Related papers: Quantile Graphical Models: Prediction and Conditio…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
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.…
This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a…
We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on…
We propose a new measure related with tail dependence in terms of correlation: quantile correlation coefficient of random variables X, Y. The quantile correlation is defined by the geometric mean of two quantile regression slopes of X on Y…
Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…
Testing (conditional) independence of multivariate random variables is a task central to statistical inference and modelling in general - though unfortunately one for which to date there does not exist a practicable workflow. State-of-art…
In genome-wide prediction, independence of marker allele substitution effects is typically assumed; however, since early stages of this technology it has been known that nature points to correlated effects. In statistics, graphical models…
Estimation of differences in conditional independence graphs (CIGs) of two time series Gaussian graphical models (TSGGMs) is investigated where the two TSGGMs are known to have similar structure. The TSGGM structure is encoded in the…
A popular measure of association is the tail dependence coefficient which measures the strength of dependence in either the lower-left or upper-right tail of a bivariate distribution. In this paper, we develop the idea of quantile…
We propose a method for inferring the conditional independence graph (CIG) of a high-dimensional Gaussian vector time series (discrete-time process) from a finite-length observation. By contrast to existing approaches, we do not rely on a…
This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the…
Heavy-tailed distributions naturally occur in many real life problems. Unfortunately, it is typically not possible to compute inference in closed-form in graphical models which involve such heavy-tailed distributions. In this work, we…
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,…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…
The graphical structure of Probabilistic Graphical Models (PGMs) encodes the conditional independence (CI) relations that hold in the modeled distribution. Graph algorithms, such as d-separation, use this structure to infer additional…
Genetical genomics experiments have now been routinely conducted to measure both the genetic markers and gene expression data on the same subjects. The gene expression levels are often treated as quantitative traits and are subject to…
Quantum graph neural networks offer a powerful paradigm for learning on graph-structured data, yet their explainability is complicated by measurement-induced stochasticity and the combinatorial nature of graph structure. In this paper, we…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…