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Jeff B Paris - One of the best experts on this subject based on the ideXlab platform.
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predicate Exchangeability and language invariance in pure inductive logic
Logique Et Analyse, 2014Co-Authors: Malte S Klies, Jeff B ParisAbstract:In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language $L$ and replacing each occurrence of a predicate in an $L$-sentence $\phi$ according to this permutation should not change our belief in the truth of $\phi$. In this paper we study when a prior probability function $w$ on a purely unary language $L$ satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.
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a survey of some recent results on spectrum Exchangeability in polyadic inductive logic
Synthese, 2011Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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a characterization of the language invariant families satisfying spectrum Exchangeability in polyadic inductive logic
Annals of Pure and Applied Logic, 2010Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.
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representation theorems for probability functions satisfying spectrum Exchangeability in inductive logic
International Journal of Approximate Reasoning, 2009Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We prove de Finetti style representation theorems covering the class of all probability functions satisfying spectrum Exchangeability in polyadic inductive logic and give an application by characterizing those probability functions satisfying spectrum Exchangeability which can be extended to a language with equality whilst still satisfying that property.
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a general representation theorem for probability functions satisfying spectrum Exchangeability
Conference on Computability in Europe, 2009Co-Authors: Jeff B Paris, Alena VencovskaAbstract:In the context of polyadic inductive logic we give a general representation theorem applicable to all probability functions satisfying Spectrum Exchangeability as the weighted difference of two probability functions satisfying Spectrum Exchangeability and Language Invariance.
Alena Vencovska - One of the best experts on this subject based on the ideXlab platform.
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a survey of some recent results on spectrum Exchangeability in polyadic inductive logic
Synthese, 2011Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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a characterization of the language invariant families satisfying spectrum Exchangeability in polyadic inductive logic
Annals of Pure and Applied Logic, 2010Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.
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representation theorems for probability functions satisfying spectrum Exchangeability in inductive logic
International Journal of Approximate Reasoning, 2009Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We prove de Finetti style representation theorems covering the class of all probability functions satisfying spectrum Exchangeability in polyadic inductive logic and give an application by characterizing those probability functions satisfying spectrum Exchangeability which can be extended to a language with equality whilst still satisfying that property.
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a general representation theorem for probability functions satisfying spectrum Exchangeability
Conference on Computability in Europe, 2009Co-Authors: Jeff B Paris, Alena VencovskaAbstract:In the context of polyadic inductive logic we give a general representation theorem applicable to all probability functions satisfying Spectrum Exchangeability as the weighted difference of two probability functions satisfying Spectrum Exchangeability and Language Invariance.
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language invariance and spectrum Exchangeability in inductive logic
European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 2007Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A sufficient condition, in terms of a de Finetti style representation, is given for a probability function in Inductive Logic (with relations of all arities) satisfying Spectrum Exchangeability to additionally satisfy Language Invariance. This condition is shown to also be necessary in the case of homogeneous probability functions. In contrast it is proved that (purely) t-heterogeneous probability functions can never be members of a language invariant family satisfying Spectrum Exchangeability.
Jurgen Landes - One of the best experts on this subject based on the ideXlab platform.
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a survey of some recent results on spectrum Exchangeability in polyadic inductive logic
Synthese, 2011Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson’s Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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a characterization of the language invariant families satisfying spectrum Exchangeability in polyadic inductive logic
Annals of Pure and Applied Logic, 2010Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A necessary and sufficient condition in terms of a de Finetti style representation is given for a probability function in Polyadic Inductive Logic to satisfy being part of a Language Invariant family satisfying Spectrum Exchangeability. This theorem is then considered in relation to the unary Carnap and Nix–Paris Continua.
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representation theorems for probability functions satisfying spectrum Exchangeability in inductive logic
International Journal of Approximate Reasoning, 2009Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:We prove de Finetti style representation theorems covering the class of all probability functions satisfying spectrum Exchangeability in polyadic inductive logic and give an application by characterizing those probability functions satisfying spectrum Exchangeability which can be extended to a language with equality whilst still satisfying that property.
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the principle of spectrum Exchangeability within inductive logic
2009Co-Authors: Jurgen LandesAbstract:We investigate the consequences of the principle of Spectrum Exchangeability in inductive logic over the polyadic fragment of first order logic. This principle roughly states that the probability of a possible world should only depend on how the inhabitants of this world behave with respect toindistinguishability. This principle is a natural generalization of Exchangeability principles that have long been investigated over the monadic predicate fragment of first order logic. It is grounded in our deep conviction that in the state of total ignorance all possible worlds that can be obtained from each other by basic symmetric transformations should have the same a priori probability. After first fixing our framework and showing some basic lemmata we prove that the principle of spectrum Exchangeability implies several simple principles of Exchangeability that are all based on our conviction that the probability functions should be invariant under basic renaming procedures. We then go on and show several representation theorems for the probability functions satisfying spectrum Exchangeability. One of these representation results shows that we can represent the probability of sentences of a polyadic language in terms of the probability of sentences of a unary language. The other main representation result is a de Finetti-style result that shows that we can write every probability function satisfying spectrum Exchangeability as an integral over some basic probability function weighted by a de Finetti prior µ. After that we use the de Finetti representation results to show a representation result for probability functions satisfying language invariance and spectrum Exchangeability. Rather surprisingly it turns out that the notion of language invariance allows us to seamlessly extend our framework to the fragment of first order logic containing the equality symbol and the predicate fragment. Thereafter we study principles that make inductive assertions. We investigate the Paris Conjecture and we prove that in some instances the principle of instantial relevance holds for t−heterogeneous probability functions. However this principle fails for the completely independent function. Furthermore we show that the assumption of the principle of constant Exchangeability and Johnsons’ sufficientness principle leads to only two trivial probability functions satisfying both these two principles.
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language invariance and spectrum Exchangeability in inductive logic
European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 2007Co-Authors: Jurgen Landes, Jeff B Paris, Alena VencovskaAbstract:A sufficient condition, in terms of a de Finetti style representation, is given for a probability function in Inductive Logic (with relations of all arities) satisfying Spectrum Exchangeability to additionally satisfy Language Invariance. This condition is shown to also be necessary in the case of homogeneous probability functions. In contrast it is proved that (purely) t-heterogeneous probability functions can never be members of a language invariant family satisfying Spectrum Exchangeability.
Kayvan Sadeghi - One of the best experts on this subject based on the ideXlab platform.
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On Finite Exchangeability and Conditional Independence
arXiv: Statistics Theory, 2019Co-Authors: Kayvan SadeghiAbstract:We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely independent or completely dependent. We also provide a sufficient condition for an exchangeable vector so that its elements are marginally independent. We then generalize these results and conditions for exchangeable random networks. In this case, it is demonstrated that the situation is more complex. We show that the independence structure of exchangeable random networks lies in one of six regimes represented by undirected and bidirected independence graphs in graphical model sense. In addition, under certain additional assumptions, we provide necessary and sufficient conditions for the exchangeable network distributions to be faithful to each of these graphs.
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random networks graphical models and Exchangeability
Journal of The Royal Statistical Society Series B-statistical Methodology, 2018Co-Authors: Steffen L Lauritzen, Alessandro Rinaldo, Kayvan SadeghiAbstract:We study conditional independence relationships for random networks and their interplay with Exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In particular, we demonstrate that the fundamental property of dissociatedness corresponds to a Markov property for exchangeable networks described by bidirected line graphs. Finally we study those exchangeable models that are also summarized in the sense that the probability of a network depends only on the degree distribution, and we identify a class of models that is dual to the Markov graphs of Frank and Strauss. Particular emphasis is placed on studying consistency properties of network models under the process of forming subnetworks and we show that the only consistent systems of Markov properties correspond to the empty graph, the bidirected line graph of the complete graph and the complete graph.
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on Exchangeability in network models
arXiv: Statistics Theory, 2017Co-Authors: Steffen L Lauritzen, Alessandro Rinaldo, Kayvan SadeghiAbstract:We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size.
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random networks graphical models and Exchangeability
arXiv: Statistics Theory, 2017Co-Authors: Steffen L Lauritzen, Alessandro Rinaldo, Kayvan SadeghiAbstract:We study conditional independence relationships for random networks and their interplay with Exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In particular, we demonstrate that the fundamental property of dissociatedness corresponds to a Markov property for exchangeable networks described by bidirected line graphs. Finally we study those exchangeable models that are also summarized in the sense that the probability of a network only depends onthe degree distribution, and identify a class of models that is dual to the Markov graphs of Frank and Strauss (1986). Particular emphasis is placed on studying consistency properties of network models under the process of forming subnetworks and we show that the only consistent systems of Markov properties correspond to the empty graph, the bidirected line graph of the complete graph, and the complete graph.
Steffen L Lauritzen - One of the best experts on this subject based on the ideXlab platform.
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random networks graphical models and Exchangeability
Journal of The Royal Statistical Society Series B-statistical Methodology, 2018Co-Authors: Steffen L Lauritzen, Alessandro Rinaldo, Kayvan SadeghiAbstract:We study conditional independence relationships for random networks and their interplay with Exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In particular, we demonstrate that the fundamental property of dissociatedness corresponds to a Markov property for exchangeable networks described by bidirected line graphs. Finally we study those exchangeable models that are also summarized in the sense that the probability of a network depends only on the degree distribution, and we identify a class of models that is dual to the Markov graphs of Frank and Strauss. Particular emphasis is placed on studying consistency properties of network models under the process of forming subnetworks and we show that the only consistent systems of Markov properties correspond to the empty graph, the bidirected line graph of the complete graph and the complete graph.
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on Exchangeability in network models
arXiv: Statistics Theory, 2017Co-Authors: Steffen L Lauritzen, Alessandro Rinaldo, Kayvan SadeghiAbstract:We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their implications, between statistical network models that are finitely exchangeable and models that define a consistent sequence of probability distributions on graphs of increasing size.
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random networks graphical models and Exchangeability
arXiv: Statistics Theory, 2017Co-Authors: Steffen L Lauritzen, Alessandro Rinaldo, Kayvan SadeghiAbstract:We study conditional independence relationships for random networks and their interplay with Exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In particular, we demonstrate that the fundamental property of dissociatedness corresponds to a Markov property for exchangeable networks described by bidirected line graphs. Finally we study those exchangeable models that are also summarized in the sense that the probability of a network only depends onthe degree distribution, and identify a class of models that is dual to the Markov graphs of Frank and Strauss (1986). Particular emphasis is placed on studying consistency properties of network models under the process of forming subnetworks and we show that the only consistent systems of Markov properties correspond to the empty graph, the bidirected line graph of the complete graph, and the complete graph.
