Related papers: Training Neural Networks for Likelihood/Density Ra…

Bayesian neural networks utilize probabilistic layers that capture uncertainty over weights and activations, and are trained using Bayesian inference. Since these probabilistic layers are designed to be drop-in replacement of their…

The state-of-the-art approaches for image classification are based on neural networks. Mathematically, the task of classifying images is equivalent to finding the function that maps an image to the label it is associated with. To rigorously…

The binary neural network, largely saving the storage and computation, serves as a promising technique for deploying deep models on resource-limited devices. However, the binarization inevitably causes severe information loss, and even…

This paper develops a novel approach to density estimation on a network. We formulate nonparametric density estimation on a network as a nonparametric regression problem by binning. Nonparametric regression using local polynomial…

Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural…

Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…

In the deep-learning community new algorithms are published at an incredible pace. Therefore, solving an image classification problem for new datasets becomes a challenging task, as it requires to re-evaluate published algorithms and their…

We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage…

Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…

We present a compact matrix formulation of the modularity, a commonly used quality measure for the community division in a network. Using this formulation we calculate the density of modularities, a statistical measure of the probability of…

Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks'…

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…

Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…

This paper considers the problem of algorithm selection for community detection. The aim of community detection is to identify sets of nodes in a network which are more interconnected relative to their connectivity to the rest of the…

The abundance of models of complex networks and the current insufficient validation standards make it difficult to judge which models are strongly supported by data and which are not. We focus here on likelihood maximization methods for…

Although the neural network (NN) technique plays an important role in machine learning, understanding the mechanism of NN models and the transparency of deep learning still require more basic research. In this study, we propose a novel…

This survey provides an in-depth and explanatory review of the approximation properties of deep neural networks, with a focus on feed-forward and residual architectures. The primary objective is to examine how effectively neural networks…

This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…