Properties, Learning Algorithms, and Applications of Chain Graphs and Bayesian Hypergraphs

Probabilistic graphical models (PGMs) use graphs, either undirected, directed, or mixed, to represent possible dependencies among the variables of a multivariate probability distri- bution. PGMs, such as Bayesian networks and Markov networks, are now widely accepted as a powerful and mature framework for reasoning and decision making under uncertainty in knowledge-based systems. With the increase of their popularity, the range of graphical models being investigated and used has also expanded. Several types of graphs with dif- ferent conditional independence interpretations - also known as Markov properties - have been proposed and used in graphical models. The graphical structure of a Bayesian network has the form of a directed acyclic graph (DAG), which has the advantage of supporting an interpretation of the graph in terms of cause-effect relationships. However, a limitation is that only asymmetric relationships, such as cause and effect relationships, can be modeled between variables in a DAG. Chain graphs, which admit both directed and undirected edges, can be used to overcome this limitation. Today there exist three main different interpretations of chain graphs in the lit- erature. These are the Lauritzen-Wermuth-Frydenberg, the Andersson-Madigan-Perlman, and the multivariate regression interpretations. In this thesis, we study these interpreta- tions based on their separation criteria and the intuition behind their edges. Since structure learning is a critical component in constructing an intelligent system based on a chain graph model, we propose new feasible and efficient structure learning algorithms to learn chain graphs from data under the faithfulness assumption. The proliferation of different PGMs that allow factorizations of different kinds leads us to consider a more general graphical structure in this thesis, namely directed acyclic hypergraphs. Directed acyclic hypergraphs are the graphical structure of a new proba- bilistic graphical model that we call Bayesian hypergraphs. Since there are many more hypergraphs than DAGs, undirected graphs, chain graphs, and, indeed, other graph-based networks, Bayesian hypergraphs can model much finer factorizations and thus are more computationally efficient. Bayesian hypergraphs also allow a modeler to represent causal patterns of interaction such as Noisy-OR graphically (without additional annotations). We introduce global, local and pairwise Markov properties of Bayesian hypergraphs and prove under which conditions they are equivalent. We also extend the causal interpretation of LWF chain graphs to Bayesian hypergraphs and provide corresponding formulas and a graphical criterion for intervention. The framework of graphical models, which provides algorithms for discovering and analyzing structure in complex distributions to describe them succinctly and extract un- structured information, allows them to be constructed and utilized effectively. Two of the most important applications of graphical models are causal inference and information ex- traction. To address these abilities of graphical models, we conduct a causal analysis, comparing the performance behavior of highly-configurable systems across environmen- tal conditions (changing workload, hardware, and software versions), to explore when and how causal knowledge can be commonly exploited for performance analysis

Spatial graphical models with discrete and continuous components

Graphical models use Markov properties to establish associations among dependent variables. To estimate spatial correlation and other parameters in graphical models, the conditional independences and joint probability distribution of the graph need to be specified. We can rely on Gaussian multivariate models to derive the joint distribution when all the nodes of the graph are assumed to be normally distributed. However, when some of the nodes are discrete, the Gaussian model no longer affords an appropriate joint distribution function. We develop methods specifying the joint distribution of a chain graph with both discrete and continuous components, with spatial dependencies assumed among all variables on the graph. We propose a new group of chain graphs known as the generalized tree networks. Constructing the chain graph as a generalized tree network, we partition its joint distributions according to the maximal cliques. Copula models help us to model correlation among discrete variables in the cliques. We examine the method by analyzing datasets with simulated Gaussian and Bernoulli Markov random fields, as well as with a real dataset involving household income and election results. Estimates from the graphical models are compared with those from spatial random effects models and multivariate regression models

Para além de pressupostos psicométricos : como desenvolver novas medidas psicológicas

Tese (doutorado)—Universidade de Brasília, Instituto de Psicologia, Programa de Pós-graduação em Psicologia Social, do Trabalho e das Organizações, 2019.O que define uma boa medida? Na presente tese, argumentamos e mostramos que definir uma boa medida pode ser muito mais complexo do que simplesmente executar uma análise fatorial ou uma análise usando a teoria da resposta ao item. O objetivo geral desta dissertação é apresentar três principais pressupostos da medida psicométrica e desenvolver alternativas para a medida psicológica tradicional. A tese está dividida em quatro estudos. O primeiro é um estudo teórico no qual são apresentados três pressupostos centrais comuns à teoria psicométrica e à prática psicométrica, e no qual é mostrado como alternativas às abordagens psicométricas tradicionais podem ser usadas para melhorar a medição psicológica. Essas alternativas foram desenvolvidas adaptando cada um desses três pressupostos: (1) o pressuposto de validade estrutural; (2) o pressuposto do processo; e (3) o pressuposto de construto. O pressuposto de validade estrutural refere-se à implementação de modelos matemáticos. O pressuposto de processo implica que um processo subjacente específico está gerando os dados observados. O pressuposto de construto infere que os dados observados por si só não constituem uma medida, mas que as medidas são as variáveis latentes que originam os dados observados. Vários exemplos de abordagens psicométricas alternativas já existentes são apresentados no primeiro estudo. O segundo estudo se refere ao pressuposto de validade estrutural e teve como objetivo desenvolver dois novos modelos de resposta aos itens para itens politômicos e binários que não assumem uma distribuição normal dos escores verdadeiros. O primeiro modelo desenvolvido, o Modelo de resposta ao item condicional (CIRM), assume uma distribuição beta- binomial. O segundo novo modelo é uma implementação Bayesiana do procedimento de escore ótimo (OS-IRM). Ambos os novos modelos foram comparados com o modelo tradicional de Rasch: os resultados indicam que os dois modelos desenvolvidos melhoram vários aspectos do modelo de Rasch. O terceiro estudo foi derivado do pressuposto do processo e tinha três objetivos. Primeiro, desenvolver uma implementação Bayesiana do framework de análise da função de otimização situacional (SOFA). Segundo, comparar essa implementação Bayesiana do SOFA com outros três modelos baseados em Máxima Verossimilhança, usados para estimar escores verdadeiros. O terceiro objetivo foi mostrar como a modelagem conjunta pode ser usada para pesquisas de validade. Uma das principais vantagens do framework SOFA em comparação com a abordagem psicométrica tradicional é que o SOFA depende de dados experimentais, melhorando a validade das medidas. O quarto e último estudo foi derivado do pressuposto de construto e seu principal objetivo era desenvolver um procedimento de aprendizado de estrutura de gráficos de cadeia de potência (PCGs). Um PCG é um tipo de gráfico que representa relações causais entre grupos de variáveis. Pode ser pensado como uma versão exploratória completa da modelagem de equações estruturais, bem como um modelo psicométrico que não depende de variáveis latentes. Esses quatro estudos pretendem mostrar que a modelagem psicométrica não deve se restringir ao uso de modelos tradicionais de mensuração, mas também deve considerar a adaptação desses modelos tradicionais de acordo com o uso pretendido e os processos teóricos que originam as medidas observadas.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).What defines a good measurement? In the present dissertation we argue, and show, that defining a good measurement can be much more complex than simply performing a factor analysis or an analysis using item response theory. The overall objective of this dissertation is to present three principal assumptions of psychometric measurement, and to develop alternatives for traditional psychological measurement. The dissertation is divided in four studies. The first one is a theoretical study in which three central assumptions common to psychometric theory and psychometric practice are presented, and in which is shown how alternatives to traditional psychometric approaches can be used to improve psychological measurement. These alternatives were developed by adapting each of these three assumptions: (1) the assumption of structural validity; (2) the process assumption; and, (3) the construct assumption. The structural validity assumption relates to the implementation of mathematical models. The process assumption implies that a specific underlying process is generating the observed data. The construct assumption infers that the observed data on its own do not constitute a measurement, but the measure are the latent variables that originate the observed data. Several examples of already existing alternative psychometric approaches are presented in the first study. The second study relates to the structural validity assumption and aimed to develop two new item response models for polytomous and binary items that do not assume a normal distribution of the true scores. The first model that was developed, the Conditional Item Response Model (CIRM), assumes a beta-binomial distribution. The second new model is a Bayesian implementation of the optimal score procedure (OS-IRM). Both new models were compared with the traditional Rasch model: the results indicate that the two developed models improve various aspects of the Rasch model. The third study was derived from the process assumption and had three objectives. First, to develop a Bayesian implementation of the situational optimization function analysis (SOFA) framework. Second, to compare this Bayesian implementation of SOFA with three other Maximum Likelihood-based models that are used to estimate true scores. The third objective was to show how joint modeling can be used for validity research. One of the main advantages of the SOFA framework compared to the traditional psychometric approach is that SOFA relies on experimental data, improving the validity of the measures. The fourth and final study was derived from the construct assumption and its main objective was to develop a procedure of structure learning of power chain graphs (PCGs). A PCG is a type of graph that represents causal relations between groups of variables. It can be thought as a full exploratory version of structural equation modeling, as well as a psychometric model that is not dependent on latent variables. These four studies intend to show that psychometric modeling should not be restricted to the use of traditional measurement models, but should also consider adapting these traditional models in accordance with the intended use and theoretical processes that originate the observed measures