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About 5,700 papers for “Conditional independence”

Conditional Independence

Nicholas T. Longford · Encyclopedia of Statistics in Behavioral Science · 2005

Abstract In principle, all independence is conditional, qualified by the context and assumptions under which it applies. In practice, conditional independence represents the first step away from (unconditional) independence toward models that account for, describe, or explain the dependence among variables.

Cited by 0

Conditional independence...

Xia Wanga, Yongmiao Hongb · 2012

We propose a characteristic function based test for conditional independence, which is applicable in both cross-sectional and time series contexts. Our test is not only asymptotically locally more powerful than Su and White’s (2007) test, but also is more flexible in inferring patterns of condi-tional dependence. In addition to our ominous test, we also propose a class of derivative tests to gauge possible patterns of conditional dependence. These derivative tests deliver some interesting model-free tests for such important hypotheses as omitted variables, Granger causality in mean and conditional uncorrelatedness. All proposed tests have a convenient asymptotic N(0, 1) distribution under the null hypotheses. Unlike many other smoothed nonparametric tests for conditional inde-pendence, we allow nonparametric estimators for both conditional joint and marginal characteristic functions to jointly determine the asymptotic distribution of our tests. This leads to a much better size performance in finite samples. Monte Carlo studies demonstrate the well behavior of our tests in finite samples. In an application to testing nonlinear Granger causality, we document the existence of nonlinear relationships between money and output, which may be ignored by the linear Granger

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Conditional Independence

Birkhäuser Basel eBooks · 2009

AbstractConditional independence constraints are simple and intuitive restrictions on probability distributions that express the notion that two sets of random variables are unrelated, typically given knowledge of the values of a third set of random variables. A conditional independence model is a family of probability distributions that satisfy a collection of conditional independence constraints. In this chapter we explore the algebraic structure of conditional independence models in the case of discrete or jointly Gaussian random variables. Conditional independence models defined by graphs, known as graphical models, are given particular emphasis. Undirected graphical models are also known as Markov random fields, whereas directed graphical models are often termed Bayesian networks.KeywordsDirect Acyclic GraphConditional IndependenceMarkov PropertyPairwise ConstraintChain GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Conditional independence.

Karin Binder (5018999), Stefan Krauss (217340), Georg Bruckmaier (5018996) et al. · Figshare · 2018

Cited by 0Open access

Conditional Independence

A. B. Dieker, Steven T. Hackman · Springer series in operations research/Springer series in operations research and financial engineering · 2024

Abstract This chapter provides the requisite foundations for the remaining chapters in Part II and for some of the results established in Part III. We use graphs to represent conditional independence among counter and label variables. This leads to a probabilistic graphical model, defined via a graph in which the vertex set is the set of counter and label variables, and the edge set effectively determines the degree of conditional independence among these variables.

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Conditional Independence, Conditional Mean Independence, and Zero\n Conditional Covariance

Rajeshwari Majumdar · arXiv (Cornell University) · 2017

Investigation of the reversibility of the directional hierarchy in the\ninterdependency among the notions of conditional independence, conditional mean\nindependence, and zero conditional covariance, for two random variables X and Y\ngiven a conditioning element Z which is not constrained by any topological\nrestriction on its range, reveals that if the first moments of X, Y, and XY\nexist, then conditional independence implies conditional mean independence and\nconditional mean independence implies zero conditional covariance, but the\ndirection of the hierarchy is not reversible in general. If the conditional\nexpectation of Y given X and Z is "affine in X," which happens when X is\nBernoulli, then the "intercept" and "slope" of the conditional expectation\n(that is, the nonparametric regression function) equal the "intercept" and\n"slope" of the "least-squares linear regression function", as a result of which\nzero conditional covariance implies conditional mean independence.\n

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Abstract Propositional Independence Conditional independence

Jérôme Lang, Paolo Liberatore, Pierre Marquis · 2008

Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong conditional independence and perfect conditional independence. Many characterizations and properties of these independence relations are provided. We show them related to many other notions of independence pointed out so far in the literature (mainly formula-variable independence, irrelevance and novelty under various forms, separability, interactivity). We identify the computational complexity of conditional independence and of all these related independence relations.

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From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Maps

Changli He, Yuan Gao, Liping Zhu et al. · ArXiv.org · 2025

Testing conditional independence between two random vectors given a third is a fundamental and challenging problem in statistics, particularly in multivariate nonparametric settings due to the complexity of conditional structures. We propose a novel method for testing conditional independence by transforming it to an unconditional independence test problem. We achieve this by constructing two transport maps that transform conditional independence into unconditional independence, this substantially simplifies the problem. These transport maps are estimated from data using conditional continuous normalizing flow models. Within this framework, we derive a test statistic and prove its asymptotic validity under both the null and alternative hypotheses. A permutation-based procedure is employed to evaluate the significance of the test. We validate the proposed method through extensive simulations and real-data analysis. Our numerical studies demonstrate the practical effectiveness of the proposed method for conditional independence

Cited by 0Open access

Valuation Networks and Conditional Independence 191 Valuation Networks and Conditional Independence

Prakash P. Shenoy · 2016

pshenoy @ ukanvm.cc.ukans.edu Valuation networks have been proposed as graph-ical representations of valuation-based systems (VBSs). The VBS framework is able to capture many uncertainty calculi including probability theory, Dempster-Shafer’s belief-function theory, Spohn’s epistemic belief theory, and Zadeh’s possibility theory. In this paper, we show how valuation networks encode conditional indepen-dence relations. For the probabilistic case, the class of probability models encoded by valuation networks includes undirected graph models, di-rected acyclic graph models, directed balloon graph models, and recursive causal graph models. 1

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Amortized Conditional Independence Testing

Duong, Bao, Hoang, Nu, Nguyen, Thin · arXiv (Cornell University) · 2025

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific disciplines. Existing methods seek to design explicit test statistics that quantify the degree of conditional dependence, which is highly challenging yet cannot capture nor utilize prior knowledge in a data-driven manner. In this study, an entirely new approach is introduced, where we instead propose to amortize conditional independence testing and devise ACID - a novel transformer-based neural network architecture that learns to test for conditional independence. ACID can be trained on synthetic data in a supervised learning fashion, and the learned model can then be applied to any dataset of similar natures or adapted to new domains by fine-tuning with a negligible computational cost. Our extensive empirical evaluations on both synthetic and real data reveal that ACID consistently achieves state-of-the-art performance against existing baselines under multiple metrics, and is able to generalize robustly to unseen sample sizes, dimensionalities, as well as non-linearities with a remarkably low inference time.

Cited by 0Open access

Amortized Conditional Independence Testing

Duong, Bao, Hoang, Nu, Nguyen, Thin · ArXiv.org · 2025

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific disciplines. Existing methods seek to design explicit test statistics that quantify the degree of conditional dependence, which is highly challenging yet cannot capture nor utilize prior knowledge in a data-driven manner. In this study, an entirely new approach is introduced, where we instead propose to amortize conditional independence testing and devise ACID - a novel transformer-based neural network architecture that learns to test for conditional independence. ACID can be trained on synthetic data in a supervised learning fashion, and the learned model can then be applied to any dataset of similar natures or adapted to new domains by fine-tuning with a negligible computational cost. Our extensive empirical evaluations on both synthetic and real data reveal that ACID consistently achieves state-of-the-art performance against existing baselines under multiple metrics, and is able to generalize robustly to unseen sample sizes, dimensionalities, as well as non-linearities with a remarkably low inference time.

Cited by 0Open access