13 citations · 26 across the 14 of their papers we have counts for
14 papers
Generative Modeling on Metric Graphs via Neural Optimal Transport
Alessandro Micheli, Yueqi Cao, Anthea Monod +1
We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target…
Riemannian Neural Optimal Transport
Alessandro Micheli, Yueqi Cao, Anthea Monod +1
Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data…
Metric Graph Kernels via the Tropical Torelli Map
Yueqi Cao, Anthea Monod
We introduce the first graph kernels for metric graphs via tropical algebraic geometry. In contrast to conventional graph kernels based on graph combinatorics such as nodes, edges,…
Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs
Yueqi Cao, Anthea Monod
Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological fe…
A Computational Tropical Geometry Framework for Neural Networks
Paul Lezeau, Thomas Walker, Yueqi Cao +2
We propose a computational tropical geometry framework for the symbolic analysis of neural networks with tropical activations. The number of linear regions of a neural network has…
Probability Metrics for Tropical Spaces of Different Dimensions
Roan Talbut, Daniele Tramontano, Yueqi Cao +2
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that…
-Means Clustering for Persistent Homology
Yueqi Cao, Prudence Leung, Anthea Monod
Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has re…
A Geometric Condition for Uniqueness of Fréchet Means of Persistence Diagrams
Yueqi Cao, Anthea Monod
The Fréchet mean is an important statistical summary and measure of centrality of data; it has been defined and studied for persistent homology captured by persistence diagrams. Ho…
Approximating Persistent Homology for Large Datasets
Yueqi Cao, Anthea Monod
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces pe…
Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
Yueqi Cao, Athanasios Vlontzos, Luca Schmidtke +2
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embeddin…
Geometric Characteristics of Wasserstein Metric on SPD(n)
Yihao Luo, Shiqiang Zhang, Yueqi Cao +1
Wasserstein distance, especially among symmetric positive-definite matrices, has broad and deep influences on development of artificial intelligence (AI) and other branches of comp…
Torsion Discriminance for Stability of Linear Time-Invariant Systems
Yuxin Wang, Huafei Sun, Yueqi Cao +1
This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion of the state trajectory. For a system where…
Efficient Weingarten Map and Curvature Estimation on Manifolds
Yueqi Cao, Didong Li, Huafei Sun +2
In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is establis…
Description of Stability for Two and Three-Dimensional Linear Time-Invariant Systems Based on Curvature and Torsion
Yuxin Wang, Huafei Sun, Yang Song +2
This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system , (i) if…