1,720,998 research outputs found
The R Package stagedtrees for Structural Learning of Stratified Staged Trees
Full text linkstagedtrees is an R package which includes several algorithms for learning the structure of staged trees and chain event graphs from data. Score-based and clustering-based algorithms are implemented, as well as various functionalities to plot the models and perform inference. The capabilities of stagedtrees are illustrated using mainly two datasets both included in the package or bundled in R
Theoretical studies on Bayesian network classifiers
No full textEn las últimas décadas, el aprendizaje automático ha adquirido importancia como una de las herramientas fundamentales en inteligencia artificial. El incremento en la disponibilidad de datos y capacidad computacional disponible a bajo coste han contribuido a extender los métodos de aprendizaje automático en casi todas las ramas de la tecnología. Mientras que gran parte de la investigación se centra en el desarrollo de nuevos algoritmos y métodos para tratar diferentes problemas, es ampliamente reconocido que el análisis formal y los resultados teóricos son necesarios para entender los algoritmos empleado, sus limitaciones y sus capacidades. El trabajo desarrollado en esta tesis se centra en éste último aspecto de la investigación en aprendizaje automático. Estudiamos los clasificadores con redes Bayesianas y en general clasificadores generativos basados en modelos gráficos probabilísticos. Los modelos gráficos probabilísticos han sido y siguen siendo ampliamente estudiados en estadística y en esta tesis los analizamos en el contexto de uno de los problemas más representativos en aprendizaje automático, la clasificación binaria. Nuestro resultado principal es la descripción, tanto para redes Bayesianas como para modelos de Markov no dirigidos, de las implicaciones de las independencias condicionadas en las funciones de decisión asociadas. En particular, describimos las familias de funciones discriminantes asociadas con las familias de clasificadores con redes Bayesianas más utilizados. Construimos polinomios que interpolan las funciones discriminantes inducidas, describiendo así las funciones de decisión. Gracias a la representación polinomial de las funciones discriminantes somos capaces de acotar el número de decisiones representables por clasificadores con redes Bayesianas. Extendemos estos resultados a clasificadores en cadena para problemas multi etiqueta, analizando su capacidad expresiva asumiendo que los modelos están basados en redes Bayesianas. Por último, describimos un método algebraico y geométrico para estudiar funciones discriminantes de clasificadores generativos bajo propiedades de Markov generales. El método empleado extiende los resultados obtenido en el caso de las redes Bayesianas y describe un marco formal, basado en diferencias finitas, para estudiar las funciones discriminantes de clasificadores generativos. ----------ABSTRACT---------- Machine learning, as one of the fundamental tools of artificial intelligence, has acquired growing importance in the last decades. The increasing availability of large amounts of data and more computational processing power available at a low price have contributed to the spread of machine learning methods in almost all branches of technology. While a great part of the current research focuses on the creation of new algorithms and methods to tackle different problems, it is widely recognized that formal analysis and theoretical results are necessary to really understand the algorithms employed, their limitations and their capabilities. The work developed in the present thesis is focused on this last aspect of the research in machine learning. We study Bayesian network classifiers and in general generative classifiers based on probabilistic graphical models. Probabilistic graphical models are widely studied in the statistic literature and in this thesis we analyze them in the context of one of the most basic problem in machine learning, binary classification. Our main result is a description of the implications, for the induced decision functions, of the conditional independence statements holding in the probability model. We will state results both for a wide class of Bayesian network classifiers and for undirected Markov network classifiers. In particular, we describe the classes of discrimination functions associated with some of the most used Bayesian network classifiers over categorical predictors variables. We obtain polynomials interpolating the induced discrimination functions, and thus representing the corresponding decision functions. Thanks to this characterization we are able to bound the number of decisions representable by Bayesian network classifiers with given structures. We extend the binary classification results to chain multi-label classifiers, analyzing their expressive power when Bayesian network are used as base models. Finally, we describe an algebraic and geometric approach to study discrimination functions of generative classifiers under general Markov properties. The given approach extends the results for Bayesian network classifiers and introduces an elegant framework, based on finite differences, to study discrimination functions of generative classifiers
Robust learning of staged tree models: A case study in evaluating transport services
Full text linkStaged trees are a relatively recent class of probabilistic graphical models that extend Bayesian networks to formally and graphically account for non-symmetric patterns of dependence. Machine learning algorithms to learn them from data have been implemented in various pieces of software. However, to date, methods to assess the robustness and validity of the learned, non-symmetric relationships are not available. Here, we introduce validation techniques tailored to staged tree models based on non-parametric bootstrap resampling methods and investigate their use in practical applications. In particular, we focus on the evaluation of transport services using large-scale survey data. In these types of applications, data from heterogeneous sources must be collated together. Staged trees provide a natural framework for this integration of data and its analysis. For the thorough evaluation of transport services, we further implement novel what-if sensitivity analyses for staged trees and their visualization using software.yesPublishe
Algebraic representation of generative classifier
No full textWe study the discrimination functions associated with classifiers induced by probabilistic graphical models and in particular Bayesian network classifiers. For every G -Markov probabilistic classifier we link the topology of the graph G with the class of discrimination functions induced, we prove that every conditional independence statement satisfied by the model implies linear constrains on the discrimination function. As an example we study the Naive Bayes model for two binary predictor variables and we formulate some questions for future work
Context-Specific Refinements of Bayesian Network Classifiers
Full text linkSupervised classification is one of the most ubiquitous tasks in machine
learning. Generative classifiers based on Bayesian networks are often used
because of their interpretability and competitive accuracy. The widely used
naive and TAN classifiers are specific instances of Bayesian network
classifiers with a constrained underlying graph. This paper introduces novel
classes of generative classifiers extending TAN and other famous types of
Bayesian network classifiers. Our approach is based on staged tree models,
which extend Bayesian networks by allowing for complex, context-specific
patterns of dependence. We formally study the relationship between our novel
classes of classifiers and Bayesian networks. We introduce and implement
data-driven learning routines for our models and investigate their accuracy in
an extensive computational study. The study demonstrates that models embedding
asymmetric information can enhance classification accuracy.Comment: arXiv admin note: text overlap with arXiv:2206.0697
Structural learning of simple staged trees
Full text linkBayesian networks faithfully represent the symmetric conditional independences existing between the components of a random vector. Staged trees are an extension of Bayesian networks for categorical random vectors whose graph represents non-symmetric conditional independences via vertex coloring. However, since they are based on a tree representation of the sample space, the underlying graph becomes cluttered and difficult to visualize as the number of variables increases. Here, we introduce the first structural learning algorithms for the class of simple staged trees, entertaining a compact coalescence of the underlying tree from which non-symmetric independences can be easily read. We show that data-learned simple staged trees often outperform Bayesian networks in model fit and illustrate how the coalesced graph is used to identify non-symmetric conditional independences.yesPublishe
Context-Specific Causal Discovery for Categorical Data Using Staged Trees
Full text linkCausal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between categorical variables. We provide a first graphical representation of the equivalence class of a staged tree, by looking only at a specific subset of its underlying independences. We further define a new pre-metric, inspired by the widely used structural intervention distance, to quantify the closeness between two staged trees in terms of their corresponding causal inference statements. A simulation study highlights the efficacy of staged trees in uncovering complexes, asymmetric causal relationships from data, and real-world data applications illustrate their use in practical causal analysis.Publishe
Highly Efficient Structural Learning of Sparse Staged Trees
Full text linkSeveral structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the first scalable structural learning algorithm for staged trees, which searches over a space of models where only a small number of dependencies can be imposed. A simulation study as well as a real-world application illustrate our routines and the practical use of such data-learned staged trees.Publishe
Highly Efficient Structural Learning of Sparse Staged Trees
Full text linkSeveral structural learning algorithms for staged tree models, an asymmetric
extension of Bayesian networks, have been defined. However, they do not scale
efficiently as the number of variables considered increases. Here we introduce
the first scalable structural learning algorithm for staged trees, which
searches over a space of models where only a small number of dependencies can
be imposed. A simulation study as well as a real-world application illustrate
our routines and the practical use of such data-learned staged trees.Comment: arXiv admin note: text overlap with arXiv:2203.0439
Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear
Full text linkBayesian networks are widely used to learn and reason about the dependence structure of discrete variables. However, they can only formally encode symmetric conditional independence, which is often too strict to hold in practice. Asymmetry-labeled DAGs have been recently proposed to extend the class of Bayesian networks by relaxing the symmetric assumption of independence and denoting the dependence between the variables of interest. Here, we introduce novel structural learning algorithms for this class of models, which, whilst efficient, allow for a straightforward interpretation of the underlying dependence structure. A comprehensive computational study highlights the efficiency of the algorithms. A real-world data application using data from the Fear of COVID-19 Scale collected in Italy showcases their use in practice.yesPublishe
- …
