5,711 research outputs found
Learning AMP Chain Graphs under Faithfulness
This paper deals with chain graphs under the alternative
Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a
constraint based algorithm for learning an AMP chain graph a given probability
distribution is faithful to. We also show that the extension of Meek's
conjecture to AMP chain graphs does not hold, which compromises the development
of efficient and correct score+search learning algorithms under assumptions
weaker than faithfulness
Sequences of regressions and their independences
Ordered sequences of univariate or multivariate regressions provide
statistical models for analysing data from randomized, possibly sequential
interventions, from cohort or multi-wave panel studies, but also from
cross-sectional or retrospective studies. Conditional independences are
captured by what we name regression graphs, provided the generated distribution
shares some properties with a joint Gaussian distribution. Regression graphs
extend purely directed, acyclic graphs by two types of undirected graph, one
type for components of joint responses and the other for components of the
context vector variable. We review the special features and the history of
regression graphs, derive criteria to read all implied independences of a
regression graph and prove criteria for Markov equivalence that is to judge
whether two different graphs imply the same set of independence statements.
Knowledge of Markov equivalence provides alternative interpretations of a given
sequence of regressions, is essential for machine learning strategies and
permits to use the simple graphical criteria of regression graphs on graphs for
which the corresponding criteria are in general more complex. Under the known
conditions that a Markov equivalent directed acyclic graph exists for any given
regression graph, we give a polynomial time algorithm to find one such graph.Comment: 43 pages with 17 figures The manuscript is to appear as an invited
discussion paper in the journal TES
Graphical modelling of multivariate time series
We introduce graphical time series models for the analysis of dynamic
relationships among variables in multivariate time series. The modelling
approach is based on the notion of strong Granger causality and can be applied
to time series with non-linear dependencies. The models are derived from
ordinary time series models by imposing constraints that are encoded by mixed
graphs. In these graphs each component series is represented by a single vertex
and directed edges indicate possible Granger-causal relationships between
variables while undirected edges are used to map the contemporaneous dependence
structure. We introduce various notions of Granger-causal Markov properties and
discuss the relationships among them and to other Markov properties that can be
applied in this context.Comment: 33 pages, 7 figures, to appear in Probability Theory and Related
Field
Graph theoretic methods for the analysis of structural relationships in biological macromolecules
Subgraph isomorphism and maximum common subgraph isomorphism algorithms from graph theory provide an effective and an efficient way of identifying structural relationships between biological macromolecules. They thus provide a natural complement to the pattern matching algorithms that are used in bioinformatics to identify sequence relationships. Examples are provided of the use of graph theory to analyze proteins for which three-dimensional crystallographic or NMR structures are available, focusing on the use of the Bron-Kerbosch clique detection algorithm to identify common folding motifs and of the Ullmann subgraph isomorphism algorithm to identify patterns of amino acid residues. Our methods are also applicable to other types of biological macromolecule, such as carbohydrate and nucleic acid structures
Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
We consider three a priori totally different setups for Hopf algebras from
number theory, mathematical physics and algebraic topology. These are the Hopf
algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for
renormalization, and a Hopf algebra constructed by Baues to study double loop
spaces. We show that these examples can be successively unified by considering
simplicial objects, co-operads with multiplication and Feynman categories at
the ultimate level. These considerations open the door to new constructions and
reinterpretations of known constructions in a large common framework, which is
presented step-by-step with examples throughout. In this first part of two
papers, we concentrate on the simplicial and operadic aspects.Comment: This replacement is part I of the final version of the paper, which
has been split into two parts. The second part is available from the arXiv
under the title "Three Hopf algebras from number theory, physics & topology,
and their common background II: general categorical formulation"
arXiv:2001.0872
Three Hopf algebras and their common simplicial and categorical background
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common frameworkPreprin
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