Related papers: Untangling Gaussian Mixtures
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
Relational machine learning studies methods for the statistical analysis of relational, or graph-structured, data. In this paper, we provide a review of how such statistical models can be "trained" on large knowledge graphs, and then used…
Clustering multivariate data is a pervasive task in many applied problems, particularly in social studies and life science. Model-based approaches to clustering rely on mixture models, where each mixture component corresponds to the kernel…
In this report, we present TAGLAS, an atlas of text-attributed graph (TAG) datasets and benchmarks. TAGs are graphs with node and edge features represented in text, which have recently gained wide applicability in training graph-language or…
Despite the increasing visibility of fine-grained recognition in our field, "fine-grained'' has thus far lacked a precise definition. In this work, building upon clustering theory, we pursue a framework for measuring dataset granularity. We…
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This…
Graphs are widely used for modeling various types of interactions, such as email communications and online discussions. Many of such real-world graphs are temporal, and specifically, they grow over time with new nodes and edges. Counting…
Graph Neural Networks (GNNs) demonstrate their significance by effectively modeling complex interrelationships within graph-structured data. To enhance the credibility and robustness of GNNs, it becomes exceptionally crucial to bolster…
Recently, knowledge graph embedding, which projects symbolic entities and relations into continuous vector space, has become a new, hot topic in artificial intelligence. This paper addresses a new issue of multiple relation semantics that a…
In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…
Tabular data, widely used in various applications such as industrial control systems, finance, and supply chain, often contains complex interrelationships among its attributes. Data disentanglement seeks to transform such data into latent…
The cosmological dynamics of gravitational clustering satisfies an approximate invariance with respect to the cosmological parameters that is often used to simplify analytical computations. We describe how this approximate symmetry gives…
Clustering is a fundamental learning task widely used as a first step in data analysis. For example, biologists use cluster assignments to analyze genome sequences, medical records, or images. Since downstream analysis is typically…
Finding densely connected subsets of vertices in an unsupervised setting, called clustering or community detection, is one of the fundamental problems in network science. The edge clustering approach instead detects communities by…
We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
High-dimensional data analysis typically focuses on low-dimensional structure, often to aid interpretation and computational efficiency. Graphical models provide a powerful methodology for learning the conditional independence structure in…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…