Related papers: From Global to Local Correlation: Geometric Decomp…
Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex…
Many online networks are measured and studied via sampling techniques, which typically collect a relatively small fraction of nodes and their associated edges. Past work in this area has primarily focused on obtaining a representative…
This paper studies high-dimensional regression with two-way structured data. To estimate the high-dimensional coefficient vector, we propose the generalized matrix decomposition regression (GMDR) to efficiently leverage any auxiliary…
We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…
This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
In this paper, we use analysis on graphs to study quantitative measures of segregation. We focus on a classical statistic from the geography and urban sociology literature known as Moran's I, which in our language is a score associated to a…
We introduce a flexible framework for modeling dependent feature allocations. Our approach addresses limitations in traditional nonparametric methods by directly modeling the logit-probability surface of the feature paintbox, enabling the…
Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
Graph convolutional networks (GCNs) have been widely used for representation learning on graph data, which can capture structural patterns on a graph via specifically designed convolution and readout operations. In many graph classification…
We introduce a novel bottom-up approach for the extraction of chart data. Our model utilizes images of charts as inputs and learns to detect keypoints (KP), which are used to reconstruct the components within the plot area. Our novelty lies…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…
We study the $k$-th nearest neighbor distance function from a finite point-set in $\mathbb{R}^d$. We provide a Morse theoretic framework to analyze the sub-level set topology. In particular, we present a simple combinatorial-geometric…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
Given two views of data, we consider the problem of finding the features of one view which can be most faithfully inferred from the other. We find that these are also the most correlated variables in the sense of deep canonical correlation…
Morse complexes are gradient-based topological descriptors with close connections to Morse theory. They are widely applicable in scientific visualization as they serve as important abstractions for gaining insights into the topology of…
We propose an efficient meta-algorithm for Bayesian estimation problems that is based on low-degree polynomials, semidefinite programming, and tensor decomposition. The algorithm is inspired by recent lower bound constructions for…
This paper introduces assignment flows for density matrices as state spaces for representing and analyzing data associated with vertices of an underlying weighted graph. Determining an assignment flow by geometric integration of the…