A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
SMP model preserves proximity and permutation in graph neural networks.
Proposes a graph pooling method leveraging node proximity for hierarchical graph representation learning.
A regularized optimization problem over a large unstructured graph is studied, where the regularization term is tied to the graph geometry. Typical regularization examples include the total variation and the Laplacian regularizations over the graph. When applying the proximal gradient algorithm to solve this problem, t…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are several fundamental problems that remain open. First, existing methods fail to preser…
Curvature regularization prevents distortion in graph embeddings.
We present a novel preconditioning technique for proximal optimization methods that relies on graph algorithms to construct effective preconditioners. Such combinatorial preconditioners arise from partitioning the graph into forests. We prove that certain decompositions lead to a theoretically optimal condition number.…
Extends GCNs to directed graphs for better performance.
We introduce a novel approach to graph-level representation learning, which is to embed an entire graph into a vector space where the embeddings of two graphs preserve their graph-graph proximity. Our approach, UGRAPHEMB, is a general framework that provides a novel means to performing graph-level embedding in a comple…
Optimizes convergence rate of stochastic proximal algorithms for composite convex problems.
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast and memory-efficient approximation to nearest-neighbor searches. Our framework is …
Proper proximality proved for various groups on non-positive curvature spaces.
We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) graph Laplace operator of a proximity graph on an epsilon-net.
New method improves structure learning on sparse graphs.
The paper analyzes the trade-off between smoothness and sparsity in GCN using lp-regularized learning.
We propose an algorithmic framework for convex minimization problems of a composite function with two terms: a self-concordant function and a possibly nonsmooth regularization term. Our method is a new proximal Newton algorithm that features a local quadratic convergence rate. As a specific instance of our framework, w…
Graph embedding has become a key component of many data mining and analysis systems. Current graph embedding approaches either sample a large number of node pairs from a graph to learn node embeddings via stochastic optimization or factorize a high-order proximity/adjacency matrix of the graph via computationally expen…
Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, -graphs and -NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…
Graphs approximate semigroups for diffusion on Riemannian manifolds.
The paper tackles finding stationary points in stochastic convex optimization problems.
CTGCN learns dynamic graph embeddings preserving both local and global graph structure.
I prove that the spectrum of the Laplace-Beltrami operator with the Neumann boundary condition on a compact Riemannian manifold with boundary admits a fast approximation by the spectra of suitable graph Laplacians on proximity graphs on the manifold, and similar graph approximation works for metric-measure spaces glued…
Deriving and applying Proximal Policy Optimization to GFlowNets for efficient training of discrete sampling policies
A new method for sparse regression models using graph structure.
Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard, Candès and Recht showed that it can be exactly relaxed if the number of observed entrie…
Develops minibatch stochastic proximal gradient for large-scale learning models.
Paper estimates differences in multi-attribute Gaussian graphical models using non-convex penalties.
We consider estimating a piecewise-constant image, or a gradient-sparse signal on a general graph, from noisy linear measurements. We propose and study an iterative algorithm to minimize a penalized least-squares objective, with a penalty given by the "l_0-norm" of the signal's discrete graph gradient. The method proce…
node2coords learns interpretable graph node representations robust to graph perturbations.
This paper improves cross-domain learning using random forests for manifold alignment.
Unified framework infers time-varying graphs from incomplete signals.
Subg-Con learns graph representations from subgraphs, improving scalability and efficiency.
This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using …
In recent years, Graph Convolutional Networks (GCNs) and their variants have been widely utilized in learning tasks that involve graphs. These tasks include recommendation systems, node classification, among many others. In node classification problem, the input is a graph in which the edges represent the association b…
Graph embedding method captures both local and global network structure.
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and find their correspondence, according to the learned optimal transport. The node …
We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regressio…
Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different temporal graphs. To this end, we propose to study dynamic time warping on temporal …
We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to decompose the graph into a set of trails which can then each be solved efficientl…
Enhances graph embeddings by preserving graph topology.
SAIL improves graph node representation learning by distilling knowledge between graphs.
The study constructs a Legendrian cycle for -sets and proves Reilly-type variational formulae.
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial intelligence and machine learning, such as fused Lasso, fused logistic regression, a…
In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure …
Eigenvalues of manifolds with cylindrical boundaries approximated by graph Laplacians.
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlappin…
Study shows convergence rates for Cheeger cuts on data clouds.
We propose a new nonlinear factorization model for graphs that are with topological structures, and optionally, node attributes. This model is based on a pseudometric called Gromov-Wasserstein (GW) discrepancy, which compares graphs in a relational way. It estimates observed graphs as GW barycenters constructed by a se…