相关论文: Generalization Error Bound for Hyperbolic Ordinal …

Spatial Transcriptomics (ST) merges the benefits of pathology images and gene expression, linking molecular profiles with tissue structure to analyze spot-level function comprehensively. Predicting gene expression from histology images is a…

Learning accurate drug representations is essential for task such as computational drug repositioning. A drug hierarchy is a valuable source that encodes knowledge of relations among drugs in a tree-like structure where drugs that act on…

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…

Hyperbolic spaces, which have the capacity to embed tree structures without distortion owing to their exponential volume growth, have recently been applied to machine learning to better capture the hierarchical nature of data. In this…

Embedding-based entity alignment (EEA) has recently received great attention. Despite significant performance improvement, few efforts have been paid to facilitate understanding of EEA methods. Most existing studies rest on the assumption…

Recently, hyperbolic space has risen as a promising alternative for semi-supervised graph representation learning. Many efforts have been made to design hyperbolic versions of neural network operations. However, the inspiring geometric…

Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichm\"uller space, right-angled Artin groups, and many other cubical groups. Given such a space $\mathcal X$, we build…

Learning accurate drug representation is essential for tasks such as computational drug repositioning and prediction of drug side-effects. A drug hierarchy is a valuable source that encodes human knowledge of drug relations in a tree-like…

A long-standing belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) -- referred to as standard BO -- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both…

Incomplete Multi-View Clustering (IMVC) faces the challenge of learning discriminative representations from fragmentary observations while maintaining robustness against missing views. However, prevalent Euclidean-based methods suffer from…

Many graph processing algorithms require determination of shortest-path distances between arbitrary numbers of node pairs. Since computation of exact distances between all node-pairs of a large graph, e.g., 10M nodes and up, is…

This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius…

We present a rotated hyperbolic wrapped normal distribution (RoWN), a simple yet effective alteration of a hyperbolic wrapped normal distribution (HWN). The HWN expands the domain of probabilistic modeling from Euclidean to hyperbolic…

We consider the numerical solution of partial differential equations with coefficients that are strongly heterogeneous in space. We provide an overview of higher-order localized orthogonal decomposition (LOD) methods for the elliptic…

We consider the task of inferring is-a relationships from large text corpora. For this purpose, we propose a new method combining hyperbolic embeddings and Hearst patterns. This approach allows us to set appropriate constraints for…

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic…

Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…

We are concerned in designing a suitable numerical scheme based on the equal-order hybrid high-order (HHO) method for the linear parabolic integro-differential equations. The spatial discretization is made using the equal-order HHO method…

Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…

Implicit neural representations (INR) suffer from worsening spectral bias, which results in overly smooth solutions to the inverse problem. To deal with this problem, we propose a universal framework for processing inverse problems called…