11 papers · ranked by Valyu relevance
Kevin L. Keys, Hua Zhou, Kenneth Lange
Proximal distance algorithms combine the classical penalty method of constrained minimization with distance majorization. If f(x) is the loss function, and C is the constraint set in a constrained minimization problem, then the proximal distance principle mandates minimizing the penalized loss…
Sorin-Mihai Grad, Felipe Lara
We introduce and investigate a new generalized convexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly convex, and DC (difference of convex) functions that are prox-convex, however…
Stanley Osher, Howard Heaton, Samy Wu Fung
Title: Significance Many objective functions do not admit explicit formulas for their proximal operators. Moreover, these operators often cannot be estimated using exact gradients (e.g., when objectives are accessible via an oracle). In this work, we give a formula for accurately approximating proximal operators using…
Georg Hahn, Sharon M. Lutz, Nilanjana Laha, Christoph Lange
Penalized linear regression approaches that include an L_1_ term have become an important tool in statistical data analysis. One prominent example is the least absolute shrinkage and selection operator (Lasso), though the class of L_1_ penalized regression operators also includes the fused and graphical Lasso, the…
Yu Huo, Hongpei Li, Xiao Wang, Xiaochen Du + 1 more
When analysing two-dimensional data sets, scientists are often interested in regions where one variable depends linearly on the other. Typically they use an ad hoc method to do so. Here we develop a statistically rigorous, Bayesian approach to infer the optimal partitioning of a data set into contiguous piece-wise…
Georg Hahn, Sharon M. Lutz, Nilanjana Laha, Michael Cho + 2 more
High dimensional linear regression problems are often fitted using LASSO-type approaches. Although the LASSO objective function is convex, it is not differentiable everywhere, making the use of gradient descent methods for minimization not straightforward. To avoid this technical issue, we apply Nesterov smoothing to…
Junjie Xia, Hoang Van Phan, Luke Vistain, Mengjie Chen + 2 more
Proximity sequencing (Prox-seq) measures gene expression, protein expression, and protein complexes at the single cell level, using information from dual-antibody binding events and a single cell sequencing readout. Prox-seq provides multi-dimensional phenotyping of single cells and was recently used to track the…
Luke Vistain, Hoang Van Phan, Christian Jordi, Mengjie Chen + 2 more
Multiplexed analysis of single-cells enables accurate modeling of cellular behaviors, classification of new cell types, and characterization of their functional states. Here we present proximity-sequencing (Prox-seq), a method for simultaneous measurement of an individual cell’s proteins, protein complexes and mRNA.…
Fuchao Wu, Ming Zhang, Guanghui Wang, Zhanyi Hu + 1 more
Line triangulation, a classical geometric problem in computer vision, is to determine the 3D coordinates of a line based on its 2D image projections from more than two views of cameras with known projection matrices. Compared to point features, line segments are more robust to matching errors, occlusions, and image…
Jan Schröder, Yair Censor, Philipp Süss, Karl-Heinz Küfer
Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at finding a point that fulfills the constraints and has the minimal value of the…
C.S. Elder, Minh Hoang, Mohsen Ferdosi, Carl Kingsford
The Beltway and Turnpike problems entail the reconstruction of circular and linear one-dimensional point sets from unordered pairwise distances. These problems arise in computational biology when the measurements provide distances but do not associate those distances with the entities that gave rise to them. Such…