Search · four archives
Search · four archives
18 papers · ranked by Valyu relevance
Aleksandr Beknazaryan, Diego Oliva, Ali Rıza Yıldız
We show that neural networks with an absolute value activation function and with network path norm, network sizes and network weights having logarithmic dependence on $(1/ε)$ can $ε$-approximate functions that are analytic on certain regions of $Cd$.
Pei-Chang Guo
The convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around 1 in the training process. We propose a new Frobenius norm…
Ali Mahzarnia, Jun Song, Mihye Ahn
In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under a high-dimensional multivariate functional data setting. In particular, we develop two methods for functional group-sparse regression…
Silvia Gazzola, Sebastian James Scott, Alastair Spence, Fabiana Zama + 1 more
'Elena Loli Piccolomini'] Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-smooth regularization terms (e.g., total…
Nurdan Ayse Saran, Fatih Nar, Charles Elkan
This study presents a novel numerical approach that improves the training efficiency of binary logistic regression, a popular statistical model in the machine learning community. Our method achieves training times an order of magnitude faster than traditional logistic regression by employing a novel Soft-Plus…
Joseph Naiman, Peter Xuekun Song, S. Ejaz Ahmed, Farouk Nathoo
Motivated by mobile devices that record data at a high frequency, we propose a new methodological framework for analyzing a semi-parametric regression model that allow us to study a nonlinear relationship between a scalar response and multiple functional predictors in the presence of scalar covariates. Utilizing…
Zhuang Fang, Tang Liming, Wu Liang, Liu Hanxin
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{TV}_q-l_1$$\end{document} TV q - l 1 regularization model and the ADMM based algorithm Authors: ['Zhuang Fang'…
Stephan Antholzer, Markus Haltmeier, Fabiana Zama, Elena Loli Piccolomini
'Elena Loli Piccolomini'] Deep learning based reconstruction methods deliver outstanding results for solving inverse problems and are therefore becoming increasingly important. A recently invented class of learning-based reconstruction methods is the so-called NETT (for Network Tikhonov Regularization), which contains…
Huanlin Liu, Hongwei Ma, Hassan Jalali, Mohammadreza Amoozgar + 1 more
'Farzad Rafieian'] How to accurately identify unknown time-varying external force from measured structural responses is an important engineering problem, which is critical for assessing the safety condition of the structure. In the context of a few available accelerometers, this paper proposes a novel time-varying…
Nikita Doikov, Yurii Nesterov
In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to the square root of the norm of the current gradient. For the basic scheme, as applied to the…
Tomokaze Shiratori, Yuichi Takano, Jianchao Bai
Sparse estimation of a Gaussian graphical model (GGM) is an important technique for making relationships between observed variables more interpretable. Various methods have been proposed for sparse GGM estimation, including the graphical lasso that uses the ℓ1 norm regularization term, and other methods that use…
Ilias Rentzeperis, Luca Calatroni, Laurent U. Perrinet, Dario Prandi + 1 more
'Xue-Xin Wei'] Growing evidence indicates that only a sparse subset from a pool of sensory neurons is active for the encoding of visual stimuli at any instant in time. Traditionally, to replicate such biological sparsity, generative models have been using the ℓ1 norm as a penalty due to its convexity, which makes it…
Loïc Shi-Garrier, Nidhal Carla Bouaynaya, Daniel Delahaye, Boris Ryabko
'Boris Ryabko'] Despite their remarkable performance, deep learning models still lack robustness guarantees, particularly in the presence of adversarial examples. This significant vulnerability raises concerns about their trustworthiness and hinders their deployment in critical domains that require certified levels of…
Mehrsa Pourya, Sebastian Neumayer, Michael Unser
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theoretically. In contrast, our scheme is interpretable because it corresponds to the…
Chuan Bi, M. Yvonne Ou, Mustapha Bouhrara, Richard G. Spencer
We present a new regularization method for the solution of the Fredholm integral equation (FIE) of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method identifies solutions within a much larger function space, spanned by this set of…
Rina Foygel Barber, Emil Y. Sidky
The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $min{f(x)+g(y):Ax+By=c}$. ADMM exhibits robust empirical performance across a range of challenging settings including nonsmoothness and nonconvexity of the objective functions…
Yuhua Fan, Ilkka Launonen, Mikko J Sillanpää, Patrik Waldmann
High-dimensional genomic datasets contain complex patterns shaped by substantial biological noise, which pose major challenges for predictive modeling in genetics and breeding. Residual neural networks (ResNets) provide a powerful framework for capturing nonlinear genomic effects, but often overfit in settings where…
Elisa Davoli, Rita Ferreira, Carolin Kreisbeck, Hidde Schönberger
We introduce a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a general topological space. Our focus lies on the situation with non-compact parameter…