Related papers: Exact rank-reduction of network models

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line…

Network representation learning has exploded recently. However, existing studies usually reconstruct networks as sequences or matrices, which may cause information bias or sparsity problem during model training. Inspired by a cognitive…

We propose a novel model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix that models the…

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs…

A feedforward neural network using rectified linear units constructs a mapping from inputs to outputs by partitioning its input space into a set of convex regions where points within a region share a single affine transformation. In order…

Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…

Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix…

One of the most significant challenges in statistical signal processing and machine learning is how to obtain a generative model that can produce samples of large-scale data distribution, such as images and speeches. Generative Adversarial…

Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…

Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

We present a probabilistic generative model and efficient algorithm to model reciprocity in directed networks. Unlike other methods that address this problem such as exponential random graphs, it assigns latent variables as community…

Learning discriminative node representations benefits various downstream tasks in graph analysis such as community detection and node classification. Existing graph representation learning methods (e.g., based on random walk and contrastive…

Neural networks are a powerful class of non-linear functions. However, their black-box nature makes it difficult to explain their behaviour and certify their safety. Abstraction techniques address this challenge by transforming the neural…

Deep Learning models have become the dominant approach in several areas due to their high performance. Unfortunately, the size and hence computational requirements of operating such models can be considerably high. Therefore, this…

Multilayer networks are in the focus of the current complex network study. In such networks multiple types of links may exist as well as many attributes for nodes. To fully use multilayer -- and other types of complex networks in…

Recent work has proposed several generative neural models for constituency parsing that achieve state-of-the-art results. Since direct search in these generative models is difficult, they have primarily been used to rescore candidate…

We give two algorithms computing representative families of linear and uniform matroids and demonstrate how to use representative families for designing single-exponential parameterized and exact exponential time algorithms. The…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…