相关论文: On estimation and inference in latent structure ra…
Connection graphs (CGs) extend traditional graph models by coupling network topology with orthogonal transformations, enabling the representation of global geometric consistency. They play a key role in applications such as synchronization,…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the…
We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges…
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…
Processes such as disease propagation and information diffusion often spread over some latent network structure which must be learned from observation. Given a set of unlabeled training examples representing occurrences of an event type of…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We investigate the Laplacian spectra of random geometric graphs (RGGs). The spectra are found to consist of both a discrete and a continuous part. The discrete part is a collection of Dirac delta peaks at integer values roughly centered…
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense,…
Images are composed as a hierarchy of object parts. We use this insight to create a generative graphical model that defines a hierarchical distribution over image parts. Typically, this leads to intractable inference due to loops in the…
Large language models are remarkably capable, yet how computation propagates through their layers remains poorly understood. A growing line of work treats depth as discrete time and the residual stream as a dynamical system, where each…
Lattice gauge theories (LGTs) provide a framework for describing dynamical systems ranging from nuclei to materials. LGTs that host concatenated conservation laws can exhibit Hilbert space fragmentation, where each subspace may be labeled…
A random geometric graph (RGG) with kernel $K$ is constructed by first sampling latent points $x_1,\ldots,x_n$ independently and uniformly from the $d$-dimensional unit sphere, then connecting each pair $(i,j)$ with probability $K(\langle…
Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. To gain some insight into the performance of various estimators for this task, we perform a theoretical study in a context…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…
Numerical simulations of coupled map lattices (CMLs) and other complex model systems show an enormous phenomenological variety that is difficult to classify and understand. It is therefore desirable to establish analytical tools for…
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…
The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with…
Denoising Diffusion Probabilistic Models (DDPMs) represent a contemporary class of generative models with exceptional qualities in both synthesis and maximizing the data likelihood. These models work by traversing a forward Markov Chain…