522 research outputs found
Mixed Cumulative Distribution Networks
Directed acyclic graphs (DAGs) are a popular framework to express
multivariate probability distributions. Acyclic directed mixed graphs (ADMGs)
are generalizations of DAGs that can succinctly capture much richer sets of
conditional independencies, and are especially useful in modeling the effects
of latent variables implicitly. Unfortunately there are currently no good
parameterizations of general ADMGs. In this paper, we apply recent work on
cumulative distribution networks and copulas to propose one one general
construction for ADMG models. We consider a simple parameter estimation
approach, and report some encouraging experimental results.Comment: 11 pages, 4 figure
A closed-form approach to Bayesian inference in tree-structured graphical models
We consider the inference of the structure of an undirected graphical model
in an exact Bayesian framework. More specifically we aim at achieving the
inference with close-form posteriors, avoiding any sampling step. This task
would be intractable without any restriction on the considered graphs, so we
limit our exploration to mixtures of spanning trees. We consider the inference
of the structure of an undirected graphical model in a Bayesian framework. To
avoid convergence issues and highly demanding Monte Carlo sampling, we focus on
exact inference. More specifically we aim at achieving the inference with
close-form posteriors, avoiding any sampling step. To this aim, we restrict the
set of considered graphs to mixtures of spanning trees. We investigate under
which conditions on the priors - on both tree structures and parameters - exact
Bayesian inference can be achieved. Under these conditions, we derive a fast an
exact algorithm to compute the posterior probability for an edge to belong to
{the tree model} using an algebraic result called the Matrix-Tree theorem. We
show that the assumption we have made does not prevent our approach to perform
well on synthetic and flow cytometry data
An assessment of gene regulatory network inference algorithms
A conceptual issue regarding gene regulatory network (GRN) inference algorithms is establishing their validity or correctness. In this study, we argue that for this purpose it is useful to conceive these algorithms as estimators of graph-valued parameters of explicit models for gene expression data. On this basis, we perform an assessment of a selection of influential GRN inference algorithms as estimators for two types of models: (i) causal graphs with associated structural equations models (SEMs), and (ii) differential equations models based on the thermodynamics of gene expression. Our findings corroborate that networks of marginal dependence fail in estimating GRNs, but they also suggest that the strength of statistical association as measured by mutual information may be indicative of GRN structure. Also, in simulations, we find that the GRN inference algorithms GENIE3 and TIGRESS outperform competing algorithms. However, more importantly, we also find that many observed patterns hinge on the GRN topology and the assumed data generating mechanism.Un problema conceptual con respecto a los algoritmos de inferencia de redes de regulación génica (RRG) es cómo establecer su validez. En este estudio sostenemos que para este objetivo conviene concebir estos algoritmos como estimadores de parámetros de modelos estadÃsticos explÃcitos para datos de expresión génica. Sobre esta base, realizamos una evaluación de una selección de algoritmos de inferencia de RRG como estimadores para dos tipos de modelos: (i) modelos de grafos causales asociados a modelos de ecuaciones estructurales (MEE), y (ii) modelos de ecuaciones diferenciales basados en la termodinámica de la expresion genica. Nuestros hallazgos corroboran que las redes de dependencias marginales fallan en la estimación de las RRG, pero también sugieren que la fuerza de la asociación estadÃstica medida por la información mutua puede reflejar en cierto grado la estructura de las RRG. Además, en un estudio de simulaciones, encontramos que los algoritmos de inferencia GENIE3 y TIGRESS son los de mejor desempeño. Sin embargo, crucialmente, también encontramos que muchos patrones observados en las simulaciones dependen de la topologÃa de la RRG y del modelo generador de datos.MaestrÃ
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