Search · four archives
Search · four archives
26 papers · ranked by Valyu relevance
Amal Rannen Triki, Maxim Berman, Matthew B. Blaschko
Deep neural networks (DNNs) have become increasingly important due to their excellent empirical performance on a wide range of problems. However, regularization is generally achieved by indirect means, largely due to the complex set of functions defined by a network and the difficulty in measuring function complexity.…
Yuichi Yoshida, Takeru Miyato
We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as…
Guillaume Lecué, Shahar Mendelson
Our approach gives a common framework that may be used in the analysis of learning problems and regularization problems alike. In particular, it sheds some light on the role various notions of sparsity have in regularization and on their connection with the size of subdifferentials of Ψ in a neighbourhood of the true…
Shuo Chen, Qiong Wu, L. Elliot Hong
We consider group-level statistical inference for networks, where outcomes are multivariate edge variables constrained in an adjacency matrix. The graph notation is used to represent a network, where nodes are identical biological units (e.g. brain regions) shared across subjects and edge-variables indicate the…
Qianru Liu, Rui Wang, Yuesheng Xu, Mingsong Yan
We consider a regularization problem whose objective function consists of a convex fidelity term and a regularization term determined by the `1 norm composed with a linear transform. Empirical results show that the regularization with the `1 norm can promote sparsity of a regularized solution. It is the goal of this…
Meena Jagadeesan, Ilya Razenshteyn, Suriya Gunasekar
We provide a function space characterization of the inductive bias resulting from minimizing the `2 norm of the weights in multi-channel convolutional neural networks with linear activations and empirically test our resulting hypothesis on ReLU networks trained using gradient descent. We define an induced regularizer…
R. Flamary, N. Jrad, R. Phlypo, M. Congedo + 1 more
This work investigates the use of mixed-norm regularization for sensor selection in event-related potential (ERP) based brain-computer interfaces (BCI). The classification problem is cast as a discriminative optimization framework where sensor selection is induced through the use of mixed-norms. This framework is…
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…
Michaël Unser
The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L and on a generic Radon-domain norm. We establish the existence of a minimizer and…
Rixon Crane, Fred Roosta
We consider regularization of non-convex optimization problems involving a non-linear leastsquares objective. By adding an auxiliary set of variables, we introduce a novel regularization framework whose corresponding objective function is not only provably invex, but it also satisfies the highly desirable…
Md. Shoaibur Rahman
This article presents an overview of the generalized formulations of the computations, optimization, and tuning of a deep feedforward neural network. A small network has been used to systematically explain the computing steps, which were then used to establish the generalized forms of the computations in forward and…
Johannes Schwab, Stephan Antholzer, Markus Haltmeier
Deep learning and (deep) neural networks are emerging tools to address inverse problems and image reconstruction tasks. Despite outstanding performance, the mathematical analysis for solving inverse problems by neural networks is mostly missing. In this paper, we introduce and rigorously analyze families of deep…
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…
Baptiste Py, Francesco Ciucci
The distribution of relaxation times (DRT) has emerged as a promising method for analyzing electrochemical impedance spectroscopy (EIS) data. The standard approach for reconstructing the DRT from measured impedances consists of regularized regression, which usually leverages the Euclidean norm. In this work, we show…
Xin Gao, Xiaowen Xu, Weikai Li, Rui Li
Functional brain network (FBN) provides an effective biomarker for understanding brain activation patterns, which also improve the diagnostic criteria for neurodegenerative diseases or the information transmission of brain. Unfortunately, despite its efficiency, FBN still suffers several challenges for accurately…
Holger Mohr, Hannes Ruge
In certain modeling approaches, activation analyses of task-based fMRI data can involve a relatively large number of predictors. For example, in the encoding model approach, complex stimuli are represented in a high-dimensional feature space, resulting in design matrices with many predictors. Similarly, single-trial…
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…
Griffin S. Hampton, Ryan Neff, Zezheng Song, Mustapha Bouhrara + 2 more
Myelin water fraction (MWF) mapping in the central nervous system is a topic of intense research activity. One framework for this requires parameter estimation from a decaying biexponential signal. However, this is often an ill-posed nonlinear problem resulting in unreliable parameter estimates. For linear…
Marta Karas, Damian Brzyski, Mario Dzemidzic, Joaquin Goni + 3 more
A challenging problem arising in brain imaging research is principled incorporation of information from different imaging modalities. Frequently each modality is analyzed separately using, for instance, dimensionality reduction techniques which result in a loss of mutual information. We propose a novel regularization…
Authors not listed
Electrochemical impedance spectroscopy (EIS) coupled with distribution of relaxation times (DRT) analysis is a robust framework for characterizing electrochemical systems. However, DRT deconvolution is often plagued by spurious peaks, hindering accurate process identification and quantitative parameter estimation. To…
Leon Bungert, Martin Burger, Yury Korolev, Carola-Bibiane Schönlieb
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and convex duality for general data fidelity terms and regularisation functionals.…
Sanjar Adilov
Machine learning models for molecular-property prediction typically work with molecular representations in the form of fingerprints, descriptors, or graphs. In case of fingerprints and descriptors, molecular representations usually comprise thousands of features, which causes the curse of dimensionality for many…
Authors not listed
Real-world datasets in chemical engineering and bioengineering processes--such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials--can often be unlabelled or disorganized, rendering the training of existing supervised learning models ineffective at learning the…
Maxwell Venetos, Mingjian Wen, Kristin Persson
The nuclear magnetic resonance (NMR) chemical shift tensor is a highly sensitive probe of the electronic structure of an atom and furthermore its local structure. Re- cently, machine learning has been applied to NMR in the prediction of isotropic chemi- cal shifts from a structure. Current machine learning models…
Mary Pitman, David Hahn, Gary Tresadern, David Mobley
Drug discovery is accelerated with computational methods such as alchemical simulations to estimate ligand affinities. In particular, relative binding free energy (RBFE) simulations are beneficial for lead optimization. To use RBFE simulations to compare prospective ligands in silico, researchers first plan the…