Peter Spirtes. Conditional Independence in Directed Cyclical Graphical Models Representing Feedback or Mixtures.

Humans excel in categorization. Yet from a computational standpoint, learning a novel probabilistic classification task involves severe computational challenges. The present paper investigates one way to address these challenges: assuming class-conditional independence of features. This feature independence assumption simplifies the inference problem, allows for informed inferences about novel feature combinations, and performs robustly across different statistical environments. We designed a new Bayesian classification learning model that incorporates varying degrees of prior belief in class-conditional independence, learns (...) whether or not independence holds, and adapts its behavior accordingly. Theoretical results from two simulation studies demonstrate that classification behavior can appear to start simple, yet adapt effectively to unexpected task structures. Two experiments—designed using optimal experimental design principles—were conducted with human learners. Classification decisions of the majority of participants were best accounted for by a version of the model with very high initial prior belief in class-conditional independence, before adapting to the true environmental structure. Class-conditional independence may be a strong and useful default assumption in category learning tasks. (shrink)

This article defends the notion of downward causation, relating it to a notion of conditional independence.

Peter Spirtes. Conditional Independence in Directed Cyclic Graphical Models for Feedback.

Recursive linear structural equation models can be represented by directed acyclic graphs. When represented in this way, they satisfy the Markov Condition. Hence it is possible to use the graphical d-separation to determine what conditional independence relations are entailed by a given linear structural equation model. I prove in this paper that it is also possible to use the graphical d-separation applied to a cyclic graph to determine what conditional independence relations are entailed to hold by (...) a given non-recursive linear structural equation model. I also give a causal intepretation to the linear coefficients in a non- recursive structural equation models, and explore the relationships between cyclic graphs and undirected graphs, directed acyclic graphs with latent variables, and chain independence graphs. (shrink)

As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations.

To be human is to be autonomous, yet this is a trait that most of us lack. We are subject to forces external to our being. We are workers; we are citizens; we are needful creatures. Humanity-proper in these times of neoliberal omnipotence is defined differently. The key terms are familiar: personal betterment, personal responsibility, productivity, pleasantness. A forked tongue slithers in our conscience, tells us that these are the traits of the human condition. Through Bataille, this paper argues the (...) substrate of these oft repeated familiar mantras are other. Neoliberal subjects, propelled by need, understand themselves along the axis of the useful choice. The paper turns to myth to understand the interdependence of need and choice, and how this interdependence posits being as always in desire but never in pleasure. Revisiting Don Giovanni, a character central to Acéphalic thought, and the commentary of Søren Kierkegaard, we think in terms of non-abstraction, of pleasurably floating in change, rather than toiling in desire. For it is by grace in the form of chance, that at the very time of transgression, that we – in and for an instant – become human, become as the sacred in the flesh. (shrink)

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence (...) for discrete datasets. The full Bayesian significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

Some statistical questions that arise in studies of Einstein-Podolsky-Rosen correlations are given precise and complete answers for a very simple but artificial set of pair distributions. Some recent results and conjectures about hidden variable representations of the more complex distributions that describe the Einstein-Podolsky-Rosen experiment are examined in the light of the behavior of the simple model.

This essay explains what the Causal Markov Condition says and defends the condition from the many criticisms that have been launched against it. Although we are skeptical about some of the applications of the Causal Markov Condition, we argue that it is implicit in the view that causes can be used to manipulate their effects and that it cannot be surrendered without surrendering this view of causation.

This paper examines definitions of independence for events and variables in the context of full conditional measures; that is, when conditional probability is a primitive notion and conditioning is allowed on null events. Several independence concepts are evaluated with respect to graphoid properties; we show that properties of weak union, contraction and intersection may fail when null events are present. We propose a concept of “full” independence, characterize the form of a full conditional measure (...) under full independence, and suggest how to build a theory of Bayesian networks that accommodates null events. (shrink)

We show a number of improvements in the use of Hidden Conditional Random Fields for phone classification on the TIMIT and Switchboard corpora. We first show that the use of regularization effectively prevents overfitting, improving over other methods such as early stopping. We then show that HCRFs are able to make use of non-independent features in phone classification, at least with small numbers of mixture components, while HMMs degrade due to their strong independence assumptions. Finally, we successfully apply (...) Maximum a Posteriori adaptation to HCRFs, decreasing the phone classification error rate in the Switchboard corpus by around 1% – 5% given only small amounts of adaptation data. (shrink)

The variety-of-evidence thesis has been criticized by Bovens and Hartmann. This article points to two limitations of their Bayesian model: the conceptualization of unreliable evidential sources as randomizing and the restriction to comparing full independence to full dependence. It is shown that the variety-of-evidence thesis is rehabilitated when unreliable sources are reconceptualized as systematically biased. However, it turns out that allowing for degrees of independence leads to a qualification of the variety-of-evidence thesis: as Bovens and Hartmann claimed, more (...) independence does not always imply stronger confirmation. (shrink)

ABSTRACTRecent research into evaluative conditioning shows that information about the relationship between the conditioned and unconditioned stimuli can exert strong effects on the size and di...

Quantum mechanics predicts non-local correlations in spatially extended entangled quantum systems, and these correlations are empirically very well confirmed. This raises philosophical questions of how nature could be that way, prompting the study of purported completions of quantum mechanics by hidden variables. Bell-type theorems connect assumptions about hidden variables with empirical predictions for the outcome of quantum correlation experiments. From among these assumptions, the Setting Independence assumption has received the least formal attention. Its violation is, however, central in the (...) recent discussion about super-deterministic models for quantum correlation experiments. In this paper, we focus on the non-local modal correlations in the GHZ experiment. We model the introduction of hidden variables in the form of instruction sets via structure extensions in the framework of Branching Space-Times. This framework allows us to show in formal detail how the introduction of non-contextual instruction sets results in a specific violation of Setting Independence; a similar result is derived for contextual instruction sets. Our discussion provides additional reasons for foregoing the introduction of local hidden variables, and for accepting non-local quantum correlations as a resource provided by nature. (shrink)

Independence of Conditionals (IC) has recently been proposed as a basic rule for causal structure learning. If a Bayesian network represents the causal structure, its Conditional Probability Distributions (CPDs) should be algorithmically independent. In this paper we compare IC with causal faithfulness (FF), stating that only those conditional independences that are implied by the causal Markov condition hold true. The latter is a basic postulate in common approaches to causal structure learning. The common spirit of FF and (...) IC is to reject causal graphs for which the joint distribution looks ‘non-generic’. The difference lies in the notion of genericity: FF sometimes rejects models just because one of the CPDs is simple, for instance if the CPD describes a deterministic relation. IC does not behave in this undesirable way. It only rejects a model when there is a non-generic relation between different CPDs although each CPD looks generic when considered separately. Moreover, it detects relations between CPDs that cannot be captured by conditional independences. IC therefore helps in distinguishing causal graphs that induce the same conditional independences (i.e., they belong to the same Markov equivalence class). The usual justification for FF implicitly assumes a prior that is a probability density on the parameter space. IC can be justified by Solomonoff’s universal prior, assigning non-zero probability to those points in parameter space that have a finite description. In this way, it favours simple CPDs, and therefore respects Occam’s razor. Since Kolmogorov complexity is uncomputable, IC is not directly applicable in practice. We argue that it is nevertheless helpful, since it has already served as inspiration and justification for novel causal inference algorithms. (shrink)

Intuitively, a classical field theory is background-in- dependent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an (...) interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails. (shrink)

It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one step (...) of revision. The paper discusses and rejects two solutions within the confines of AGM theory. It then introduces ranking functions (as I prefer to call them now; in the paper they are still called ordinal conditional functions) as the proper (and, I find, still the best) solution of the problem, proves that conditional independence w.r.t. ranking functions satisfies the so-called graphoid axioms, and proposes general rules of belief change (in close analogy to Jeffrey's generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory. Indeed, the parallel to probability theory is amazing. Probability theory can profit from ranking theory as well since it is also plagued by the problem of iterated belief revision even if probability measures are conceived as Popper measures (see No. 11). Finally, the theory is compared with predecessors which are numerous and impressive, but somehow failed to explain the all-important conditional ranks in the appropriate way. (shrink)

While it is a point of agreement in contemporary republican political theory that property ownership is closely connected to freedom as non-domination, surprisingly little work has been done to elucidate the nature of this connection or the constraints on property regimes that might be required as a result. In this paper, I provide a systematic model of the boundaries within which republican property systems must sit and explore some of the wider implications that thinking of property in these terms may (...) have for republicans. The boundaries I focus on relate to the distribution of property and the application of types of property claims over particular kinds of goods. I develop this model from those elements of non-domination most directly related to the operation of a property regime: (a) economic independence, (b) limiting material inequalities, and (c) the promotion of common goods. The limits that emerge from this analysis support intuitive judgments that animate much republican discussion of property distribution. My account diverges from much orthodox republican theory, though, in challenging the primacy of private property rights in the realization of economic independence. The value of property on republican terms can be realized without private ownership of the means of production. (shrink)

Independence is a central and recurring theme in Wollstonecraft’s work. Independence should not be understood as an individualistic ideal that is in tension with the value of community but as an essential ingredient in successful and flourishing social relationships. I examine three aspects of this rich and complex concept that Wollstonecraft draws on as she develops her own notion of independence as a powerful feminist tool. First, independence is an egalitarian ideal that requires that all individuals, (...) regardless of sex, are protected to a comparable extent in all areas of social, political and economic life, no matter whether this is in the public or private sphere. Secondly, so long as this egalitarian condition is not compromised, independence allows for individuals to perform differentiated social roles, including along gendered lines. Finally, the on-going and collective input of both women and men is required to ensure that the conditions necessary for social independence are maintained. In Wollstonecraft’s hands, then, independence is a powerful ideal that allows her to argue that women must be able to act on their own terms as social and political equals, doing so as women whose perspectives and interests may differ from men’s. (shrink)

Two recent and influential papers, van Rooij 2007 and Lassiter 2012, propose solutions to the proviso problem that make central use of related notions of independence—qualitative in the first case, probabilistic in the second. We argue here that, if these solutions are to work, they must incorporate an implicit assumption about presupposition accommodation, namely that accommodation does not interfere with existing qualitative or probabilistic independencies. We show, however, that this assumption is implausible, as updating beliefs with conditional information (...) does not in general preserve independencies. We conclude that the approach taken by van Rooij and Lassiter does not succeed in resolving the proviso problem. (shrink)

The aim of the paper is to explicate the concept of causal independence between sets of factors and Reichenbach's screening-off-relation in probabilistic terms along the lines of Suppes' probabilistic theory of causality (1970). The probabilistic concept central to this task is that of conditional stochastic independence. The adequacy of the explication is supported by proving some theorems about the explicata which correspond to our intuitions about the explicanda.

The notion $J$ is independent in $(M,M_0,N)$ was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal $\lambda$ and has a non-forking relation, satisfying the good $\lambda$-frame axioms and some additional hypotheses. Shelah uses independence to define dimension. Here, we show the connection between the continuity property and dimension: if a non-forking satisfies natural conditions and the continuity property, then the dimension is well-behaved. As a corollary, we weaken the stability hypothesis and two (...) additional hypotheses, that appear in Shelah's theorem. (shrink)

We initiate the study of a generalization of Kim-independence, Conant-independence, based on the notion of strong Kim-dividing of Kaplan, Ramsey and Shelah. A version of Conant-independence was originally introduced to prove that all [Formula: see text] theories are [Formula: see text]. We introduce an axiom on stationary independence relations, essentially generalizing the “freedom” axiom in some of the free amalgamation theories of Conant, and show that this axiom provides the correct setting for carrying out arguments of (...) Chernikov, Kaplan and Ramsey on [Formula: see text] theories relative to a stationary independence relation. Generalizing Conant’s results on free amalgamation to the limits of our knowledge of the [Formula: see text] hierarchy, we show using methods from Conant as well as our previous work that any theory where the equivalent conditions of this local variant of [Formula: see text] holds is either [Formula: see text] or [Formula: see text] and is either simple or [Formula: see text]. We observe that these theories give an interesting class of examples of theories where Conant-independence is symmetric. This includes all of Conant’s examples, the small cycle-free random graphs of Shelah, and the (finite-language) [Formula: see text]-categorical Hrushovski constructions of Evans and Wong. We then answer Conant’s question on the existence of non-modular free amalgamation theories. We show that the generic functional structures of Kruckman and Ramsey are examples of non-modular free amalgamation theories. We also show that any free amalgamation theory is [Formula: see text] or [Formula: see text], while an [Formula: see text] free amalgamation theory is simple if and only if it is modular. Finally, we show that every theory where Conant-independence is symmetric is [Formula: see text]. Therefore, symmetry for Conant-independence gives the next known neostability-theoretic dividing line on the [Formula: see text] hierarchy beyond [Formula: see text]. We explain the connection to some established open questions. (shrink)

We prove independence results concerning the number of nonisomorphic models (using the S-chain condition and S-properness) and the consistency of "ZCF + 2 ℵ 0 = ℵ 2 + there is a universal linear order of power ℵ 1 ". Most of these results were announced in [Sh 4], [Sh 5]. In subsequent papers we shall prove an analog f MA for forcing which does not destroy stationary subsets of ω 1 , investigate D-properness for various filters and prove (...) the consistency with G.C.H. of an axiom implying SH (for ℵ 1 ), and connected results. (shrink)

Journal of Mathematical Logic, Ahead of Print. We initiate the study of a generalization of Kim-independence, Conant-independence, based on the notion of strong Kim-dividing of Kaplan, Ramsey and Shelah. A version of Conant-independence was originally introduced to prove that all [math] theories are [math]. We introduce an axiom on stationary independence relations, essentially generalizing the “freedom” axiom in some of the free amalgamation theories of Conant, and show that this axiom provides the correct setting for carrying (...) out arguments of Chernikov, Kaplan and Ramsey on [math] theories relative to a stationary independence relation. Generalizing Conant’s results on free amalgamation to the limits of our knowledge of the [math] hierarchy, we show using methods from Conant as well as our previous work that any theory where the equivalent conditions of this local variant of [math] holds is either [math] or [math] and is either simple or [math]. We observe that these theories give an interesting class of examples of theories where Conant-independence is symmetric. This includes all of Conant’s examples, the small cycle-free random graphs of Shelah, and the (finite-language) [math]-categorical Hrushovski constructions of Evans and Wong. We then answer Conant’s question on the existence of non-modular free amalgamation theories. We show that the generic functional structures of Kruckman and Ramsey are examples of non-modular free amalgamation theories. We also show that any free amalgamation theory is [math] or [math], while an [math] free amalgamation theory is simple if and only if it is modular. Finally, we show that every theory where Conant-independence is symmetric is [math]. Therefore, symmetry for Conant-independence gives the next known neostability-theoretic dividing line on the [math] hierarchy beyond [math]. We explain the connection to some established open questions. (shrink)

The distinguishing feature of ‘modal’ interpretations of quantum mechanics is their abandonment of the orthodox eigenstate–eigenvalue rule, which says that an observable possesses a definite value if and only if the system is in an eigenstate of that observable. Kochen's and Dieks' new biorthogonal decomposition rule for picking out which observables have definite values is designed specifically to overcome the chief problem generated by orthodoxy's rule, the measurement problem, while avoiding the no-hidden-variable theorems. Otherwise, their new rule seems completely ad (...) hoc. The ad hoc charge can only be laid to rest if there is some way to give Kochen's and Dieks' rule for picking out which observables have definite values some independent motivation. And there is, or so I will argue here. Specifically, I shall show that theirs is the only rule able to save Schrödinger's cat from a fate worse than death, and sidestep the Bell–Kochen–Specker no-hidden-variables theorem, once we impose four independently natural conditions on such rules. (shrink)

In this paper, the independence of irrelevant alternatives and the Pareto principle are simultaneously weakened in the Arrovian framework of social choice. Moreover, we also relax transitivity of social preferences. We show that impossibility remains under weaker versions of Arrow’s original conditions. Our results complement the recent work by Coban and Sanver (Soc Choice Welf 43(4):953–961, 2014).

We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics and statistics.

This article examines initial-condition dependence and initial-condition uncertainty for climate projections and predictions. The first contribution is to provide a clear conceptual characterization of predictions and projections. Concerning initial-condition dependence, projections are often described as experiments that do not depend on initial conditions. Although prominent, this claim has not been scrutinized much and can be interpreted differently. If interpreted as the claim that projections are not based on estimates of the actual initial conditions of the world or that what makes (...) projections true are conditions in the world, this claim is true. However, it can also be interpreted as the claim that simulations used to obtain projections are independent of initial-condition ensembles. This article argues that evidence does not support this claim. Concerning initial-condition uncertainty, three kinds of initial-condition uncertainty are identified. The first is the uncertainty associated with the spread of the ensemble simulations. The second arises because the theoretical initial ensemble cannot be used in calculations and has to be approximated by finitely many initial states. The third uncertainty arises because it is unclear how long the model should be run to obtain potential initial conditions at pre-industrial times. Overall, the discussion shows that initial-condition dependence and uncertainty in climate science are more complex and important issues than usually acknowledged. 1Introduction2Projections and Predictions 2.1Predictions2.2Projections3Initial-Condition Dependence 3.1Projections 3.1.1Dynamical conditions justifying independence of initial conditions?3.1.2What projections can and cannot provide3.2Predictions4Initial-Condition Uncertainty 4.1Projections4.2Predictions5ConclusionAppendix. (shrink)

Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent (threatening the ‘wisdom of crowds’) even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how (...) individuals are causally affected by environmental factors such as commonly perceived evidence. In a general theorem, we identify causal conditions guaranteeing each kind of opinion independence. These results have implications for whether and how ‘wisdom of crowds’ arguments are possible, and how truth-conducive institutions can be designed. (shrink)

This article chronicles the material conditions of producing a film in the Philippine independent film scene which has experienced a marked resurgence at the turn of the century, and has been credited for having revived the ailing Filipino film industry. By way of case study, I use my own film Ang Panggagahasa kay Fe (international title: The Rapture of Fe), awarded the best feature-length digital film at the 33rd Cairo Film Festival in 2009. I co-produced, wrote and directed this film. (...) I recount the different factors that helped shape the film, from scripting to film financing, and provide further evidence of the significance of the private sector, in infusing new money and in reviving the national Filipino film industry as a whole. (shrink)

I argue that the freedom which is to coexist with the freedom of choice of others in accordance with a universal law mentioned in Kant's Rechtslehre is not itself freedom of choice. Rather, it is the independence which is a condition of being able to exercise genuine free choice by not having to act in accordance with the choices of others. Kant's distinction between active and passive citizenship appears, however, to undermine this idea of independence, because the possession (...) of a certain type of property right on the part of some citizens makes it possible for them to dominate others. Kant's account of property in this way turns out to be central to the question as to whether his Rechtslehre represents an internally consistent account of how freedom can be guaranteed within a legal and political community. I go on to argue that Kant's attempt to justify a pre-political right of property cannot be viewed as a successful justification of private property, and that he should have abandoned the notion of su... (shrink)

Evaluative conditioning (EC) refers to the change in the valence of a conditioned stimulus (CS) due to its pairing with a positive or negative unconditioned stimulus (US). To the extent that core affect can be characterised by the two dimensions of valence and arousal, EC has important implications for the origin of affective responses. However, the distinction between valence and arousal is rarely considered in research on EC or conditioned responses more generally. Measuring the subjective feelings elicited by a CS, (...) the results from two experiments showed that (1) repeated pairings of a CS with a positive or negative US of either high or low arousal led to corresponding changes in both CS valence and CS arousal, (2) changes in CS arousal, but not changes in CS valence, were significantly related to recollective memory for CS–US pairings, (3) subsequent presentations of the CS without the US reduced the conditioned valence of the CS, with conditioned arousal being less susceptible to extinction and (4) EC effects were stronger for high arousal than low arousal USs. The results indicate that the conditioning of affective responses can occur simultaneously along two independent dimensions, supporting evidence in related areas that calls for a consideration of both valence and arousal. Implications for research on EC and the acquisition of emotional dispositions are discussed. (shrink)

In this article the author presents the history of the development of independent ethics in Poland, which was developed by followers of the Lvov-Warsaw School, the most famous Polish school of philosophy in the world. The general specificity of all branches, defined as independent ethics is presented first. Next, the author presents the historical and political conditions for the creation of this type of ethical concept. In Poland, such ethics was established in two forms, the first of which exhibited its (...) separation from the whole ethical tradition while the second, in contrast, tried to generalise this tradition in a form, named by Tadeusz Czeżowski, as metaethics. This article discusses in depth only the most well-known concept of independent ethics developed by Tadeusz Kotarbiński. (shrink)

This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the (...) authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation"--Publisher. (shrink)

Quanti cateurs Q1 et Q2 du type <1> sont faiblement indépendants si et seulement si Q1Q2(R) = Q2Q1(R1) pour toute relation- produit R. On donne une condition suf sante et nécessaire pour que deux quanti cateurs soient faiblement indépendants.

Autonomy is conceptualized as the need for agency, self-actualization and independence. Nowadays, financial independence and academic achievement for young populations may be considered as key aspects in the transition to adulthood in response to some contextual demands of different cultural environments. By means of a multi-level model, the present study aims to determine the influence and contribution of factors at individual-level (e.g. sex, age, socioeconomic status, family financial support, awarded scholarships, personal finance, student loans) and school-level (e.g. programme (...) quality, online programs, face to face programs) on the academic achievement of young higher education Colombian students. Data come from the scores of the national standardized academic achievement test administered in 2018 in Colombia. The sample included 234,386 students enrolled in 3,389 higher education institutions in Colombia. After controlling the effects of program quality, and the student's previous academic abilities and socio-economic conditions, results showed that students with scholarships had higher scores than financially-dependent students (those who had students loans) and financially-independent students (those who self-funded their studies or who worked during the week) who had low-scores in the national standardized academic achievement test. (shrink)