Related papers: A note on intrinsic Conditional Autoregressive mod…
Conditional auto-regressive (CAR) distributions are widely used to induce spatial dependence in the geographic analysis of areal data. These distributions establish multivariate dependence networks by defining conditional relationships…
We clarify relationships between conditional (CAR) and simultaneous (SAR) autoregressive models. We review the literature on this topic and find that it is mostly incomplete. Our main result is that a SAR model can be written as a unique…
The conditional autoregressive model is a routinely used statistical model for areal data that arise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have…
Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The…
The use of directed acyclic graphs (DAGs) to represent conditional independence relations among random variables has proved fruitful in a variety of ways. Recursive structural equation models are one kind of DAG model. However,…
Graphs are an intuitive way to represent relationships between variables in fields such as finance and neuroscience. However, these graphs often need to be inferred from data. In this paper, we propose a novel framework to infer a latent…
We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully…
Conditional Independence (CI) graphs are a type of probabilistic graphical models that are primarily used to gain insights about feature relationships. Each edge represents the partial correlation between the connected features which gives…
We introduce priors and algorithms to perform Bayesian inference in Gaussian models defined by acyclic directed mixed graphs. Such a class of graphs, composed of directed and bi-directed edges, is a representation of conditional…
Graph data structures are fundamental for studying connected entities. With an increase in the number of applications where data is represented as graphs, the problem of graph generation has recently become a hot topic. However, despite its…
Causal models seek to unravel the cause-effect relationships among variables from observed data, as opposed to mere mappings among them, as traditional regression models do. This paper introduces a novel causal discovery algorithm designed…
The conditional autoregressive (CAR) model, simultaneous autoregressive (SAR) model, and its variants have become the predominant strategies for modeling regional or areal-referenced spatial data. The overwhelming wide-use of the CAR/SAR…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable…
We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers ``simple'' problems such as graph classification or regressing real-valued graph properties. For such tasks, the…
Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be…
This paper introduces sparse dynamic chain graph models for network inference in high dimensional non-Gaussian time series data. The proposed method parametrized by a precision matrix that encodes the intra time-slice conditional…
Deep learning-based graph generation approaches have remarkable capacities for graph data modeling, allowing them to solve a wide range of real-world problems. Making these methods able to consider different conditions during the generation…
This paper proposes an autoregressive (AR) model for sequences of graphs, which generalises traditional AR models. A first novelty consists in formalising the AR model for a very general family of graphs, characterised by a variable…
Over the last decade, large-scale multiple testing has found itself at the forefront of modern data analysis. In many applications data are correlated, so that the observed test statistic used for detecting a non-null case, or signal, at…