Probabilistic Conditional Independence Structuresand
ثبت نشده
چکیده
1 Franti sek Mat u s Prague ABSTRACT. Special conditional independence structures have been recognized to be matroids. This opens new possibilities for the application of matroid theory methods (duality, minors, expansions) to the study of conditional independence and, on the other hand, starts a new probabilistic branch of matroid representation theory. 2
منابع مشابه
Declarations of independence
According to orthodox (Kolmogorovian) probability theory, conditional probabilities are by definition certain ratios of unconditional probabilities. As a result, orthodox conditional probabilities are undefined whenever their antecedents have zero unconditional probability. This has important ramifications for the notion of probabilistic independence. Traditionally, independence is defined in t...
متن کاملGeneralized Conditional Independence and Decomposition Cognizant Curvature: Implications for Function Optimization
We introduce conditional independence for real-valued set functions which generalizes probabilistic conditional independence. We show that a natural semantics of conditional independence is that of local modularity. Generalized conditional independence leads to a spectrum between two extremes: modular functions and functions without any local modularity. We develop a decomposition theory and re...
متن کاملOn the Properties of Conditional Independence
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 ...
متن کاملConditional products: An alternative approach to conditional independence
We introduce a new abstract approach to the study of conditional independence, founded on a concept analogous to the factoriza-tion properties of probabilistic independence, rather than the separation properties of a graph. The basic ingredient is the \con-ditional product", which provides a way of combining the objects under consideration while preserving as much independence as possible. We i...
متن کاملTractability through Exchangeability: A New Perspective on Efficient Probabilistic Inference
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical property that renders probabilistic inference tractable is less well-understood. We develop a theory of finite exchangeability and its relation to tractable probab...
متن کامل