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We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose…
The d-separation criterion detects the compatibility of a joint probability distribution with a directed acyclic graph through certain conditional independences. In this work, we study this problem in the context of categorical probability…
In this paper we develop a novel hidden Markov graphical model to investigate time-varying interconnectedness between different financial markets. To identify conditional correlation structures under varying market conditions and…
Graph Networks (GNs) enable the fusion of prior knowledge and relational reasoning with flexible function approximations. In this work, a general GN-based model is proposed which takes full advantage of the relational modeling capabilities…
Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences…
Most real-world networks contain well-defined community structures where nodes are densely connected internally within communities. To learn from these networks, we develop MarkovGNN that captures the formation and evolution of communities…
To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process…
Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in…
A causal model is an abstract representation of a physical system as a directed acyclic graph (DAG), where the statistical dependencies are encoded using a graphical criterion called `d-separation'. Recent work by Wood & Spekkens shows that…
Graphical causal models led to the development of complete non-parametric identification theory in arbitrary structured systems, and general approaches to efficient inference. Nevertheless, graphical approaches to causal inference have not…
In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…
The problem of estimating high-dimensional network models arises naturally in the analysis of many physical, biological and socio-economic systems. Examples include stock price fluctuations in financial markets and gene regulatory networks…
Full Bayesian computational inference for model determination in undirected graphical models is currently restricted to decomposable graphs, except for problems of very small scale. In this paper we develop new, more efficient methodology…
We consider the problem of learning a directed graph $G^\star$ from observational data. We assume that the distribution which gives rise to the samples is Markov and faithful to the graph $G^\star$ and that there are no unobserved…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that…
Finite mixture and Markov-switching models generalize and, therefore, nest specifications featuring only one component. While specifying priors in the two: the general (mixture) model and its special (single-component) case, it may be…
We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable specific…
This paper is the second in a series of papers which combine graphical modelling and marked spatial point patterns. Extending the previous results of \cite Eckardt (2016a), we introduce a marked spatial dependence graph model which depicts…
Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions…