Related papers: On Graphical Models and Convex Geometry

A graph neural network transforms features in each vertex's neighborhood into a vector representation of the vertex. Afterward, each vertex's representation is used independently for predicting its label. This standard pipeline implicitly…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…

Probabilistic graphical models are a powerful concept for modeling high-dimensional distributions. Besides modeling distributions, probabilistic graphical models also provide an elegant framework for performing statistical inference;…

Graphical models with bi-directed edges (<->) represent marginal independence: the absence of an edge between two vertices indicates that the corresponding variables are marginally independent. In this paper, we consider maximum likelihood…

Performance analysis based on modelling consists of two major steps: model construction and model analysis. Formal modelling techniques significantly aid model construction but can exacerbate model analysis. In particular, here we consider…

A current challenge for data management systems is to support the construction and maintenance of machine learning models over data that is large, multi-dimensional, and evolving. While systems that could support these tasks are emerging,…

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health…

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…

A scale mixture of normals is a distribution formed by mixing a collection of normal distributions with fixed mean but different variances. A generalized gamma scale mixture draws the variances from a generalized gamma distribution.…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

Nonparametric maximum likelihood (NPML) for mixture models is a technique for estimating mixing distributions that has a long and rich history in statistics going back to the 1950s, and is closely related to empirical Bayes methods.…

We describe a simple and yet surprisingly powerful probabilistic technique which shows how to find in a dense graph a large subset of vertices in which all (or almost all) small subsets have many common neighbors. Recently this technique…

Text-to-image diffusion models generate highly detailed textures, yet they often rely on surface appearance and fail to follow strict geometric constraints, particularly when those constraints conflict with the style implied by the text…

Finite mixtures of regression models provide a flexible modeling framework for many phenomena. Using moment-based estimation of the regression parameters, we develop unbiased estimators with a minimum of assumptions on the mixture…

We study a recent class of models which uses graph neural networks (GNNs) to improve forecasting in multivariate time series. The core assumption behind these models is that there is a latent graph between the time series (nodes) that…

Some remarkable properties of the beta distribution are based on relations involving independence between beta random variables such that a parameter of one among them is the sum of the parameters of an other (see (1.1) et (1.2) below).…

Probabilistic Graphical Models are often used to understand dynamics of a system. They can model relationships between features (nodes) and the underlying distribution. Theoretically these models can represent very complex dependency…

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…