This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.

Whenever the use of non-experimental data for discovering causal relations or predicting the outcomes of experiments or interventions is contemplated, two difficulties are routinely faced. One is the problem of latent variables, or confounders: factors influencing two or more measured variables may not themselves have been measured or recorded. The other is the problem of sample selection bias: values of the variables or features under study may themselves influence whether a unit is included in the data sample.

The introduction of statistical models represented by directed acyclic graphs (DAGs) has proved fruitful in the construction of expert systems, in allowing efficient updating algorithms that take advantage of conditional independence relations (Pearl, 1988, Lauritzen et al. 1993), and in inferring causal structure from conditional independence relations (Spirtes and Glymour, 1991, Spirtes, Glymour and Scheines, 1993, Pearl and Verma, 1991, Cooper, 1992). As a framework for representing the combination of causal and statistical hypotheses, DAG models have shed light on a (...) number of issues in statistics ranging from Simpson’s Paradox to experimental design (Spirtes, Glymour and Scheines, 1993). The relations of DAGs with statistical constraints, and the equivalence and distinguishability properties of DAG models, are now well understood, and their characterization and computation involves three properties connecting graphical structure and probability distributions: (i) a local directed Markov property, (ii) a global directed Markov property, (iii) and factorizations of joint densities according to the structure of a graph (Lauritizen, et al., 1990). (shrink)

This essay works to bridge conversations in philosophy of education with decolonial theory. The author considers Margonis’ ( 1999 , 2011a , b ) use of Rousseau ( 1979 ) and Heidegger ( 1962 ) in developing an ontological attitude that counters social hierarchies and promotes anti-colonial relations. While affirming this effort, the essay outlines a coloniality of being at work in Rousseau and Heidegger through thier reliance on the colonial conceptualization of African Americans and Native Americans as savage and (...) primitive. The essay turns to decolonial theory and the work of Maldenado-Torres (Cult Stud 21(2–3):240–270, 2007 , 2009 ) to highlight how a decolonial attitude complicates, yet enriches Margonis’ philosophical framework. (shrink)

It is well known that there may be many causal explanations that are consistent with a given set of data. Recent work has been done to represent the common aspects of these explanations into one representation. In this paper, we address what is less well known: how do the relationships common to every causal explanation among the observed variables of some DAG process change in the presence of latent variables? Ancestral graphs provide a class of graphs that can encode conditional (...) independence relations that arise in DAG models with latent and selection variables. In this paper we present a set of orientation rules that construct the Markov equivalence class representative for ancestral graphs, given a member of the equivalence class. These rules are sound and complete. We also show that when the equivalence class includes a DAG, the equivalence class representative is the essential graph for the said DAG. (shrink)

Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error” or “disturbance” terms), and an associated path diagram corresponding to the functional composition of variables specified by the structural equations and the correlations among the error terms. It is often thought that the path diagram is (...) nothing more than a heuristic device for illustrating the assumptions of the model. However, in this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling. (shrink)

This paper describes the application of eight statistical and machine-learning methods to derive computer models for predicting mortality of hospital patients with pneumonia from their findings at initial presentation. The eight models were each constructed based on 9847 patient cases and they were each evaluated on 4352 additional cases. The primary evaluation metric was the error in predicted survival as a function of the fraction of patients predicted to survive. This metric is useful in assessing a model’s potential to assist (...) a clinician in deciding whether to treat a given patient in the hospital or at home. We examined the error rates of the models when predicting that a given fraction of patients will survive. We examined survival fractions between 0.1 and 0.6. Over this range, each model’s predictive error rate was within 1% of the error rate of every other model. When predicting that approximately 30°K of the patients will survive, all the models have an error rate of less than 1.5%. The models are distinguished more by the number of variables and parameters that they contain than by their error rates; these differences suggest which models may be the most amenable to future implementation as paper-based guidelines. (shrink)

Machine Learning (ML) and Artificial Intelligence (AI) are for many the defining features of the early twenty-first century. With such a provocation, this essay considers how one might understand the relational philosophies articulated by Indigenous learning scientists, Indigenous technologists and feminine philosophers of education as co-constitutive of an ensemble mediating or regulating an educative philosophy interfacing with ML/AI. In these mediations, differing vocabularies – kin, the one caring, cooperative – are recognized for their ethical commitments, yet challenging epistemic claims in (...) the contexts of ML. Similarly, ML poses some questions to claims made about relational and Indigenous epistemologies, where the latter is perceived as separated from and unaffected by computation specifically or algorithmic societies generally. This essay seeks to gain several vantage points to explore and complicate how diverse relational philosophies can address ML and perhaps reconsider their own critical practices. (shrink)

This essay explores some of the affinities between current theories of North American Indigenous trickster narratives and continental philosophy where they are both concerned with the question of responsibility in subject formations. Taking up the work of Judith Butler, Franz Kafka and Gerald Vizenor, the author works to show how both continental and Indigenous intellectual traditions work against any assumed stability for the ‘I’ in the narration of the self, yet toward responsible relationality. Such affinities, however, emerge from differing socio‐cultural (...) and linguistic horizons that are not reducible one to the other. This is particularly so with regard to the natural world and the ways in which Indigenous narratives are developed to foster responsible subjects to a larger biotic environment. Through discussion of such affinities and differences, the author seeks to broaden and multiculturalize contemporary debates in philosophy. (shrink)

This article considers how diplomacy can be refined and amplified within the field of multicultural education. Focusing on Native American peoples in particular, I argue that the multiculturalist emphasis on cultural diplomacy overlooks the political difference of First Nations peoples. In contrast to a multiculturalist cultural diplomacy, the article develops diplomacy according to a decolonial framework that seeks to dismantle colonial perspectives of Native American political difference. Drawing upon theorists and historians of diplomacy, as well as Indigenous and decolonial writers, (...) the article seeks to provide the terms through which teacher identifications as decolonial diplomats can be fostered toward Native Americans. (shrink)

Patronizing the Public is the first detailed and comprehensive examination of how American philanthropy has transformed culture, communication, and the humanities. Drawing on an impressive range of archival and secondary sources, the chapters in the volume shed light on philanthropic foundations have shaped numerous fields, including film, television, radio, journalism, drama, local history, museums, as well as art and the humanities in general.

Much else was done by Rose and Sullivan in their possibly conclusive attempt to restore sense to the rebus passage, but the reading super scorpionem locustam was Gaselee's, as Rose and Sullivan clearly acknowledge. This seems unluckily to have escaped B. Baldwin, otherwise he would have noticed that Gaselee also fancied in his correction an allusion to the poisoner Locusta. For those who may have difficulty in obtaining Gaselee's collotype reproduction, I quote the relevant part: ‘But what have lobsters to (...) do with poisoners? Is it permissible to see a more or less open reference to Locusta, the queen of all poisoners? If so, we have here another little piece of evidence which will help us to date the Satyricon.’. (shrink)

Much else was done by Rose and Sullivan in their possibly conclusive attempt to restore sense to the rebus passage, but the reading super scorpionem locustam was Gaselee's, as Rose and Sullivan clearly acknowledge. This seems unluckily to have escaped B. Baldwin, otherwise he would have noticed that Gaselee also fancied in his correction an allusion to the poisoner Locusta. For those who may have difficulty in obtaining Gaselee's collotype reproduction, I quote the relevant part: ‘But what have lobsters to (...) do with poisoners? Is it permissible to see a more or less open reference to Locusta, the queen of all poisoners? If so, we have here another little piece of evidence which will help us to date the Satyricon.’. (shrink)

In this essay Troy Richardson works to develop a conceptual framework and set of terms by which a diplomatic reception of different forms of law can be developed in multicultural education. Taking up the trope of the door in multiculturalist discourse as a site in which a welcoming of the difference of others is organized, Richardson interrogates the complex nature of receptivity to Indigenous customary law, in particular. He argues that, within this trope, a metonymic structure operates in relation to (...) the deployment of “policy” that maintains a perspective of customary law as premodern and primitive. This structure leads to an impoverished set of terms and a lack of diplomacy toward difference. Richardson proceeds by considering the notion of extraterritoriality and the metonyms that organize Emmanuel Levinas's discourse of “doors” in conceptualizing a welcoming receptivity. The term “extraterritoriality” anticipates the law of the other as it approaches the door and implies a diplomatic moment of reception of such difference. Richardson concludes by highlighting Jacques Derrida's evaluation of Levinas's discourse of receptivity and by considering the possibilities for a diplomatic engagement with the laws of others toward a mutation in the current geopolitical moment. (shrink)

This essay argues strongly that racism in the United States hurts thefuture of all children. To eradicate this pernicious mindset inits institutional forms requires that we understand that race,as an idea that shapes social organization in this country,is a unique historical product dating from the colonial periodof the southern colonies of mainland British North America.Further, the mythology about American history, as it is taughtin school, excuses and legitimates continued inequality,oppression, and racism today. This essay traces the historyof class oppression from (...) the 17th century, when the institutionof slavery was invented as a means of securing the unpaidchattel bonded labor of Anglo-Europeans, to the emergenceof unfree labor as a form of racial oppression, and subsequently the institutionalization of racial slavery inthe 18th century. Racial slavery, which elevated whitesupremacy and privilege, was still not synonymous with themodern form of pseudo-scientific racism that emerged as adefense of slavery in the antebellum period and its aftermathin the Civil War and Reconstruction. Racism and the legacyof white privilege is still used as a means of social controlto mask class relations and to thereby control and diminishcollective social action that potentially would occurin the absence of the color line. Knowledge of race as anhistorical construct created by human beings in particularcircumstances raises the possibility that race, racism, and its effects can also be changed by human beings acting in opposition to the conditions that artificially separate us. (shrink)

Thomas Richardson and Peter Spirtes. Parameterizing and Scoring Mixed Ancestral Graphs.

Thomas Richardson and Peter Spirtes. Scoring Ancestral Graph Models.

This book brings together contemporary theorists and practitioners to critically explore the state of psychogeography today.

It has been shown in Spirtes(1995) that X and Y are d-separated given Z in a directed graph associated with a recursive or non-recursive linear model without correlated errors if and only if the model entails that ρXY.Z = 0. This result cannot be directly applied to a linear model with correlated errors, however, because the standard graphical representation of a linear model with correlated errors is not a directed graph. The main result of this paper is to show how (...) to associate a directed graph with a linear model L with correlated errors, and then use d-separation in the associated directed graph to determine whether L entails that a particular partial correlation is zero. (shrink)