Related papers: The neighborhood lattice for encoding partial corr…

We study the problem of learning multivariate dependencies in nonparametric and high-dimensional settings. This includes but is not limited to graphical models. Our approach effectively combines several features that are missing from…

Graphical models have been popularly used for capturing conditional independence structure in multivariate data, which are often built upon independent and identically distributed observations, limiting their applicability to complex…

Graph embedding has been widely applied in areas such as network analysis, social network mining, recommendation systems, and bioinformatics. However, current graph construction methods often require the prior definition of neighborhood…

We introduce a simple initial working system in which relations (such as part-whole) are directly represented via an architecture with operating and learning rules fundamentally distinct from standard artificial neural network methods.…

A neighborhood graph, which represents the instances as vertices and their relations as weighted edges, is the basis of many semi-supervised and relational models for node labeling and link prediction. Most methods employ a sequential…

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…

We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…

Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately…

A graph neural network transforms features in each vertex's neighborhood into a vector representation of the vertex. Afterward, each vertex's representation is used independently for predicting its label. This standard pipeline implicitly…

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…

We present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov Random Field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable…

The edge structure of the graph defining an undirected graphical model describes precisely the structure of dependence between the variables in the graph. In many applications, the dependence structure is unknown and it is desirable to…

Lattice gauge theories (LGTs) provide a framework for describing dynamical systems ranging from nuclei to materials. LGTs that host concatenated conservation laws can exhibit Hilbert space fragmentation, where each subspace may be labeled…

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…

It is well known that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial…

Many prediction problems can be phrased as inferences over local neighborhoods of graphs. The graph represents the interaction between entities, and the neighborhood of each entity contains information that allows the inferences or…

In social networks, neighborhood is crucial for understanding individual behavior in response to environments, and thus it is essential to analyze an individual's local perspective within the global network. This paper studies how to…

The algebraic structure of the attractors in a dynamical system determine much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods,…

In various application fields, such as fluid-, cell-, or crowd-simulations, spatial data structures are very important. They answer nearest neighbor queries which are instrumental in performing necessary computations for, e.g., taking the…

Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…