arXiv research

Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.

A new method improves graph node embeddings by considering both nearby and distant node similarities.

An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on the number of nodes in networks with two hidden layers such that linear separabili…

The paper explores how different patterns of heterophily affect Graph Neural Networks.

Many successful methods have been proposed for learning low dimensional representations on large-scale networks, while almost all existing methods are designed in inseparable processes, learning embeddings for entire networks even when only a small proportion of nodes are of interest. This leads to great inconvenience,…

New method separates graph structure from node attributes to recover lost signal.

A new technique normalizes nodes within groups to improve GNN performance.

We address the problem of finding a minimal separator in an Andersson-Madigan-Perlman chain graph (AMP CG), namely, finding a set Z of nodes that separates a given nonadjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial-time algorit…

Poly-GNNs achieve similar performance regardless of depth, highlighting graph noise's dominance.

Due to myriads of classes, designing accurate and efficient classifiers becomes very challenging for multi-class classification. Recent research has shown that class structure learning can greatly facilitate multi-class learning. In this paper, we propose a novel method to learn the class structure for multi-class clas…

Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation o…

Graph convolution improves linear separability and generalizes to out-of-distribution data.

Graph convolutional neural networks (GCN) have been the model of choice for graph representation learning, which is mainly due to the effective design of graph convolution that computes the representation of a node by aggregating those of its neighbors. However, existing GCN variants commonly use 1-D graph convolution …

For any positive integer $k$, there exist neural networks with $Θ(k^3)$ layers, $Θ(1)$ nodes per layer, and $Θ(1)$ distinct parameters which can not be approximated by networks with $\mathcal{O}(k)$ layers unless they are exponentially large --- they must possess $Ω(2^k)$ nodes. This result is proved here for a class o…

HawkesLLM models text generation with temporal influence, improving semantic alignment under limited memory.

ES-MLP combines Graph-MLP with edge splitting for node classification on both homophilic and heterophilic graphs.

In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks(MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node att…

A new measure of causal influence quantifies intrinsic contributions in DAGs.

Community detection algorithms are fundamental tools to understand organizational principles in social networks. With the increasing power of social media platforms, when detecting communities there are two possi- ble sources of information one can use: the structure of social network and node attributes. However struc…

Graph neural networks struggle with heterophily, but new designs improve their performance.

EPFGNN models graph connections for better node classification.

A lot of effort has been invested into characterizing the convergence rates of gradient based algorithms for non-linear convex optimization. Recently, motivated by large datasets and problems in machine learning, the interest has shifted towards distributed optimization. In this work we present a distributed algorithm …

Heterophily affects GNN robustness; separating ego- and neighbor-embeddings improves defense.

We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous approaches either fail to encode the edge directionality or their encodings cannot b…

Given a graph embedded in an orientable surface, a process consisting of random excitations and random node and face balancing is constructed and analyzed. It is shown that given a priori bounds g' on the genus and n' on the number of nodes, one can determine the genus of the surface from local observations of the proc…

Graph attention improves node classification by distinguishing important edges.

MoNODEs improve neural ODEs by separating dynamic states from static factors.

A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds optimal values of function (value-nodes) and the corresponding weights. The Gaussi…

New bounds improve graph node classification using optimal transport.

GNNs improve semi-supervised node regression, but why? We explain.

This work evaluates graph models' robustness to structural distributional shifts.

Deep neural networks and decision trees operate on largely separate paradigms; typically, the former performs representation learning with pre-specified architectures, while the latter is characterised by learning hierarchies over pre-specified features with data-driven architectures. We unite the two via adaptive neur…

In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex function. The theoretical speedup, as compared to the serial method, and referring…

We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the pres…

Generative model reveals hidden interaction preferences in networks.

AP-Calculus offers a new framework for causal inference in Bayesian networks.

The analysis of scientific data of increasing size and complexity requires statistical machine learning methods that are both interpretable and predictive. Union of Intersections (UoI), a recently developed framework, is a two-step approach that separates model selection and model estimation. A linear regression algori…

We investigate the problem of nodes clustering under privacy constraints when representing a dataset as a graph. Our contribution is threefold. First we formally define the concept of differential privacy for structured databases such as graphs, and give an alternative definition based on a new neighborhood notion betw…

CDF uses centroids to split features for high-dimensional classification.

A novel GNN architecture improves link prediction by combining positive and negative samples.

Analyzing the temporal behavior of nodes in time-varying graphs is useful for many applications such as targeted advertising, community evolution and outlier detection. In this paper, we present a novel approach, STWalk, for learning trajectory representations of nodes in temporal graphs. The proposed framework makes u…

A new multi-task learning estimator improves Gaussian graphical regression model fitting.

In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data,…

Graph Neural Networks (GNNs) have been emerging as a promising method for relational representation including recommender systems. However, various challenging issues of social graphs hinder the practical usage of GNNs for social recommendation, such as their complex noisy connections and high heterogeneity. The oversm…

This chapter deals with decentralized learning algorithms for in-network processing of graph-valued data. A generic learning problem is formulated and recast into a separable form, which is iteratively minimized using the alternating-direction method of multipliers (ADMM) so as to gain the desired degree of paralleliza…

Max-Cut decision tree improves classification accuracy and reduces computation time.

The paper studies conditions for exact posterior modeling in Bayesian networks.

Multitask algorithms typically use task similarity information as a bias to speed up and improve the performance of learning processes. Tasks are learned jointly, sharing information across them, in order to construct models more accurate than those learned separately over single tasks. In this contribution, we present…