Related papers: The neural network approach to parton distribution…
Neural networks have been able to achieve groundbreaking accuracy at tasks conventionally considered only doable by humans. Using stochastic gradient descent, optimization in many dimensions is made possible, albeit at a relatively high…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…
We consider minimization of a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of distributed…
Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution -- also theoretically not understood -- concerns their ability to serve as generative models for complicated types of data such as images…
We propose a generic ansatz for the extension of parton distributions of the real photon to those of the virtual photon. Alternatives and approximations are studied that allow closed-form parametrizations.
In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In…
A short review of problems with parton distribution functions in nucleons, non-polarized and polarized, is given. The main part is devoted to the transversity distribution its possible measurement and its first experimental probe via spin…
Generalised parton distributions are instrumental to study both the three-dimensional structure and the energy-momentum tensor of the nucleon, and motivate numerous experimental programmes involving hard exclusive measurements. Based on a…
Nuclear parton distribution functions are obtained by a chi^2 analysis of lepton deep inelastic experimental data. It is possible to determine valence-quark distributions at medium x and antiquark distributions at small x; however, the…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
Pooling operations, which can be calculated at low cost and serve as a linear or nonlinear transfer function for data reduction, are found in almost every modern neural network. Countless modern approaches have already tackled replacing the…
We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared…
In population studies, it is standard to sample data via designs in which the population is divided into strata, with the different strata assigned different probabilities of inclusion. Although there have been some proposals for including…
We present a new regression model for the determination of parton distribution functions (PDF) using techniques inspired from deep learning projects. In the context of the NNPDF methodology, we implement a new efficient computing framework…
Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…
We present a method which allows to extract theoretical informations out of a limited set of experimental data and observables, forming up in general an under- constrained system. It has been applied to the field of nucleon structure, in…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
Graphical Gaussian models have proven to be useful tools for exploring network structures based on multivariate data. Applications to studies of gene expression have generated substantial interest in these models, and resulting recent…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…