Related papers: Information-geometry-driven graph sequential growt…
Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
In this paper we investigate the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way. Apart from the typical rates of growth, i.e. exponential or polynomial, we identify…
This paper develops a general approach to characterize the long-time trajectory behavior of nonconvex gradient descent in generalized single-index models in the large aspect ratio regime. In this regime, we show that for each iteration the…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…
Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…
Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…
We propose a new type of approximate counting algorithms for the problems of enumerating the number of independent sets and proper colorings in low degree graphs with large girth. Our algorithms are not based on a commonly used Markov chain…
Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing the number of instances a specific graphlet appears in a large graph…
Ramsey-good graphs are graphs that contain neither a clique of size $s$ nor an independent set of size $t$. We study doubly saturated Ramsey-good graphs, defined as Ramsey-good graphs in which the addition or removal of any edge necessarily…
Graph generation is one of the most challenging tasks in recent years, and its core is to learn the ground truth distribution hiding in the training data. However, training data may not be available due to security concerns or unaffordable…
3D Gaussian Splatting has demonstrated superior performance in rendering efficiency and quality, yet the generation of 3D Gaussians still remains a challenge without proper geometric priors. Existing methods have explored predicting point…
In document classification, graph-based models effectively capture document structure, overcoming sequence length limitations and enhancing contextual understanding. However, most existing graph document representations rely on heuristics,…
Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…
Kernel and linear regression have been recently explored in the prediction of graph signals as the output, given arbitrary input signals that are agnostic to the graph. In many real-world problems, the graph expands over time as new nodes…
We initiate the study of deterministic distributed graph algorithms with predictions in synchronous message passing systems. The process at each node in the graph is given a prediction, which is some extra information about the problem…
Graphical models based on Directed Acyclic Graphs (DAGs) are widely used to answer causal questions across a variety of scientific and social disciplines. However, observational data alone cannot distinguish in general between DAGs…
Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…