9 papers · ranked by Valyu relevance
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
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…
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…
Wei Yang, Jacob Schreiber, Jeffrey Bilmes, William Stafford Noble
Analyzing and sharing massive single-cell RNA-seq data sets can be facilitated by creating a “sketch” of the data—a selected subset of cells that accurately represent the full data set. Using an existing benchmark, we demonstrate the utility of submodular optimization in efficiently creating high quality sketches of…
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…
Huaxu Yu, Puja Biswas, Elizabeth Rideout, Yankai Cao + 1 more
Liquid chromatography (LC) with gradient elution is a routine practice for separating complex chemical mixtures in mass spectrometry (MS)-based untargeted analysis. Despite its prevalence, systematic optimization of LC gradients has remained challenging. Here we develop a Bayesian optimization method, BAGO, for…
Maxwell W. Libbrecht, Jeffrey A. Bilmes, William Stafford Noble
Submodular optimization, a discrete analogue to continuous convex optimization, has been used with great success in many fields but is not yet widely used in biology. We apply submodular optimization to the problem of removing redundancy in protein sequence data sets. This is a common step in many bioinformatics and…
Madalina Ciortan, Matthieu Defrance
Subspace clustering identifies multiple feature subspaces embedded in a dataset together with the underlying sample clusters. When applied to omic data, subspace clustering is a challenging task, as additional problems have to be addressed: the curse of dimensionality, the imperfect data quality and cluster separation…
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…