arXiv research

LGKDE learns graph density using neural networks and perturbations.

Polynomial-time algorithm estimates edge density of random graphs with privacy and robustness.

Graph Mixture Density Networks model multimodal data on graphs.

New method avoids curse of dimensionality in structured density estimation.

Estimating dimension from sparse random geometric graphs.

We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…

We prove that the marginal densities of a global probability mass function in a primal normal factor graph and the corresponding marginal densities in the dual normal factor graph are related via local mappings. The mapping depends on the Fourier transform of the local factors of the models. Details of the mapping, inc…

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univaria…

Proposes a neural network for estimating traffic density uncertainty.

In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a piecewise constant estimation of the density of the edges across the clusters, and ad…

Estimates log-concave densities in graphical models using tent functions.

Algorithm learns graph ARMA processes for missing signal estimation.

Following Hartigan, a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two step…

New graph properties inherited by Frechet mean and median.

Equivariant graph neural networks predict electron density for molecules, liquids, and solids.

CUQ-GNN adapts uncertainty quantification for graph data, improving on GPN.

GANF uses normalizing flows to detect anomalies in multiple time series.

We improve density-based distances using normalizing flows and score matching.

We present a simple, yet effective, approach to Semi-Supervised Learning. Our approach is based on estimating density-based distances (DBD) using a shortest path calculation on a graph. These Graph-DBD estimates can then be used in any distance-based supervised learning method, such as Nearest Neighbor methods and SVMs…

For a given boundary set consisting of arcs and vertices, with two or more arcs meeting at each vertex, we treat the problem of estimating the area density of a soap film-like surface spanning the boundary.

BMTI method estimates densities without bins, outperforming traditional estimators.

Unified framework models graph data as a mixture of graphons using graph moments.

The paper proves stability of certain graph types in Euclidean space with specific densities.

Unbalanced data arises in many learning tasks such as clustering of multi-class data, hierarchical divisive clustering and semisupervised learning. Graph-based approaches are popular tools for these problems. Graph construction is an important aspect of graph-based learning. We show that graph-based algorithms can fail…

A new tensor ring mixture model improves density estimation efficiency.

Let $M$ be an $n$-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant $-κ^2$. Using the cone total curvature $TC(Γ)$ of a graph $Γ$ which was introduced by Gulliver and Yamada Math. Z. 2006, we prove that the density at any point of a soap film-like…

The paper analyzes rates of approximation for eigenpairs of Laplace-Beltrami operators on manifolds.

Sketching reduces data size for accurate spectral estimation.

Exchangeable graphs arise via a sampling procedure from measurable functions known as graphons. A natural estimation problem is how well we can recover a graphon given a single graph sampled from it. One general framework for estimating a graphon uses step-functions obtained by partitioning the nodes of the graph accor…

Improved model for grouping nodes in bipartite networks.

A new clustering algorithm GDT improves on HDBSCAN for uneven data.

The vast majority of the neural network literature focuses on predicting point values for a given set of response variables, conditioned on a feature vector. In many cases we need to model the full joint conditional distribution over the response variables rather than simply making point predictions. In this paper, we …

Kernel smoothing on unknown manifolds with bounds and asymptotic normality.

Paper estimates differences in conditional independence graphs from time-dependent data.

This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field. This is the first generative model of its kind for directed graphs. We introduce…

This paper has been withdrawn by the author due to an extended and largely modified version of the paper was published in arXiv (see arXiv:0807.3694, Disjoint minimal graphs).

Graph diffusion processes approximate manifold heat semigroups using graph transition matrices.

Graph Laplace operators uniquely identify metrics and densities on manifolds.

We study the connections between spectral clustering and the problems of maximum margin clustering, and estimation of the components of level sets of a density function. Specifically, we obtain bounds on the eigenvectors of graph Laplacian matrices in terms of the between cluster separation, and within cluster connecti…

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide …

Parameter-free clustering method using cluster catch digraphs (CCDs).

New algorithm estimates edge density of random graphs robustly, achieving optimal breakdown point.

We present a framework for incorporating prior information into nonparametric estimation of graphical models. To avoid distributional assumptions, we restrict the graph to be a forest and build on the work of forest density estimation (FDE). We reformulate the FDE approach from a Bayesian perspective, and introduce pri…

This work introduces a novel nonparametric density index defined on graphs, the Sum-over-Forests (SoF) density index. It is based on a clear and intuitive idea: high-density regions in a graph are characterized by the fact that they contain a large amount of low-cost trees with high outdegrees while low-density regions…

For a density $f$ on ${\mathbb R}^d$, a {\it high-density cluster} is any connected component of $\{x: f(x) \geq λ\}$, for some $λ> 0$. The set of all high-density clusters forms a hierarchy called the {\it cluster tree} of $f$. We present two procedures for estimating the cluster tree given samples from $f$. The first…

A-DOGE embeds attributed graphs efficiently using density of states.

Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change flexibly with features, which are massive-dimensional. We propose a multiscale dic…

The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propag…