Related papers: Learning with latent group sparsity via heat flow …

Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike. In this work we contribute an approach to sparse…

We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…

Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…

Graph generative modelling has become an essential task due to the wide range of applications in chemistry, biology, social networks, and knowledge representation. In this work, we propose a novel framework for generating graphs by adapting…

Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation.…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

Scientific studies increasingly collect multiple modalities of data to investigate a phenomenon from several perspectives. In integrative data analysis it is important to understand how information is heterogeneously spread across these…

Latent stochastic block models are flexible statistical models that are widely used in social network analysis. In recent years, efforts have been made to extend these models to temporal dynamic networks, whereby the connections between…

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…

Learning governing equations from a family of data sets which share the same physical laws but differ in bifurcation parameters is challenging. This is due, in part, to the wide range of phenomena that could be represented in the data sets…

The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…

We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…

We explore the usage of meta-learning to derive the causal direction between variables by optimizing over a measure of distribution simplicity. We incorporate a stochastic graph representation which includes latent variables and allows for…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…

Modeling dynamical systems and unraveling their underlying causal relationships is central to many domains in the natural sciences. Various physical systems, such as those arising in cell biology, are inherently high-dimensional and…

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and…

We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling…

Citation and coauthor networks offer an insight into the dynamics of scientific progress. We can also view them as representations of a causal structure, a logical process captured in a graph. From a causal perspective, we can ask questions…

Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…