A New Look at Causal Independence (original) (raw)
Related papers
On the impact of causal independence
1998
Reasoning in Bayesian networks is exponential in a graph parameter w 3 known as induced width (also known as tree-width and max-clique size). In this paper, we investigate the potential of causal independence (CI) for improving this performance.
On the modeling of causal belief networks
2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO), 2013
ABSTRACT Causality is compactly and simply represented with graphical models. On these causal networks, we can compute the simultaneous effect of observing the natural behavior of the system and external actions forcing some variables to take specific values. This paper proposes an alternative causal graphical model offering more flexibility and reducing the storage complexity under an uncertain environment where the uncertainty is represented by belief assignments, the so-called causal belief network with conditional beliefs. Indeed, in this representation conditional distributions are defined for either one or more than one cause. To compute the global joint distribution on this network, we also propose a new method for the vacuous extension allowing a uniform transfer of beliefs.
Probabilistic independence of causal influences
2006
One practical problem with building large scale Bayesian network models is an exponential growth of the number of numerical parameters in conditional probability tables. Obtaining large number of probabilities from domain experts is too expensive and too time demanding in practice. A widely accepted solution to this problem is the assumption of independence of causal influences (ICI) which allows for parametric models that define conditional probability distributions using only a number of parameters that is linear in the number of causes. ICI models, such as the noisy-OR and the noisy-AND gates, have been widely used by practitioners. In this paper we propose PICI, probabilistic ICI, an extension of the ICI assumption that leads to more expressive parametric models. We provide examples of three PICI models and demonstrate how they can cope with a combination of positive and negative influences, something that is hard for noisy-OR and noisy-AND gates.
Demonstratio Mathematica, 1999
Spirtes, Glymour and Scheines [19] formulated a Conjecture that a direct dependence test and a head-to-head meeting test would suffice to construe directed acyclic graph decompositions of a joint probability distribution (Bayesian network) for which Pearl's d-separation [2] applies. This Conjecture was later shown to be a direct consequence of a result of Pearl and Verma [21], cited as Theorem 1 in [13], see also Theorem 3.4. in [20]). This paper is intended to prove this Conjecture in a new way, by introducing the concept of p-d-separation (partial dependency separation). While Pearl's d-separation works with Bayesian networks, p-d-separation is intended to apply to causal networks: that is partially oriented networks in which orientations are given to only to those edges, that express statistically confirmed causal influence, whereas undirected edges express existence of direct influence without possibility of determination of direction of causation. As a consequence of the particular way of proving the validity of this Conjecture, an algorithm for construction of all the directed acyclic graphs (dags) carrying the available independence information is also presented. The notion of a partially oriented graph (pog) is introduced and within this graph the notion of p-d-separation is defined. It is demonstrated that the p-d-separation within the pog is equivalent to d-separation in all derived dags.
Communications in Computer and Information Science, 2014
Interventions are important for an efficient causal analysis. To represent and reason with interventions, the graphical structure is needed, the so-called causal networks are therefore used. This paper deals with the handling of uncertain causal information where uncertainty is represented with a belief function knowledge. To simplify knowledge acquisition and storage, we investigate the representational point of view of interventions when conditional distributions are defined per single parent. The mutilated and augmented causal belief networks are used in order to efficiently infer the effect of both observations and interventions.
Beyond Markov: Accounting for independence violations in causal reasoning
Cognitive Psychology, 2018
Although many theories of causal cognition are based on causal graphical models, a key property of such models-the independence relations stipulated by the Markov condition-is routinely violated by human reasoners. Two accounts of why people violate independence are formalized and subjected to experimental test. Subjects' inferences were more consistent with a dual prototype model in which people favor network states in which variables are all present or all absent than a leaky gate model in which information is transmitted through network nodes when it should normatively be blocked. The article concludes with a call for theories of causal cognition that rest on foundations that are faithful to the kinds of causal inferences people actually draw.
Causal independence for probability assessment and inference using Bayesian networks
IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 1996
This material is posted here with permission of the IEEE. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org.
A generic qualitative characterization of independence of causal influence
International Journal of Approximate Reasoning, 2008
Independence of causal influence (ICI) offer a high level starting point for the design of Bayesian networks. However, these models are not as widely applied as they could, as their behavior is often not well-understood. One approach is to employ qualitative probabilistic network theory in order to derive a qualitative characterization of ICI models. In this paper we analyze the qualitative properties of ICI models with binary random variables. Qualitative properties are shown to follow from the characteristics of the Boolean function underlying the model. In addition, it is demonstrated that the theory also allows finding constraints on the model parameters given knowledge of the qualitative properties. This highlevel qualitative characterization offers a new way of identifying suitable ICI models and may facilitate their exploitation in developing real-world Bayesian networks.
A Factorized Representation of Independence of Causal Influence and Lazy Propagation
The Florida AI Research Society Conference, 1999
The efficiency of algorithms for probabilistic inference in Bayesian networks can be improved by exploiting independence of causal influence. The factorized rep- resentation of independence of causal influence offers a factorized decomposition of certain independence of causal influence models. We describe how lazy prop- agation - a junction tree based inference algorithm - easily can be extended to take advantage