Nested Markov Properties for Acyclic Directed Mixed Graphs

Directed acyclic graph (DAG) models may be characterized in at least four different ways: via a factorization, the d-separation criterion, the moralization criterion, and the local Markov property. As pointed out by Robins (1986, 1999), Verma and Pearl (1990), and Tian and Pearl (2002b), marginals of DAG models also imply equality constraints that are not conditional independences. The well-known `Verma constraint' is an example. Constraints of this type were used for testing edges (Shpitser et al., 2009), and an efficient marginalization scheme via variable elimination (Shpitser et al., 2011). We show that equality constraints like the `Verma constraint' can be viewed as conditional independences in kernel objects obtained from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, via Markov properties and a factorization, a graphical model associated with acyclic directed mixed graphs (ADMGs). We show that marginal distributions of DAG models lie in this model, prove that a characterization of these constraints given in (Tian and Pearl, 2002b) gives an alternative definition of the model, and finally show that the fixing operation we used to define the model can be used to give a particularly simple characterization of identifiable causal effects in hidden variable graphical causal models.Comment: 67 pages (not including appendix and references), 8 figure

Smooth, identifiable supermodels of discrete DAG models with latent variables

We provide a parameterization of the discrete nested Markov model, which is a supermodel that approximates DAG models (Bayesian network models) with latent variables. Such models are widely used in causal inference and machine learning. We explicitly evaluate their dimension, show that they are curved exponential families of distributions, and fit them to data. The parameterization avoids the irregularities and unidentifiability of latent variable models. The parameters used are all fully identifiable and causally-interpretable quantities.Comment: 30 page

Temporal and Relational Models for Causality: Representation and Learning

Discovering causal dependence is central to understanding the behavior of complex systems and to selecting actions that will achieve particular outcomes. The majority of work in this area has focused on propositional domains, where data instances are assumed to be independent and identically distributed (i.i.d.). However, many real-world domains are inherently relational, i.e., they consist of multiple types of entities that interact with each other, and temporal, i.e., they change over time. This thesis focuses on causal modeling for these more complex relational and temporal domains. This thesis provides an in-depth investigation of the properties of relational models and is extending their expressivity to include a temporal dimension. Specifically, we first investigate alternative ways to ground relational models, and we provide an in-depth analysis of the impact of alternative grounding semantics for feature construction, causal effect estimation, and model selection. Then, we extend relational models to represent discrete time. We generalize the theory of d-separation for this class of temporal and relational models. Finally, we provide a constraint-based algorithm, TRCD, to learn the structure of temporal relational models from data

Marginalization and conditioning for LWF chain graphs

In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.Supported by Grant #FA9550-12-1-0392 from the U.S. Air Force Office of Scientific Research (AFOSR) and the Defense Advanced Research Projects Agency (DARPA)

Informed Search for Learning Causal Structure

Over the past twenty-five years, a large number of algorithms have been developed to learn the structure of causal graphical models. Many of these algorithms learn causal structures by analyzing the implications of observed conditional independence among variables that describe characteristics of the domain being analyzed. They do so by applying inference rules, data analysis operations such as the conditional independence tests, each of which can eliminate large parts of the space of possible causal structures. Results show that the sequence of inference rules used by PC, a widely applied algorithm for constraint-based learning of causal models, is effective but not optimal. This is because algorithms such as PC ignore the probability of the outcomes of these inference rules. We demonstrate how an alternative algorithm can reliably outperform PC by taking into account the probability of inference rule outcomes. Specifically we show that an informed search that bases the order of causal inference on a prior probability distribution over the space of causal constraints can generate a flexible sequence of analysis that efficiently identifies the same results as PC. This class of algorithms is able to outperform PC even under uniform or erroneous priors

Education for Global Responsibility : Finnish Perspectives

Education for Global Responsibility – Finnish Perspectives is the first outcome of the three-year project Education for Global Responsibility launched in spring 2007. The publication consists of articles by researchers from different scientific fields probing the central themes of global education. In addition, it contains addresses that reflect and in part sum up the themes covered in the more formally written articles. The publication is illustrated with artwork by Lily Maria Ehnborg, a Swedish artist. In the first chapter under the title Prologue Professor Martin Scheinin, the United Nations Special Rapporteur on the Protection and Promotion of Human Rights while Countering Terrorism, shares his thoughts on global education in the light of globalisation and human rights. In her address the leader of the project Monica Melén-Paaso considers the dialogue between science and art and their roles in deepening our understanding about global issues. The following article is written by Professor Rauni Räsänen. She introduces and discusses various definitions of and approaches to intercultural education, and looks at theories of intercultural and multicultural learning. The essential role of human rights education in global education is pointed out by Dr Reetta Toivanen. She discusses the global efforts undertaken by the United Nations and analyses how the objectives of the Decade for Human Rights Education (1995–2004) have been put into action in Finland. According to researcher Unto Vesa, peace education as a concept is relatively new, but the contents of the term have a long history. Definitions in international declarations and statements can vary from broad umbrella definitions to case sensitive explications. Professor Liisa Laakso continues by calling for citizen opportunities to learn skills for interacting and cooperating that would help them to contribute to and monitor the discussion on development and development cooperation. Intercultural competence is needed for successful intercultural interactions in multicultural societies both locally and globally, but what is it really? This is what Professor Liisa Salo-Lee explores in her article entitled Towards Cultural Literacy. The objectives of the United Nations Decade of Education for Sustainable Development (ESD) in 2005–2014 are currently put into action in all educational sectors in Finland. Director Paula Lindroos and Project Coordinator Mikko Cantell sum up the recent discussion on education for sustainability, mostly from the point of view of educational policies. The last article is written by Lars Rydén, former professor at Uppsala University, Sweden. He explores the essential values underpinning the agenda for global education and citizenship from the view point of international cooperation and competence requirements. The publication ends with a reflective Epilogue by the editors Taina Kaivola and Monica Melén-Paaso. The themes presented by the authors, key concepts and how they relate to each other are clarified in a concept map, which will serve as a starting point for the next phase of the project