Related papers: On a hypergraph probabilistic graphical model
Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the…
Many problems in robotics involve both continuous and discrete components, and modeling them together for estimation tasks has been a long standing and difficult problem. Hybrid Factor Graphs give us a mathematical framework to model these…
We introduce and study analogues of expander and hyperfinite graph sequences in the context of directed acyclic graphs, which we call "extender" and "hypershallow" graph sequences, respectively. Our main result is a probabilistic…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modeling of such different data-types, based on global parameters consisting of a directed acyclic…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected.…
We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a…
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…
Directed acyclic graphical (DAG) models are a powerful tool for representing causal relationships among jointly distributed random variables, especially concerning data from across different experimental settings. However, it is not always…
Joint modeling of multiview graphs with a common set of nodes between views and auxiliary predictors is an essential, yet less explored, area in statistical methodology. Traditional approaches often treat graphs in different views as…
The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model…
In this document I aim to give an informal treatment of automatic Backward Filtering Forward Guiding, a general algorithm for conditional sampling from a Markov process on a directed acyclic graph. I'll show that the underlying ideas can be…
Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…
Bayesian networks (BN) are directed acyclic graphical (DAG) models that have been adopted into many fields for their strengths in transparency, interpretability, probabilistic reasoning, and causal modeling. Given a set of data, one hurdle…
Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into…
Bayesian network is a frequently-used method for fault detection and diagnosis in industrial processes. The basis of Bayesian network is structure learning which learns a directed acyclic graph (DAG) from data. However, the search space…
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…