Hasenauer
Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence. Here, we propose an efficient…
Abbas Kazemipour, Behtash Babadi, Min Wu, Kaspar Podgorski + 1 more
We consider the problem of optimizing general convex objective functions with nonnegativity constraints. Using the Karush-Kuhn-Tucker (KKT) conditions for the nonnegativity constraints we will derive fast multiplicative update rules for several problems of interest in signal processing, including non-negative…
Christine H. Lind, Angela J. Yu
Several recent papers have studied the double descent phenomenon: a classic U-shaped empirical risk curve when the number of parameters is smaller or equal to the number of data points, followed by a decrease in empirical risk (referred to as “second descent”) as the number of features is increased past the…
Georges Czaplicki, Serge Mazeres
Model validation depends on the agreement between the predicted and experimental data. However, finding solutions to problems, described by equations with many parameters, for which virtually nothing is known, is a difficult task. For example, the extraction of kinetic parameters from complex schemes representing the…