178 research outputs found
Markov Properties for Graphical Models with Cycles and Latent Variables
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 can model latent (dependent) variables, and directed mixed graphs
(DMGs) that can model cycles. We define and analyse several different Markov
properties that relate the graphical structure of a HEDG with a probability
distribution on a corresponding product space over the set of nodes, for
example factorization properties, structural equations properties,
ordered/local/global Markov properties, and marginal versions of these. The
various Markov properties for HEDGes are in general not equivalent to each
other when cycles or hyperedges are present, in contrast with the simpler case
of directed acyclic graphical (DAG) models (also known as Bayesian networks).
We show how the Markov properties for HEDGes - and thus the corresponding
graphical Markov models - are logically related to each other.Comment: 131 page
Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders
We address the problem of causal discovery from data, making use of the
recently proposed causal modeling framework of modular structural causal models
(mSCM) to handle cycles, latent confounders and non-linearities. We introduce
{\sigma}-connection graphs ({\sigma}-CG), a new class of mixed graphs
(containing undirected, bidirected and directed edges) with additional
structure, and extend the concept of {\sigma}-separation, the appropriate
generalization of the well-known notion of d-separation in this setting, to
apply to {\sigma}-CGs. We prove the closedness of {\sigma}-separation under
marginalisation and conditioning and exploit this to implement a test of
{\sigma}-separation on a {\sigma}-CG. This then leads us to the first causal
discovery algorithm that can handle non-linear functional relations, latent
confounders, cyclic causal relationships, and data from different (stochastic)
perfect interventions. As a proof of concept, we show on synthetic data how
well the algorithm recovers features of the causal graph of modular structural
causal models.Comment: Accepted for publication in Conference on Uncertainty in Artificial
Intelligence 201
Thouaré-sur-Loire – Zac des Deux Ruisseaux 1
Malgré une implantation à proximité des rives de la Loire, habituellement riches en indices archéologiques, les investigations réalisées sur l’emprise de la tranche 1 de la future Zac des Deux Ruisseaux ont livré une faible quantité de vestiges anthropiques. Les sondages ont mis en évidence de nombreux tronçons de fossés dans le secteur est de l’emprise. Ces fossés sont probablement à mettre en relation avec des parcellaires. De ces systèmes fossoyés, deux ensembles ont pu être identifiés. L’..
Chambellay – La Terrinière
Malgré la proximité de deux fosses, découvertes dans un rayon de moins d’1 km en 1971, dont une sépulture de l’âge du Bronze, les investigations réalisées sur l’emprise de l’extension de la carrière de la Terrinière sur la commune de Chambellay n’ont pas livré de vestiges conséquents d’implantation humaine. Les sondages ont mis en évidence de nombreux fossés répartis selon deux orientations. La première trame est orientée nord-sud et est-ouest. Elle s’aligne avec le parcellaire actuel et part..
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