Results 1  10
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11
Enumerating unlabeled and root labeled trees for causal model acquisition
, 2009
"... To specify a Bayes net (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, needs to be assessed for each node. It generally has the complexity exponential on n. The nonimpeding noisyAND (NINAND) tree is a recently developed causal model that reduces the c ..."
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To specify a Bayes net (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, needs to be assessed for each node. It generally has the complexity exponential on n. The nonimpeding noisyAND (NINAND) tree is a recently developed causal model that reduces the complexity to linear, while modeling both reinforcing and undermining interactions among causes. Acquisition of an NINAND tree model involves elicitation of a linear number of probability parameters and a tree structure. Instead of asking the human expert to describe the structure from scratch, in this work, we develop a twostep menu selection technique that aids structure acquisition.
Towards effective elicitation of NINAND tree causal models
, 2009
"... Abstract. To specify a Bayes net (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, needs assessed for each node. It generally has the complexity exponential on n. NoisyOR reduces the complexity to linear, but can only represent reinforcing causal interacti ..."
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Cited by 6 (4 self)
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Abstract. To specify a Bayes net (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, needs assessed for each node. It generally has the complexity exponential on n. NoisyOR reduces the complexity to linear, but can only represent reinforcing causal interactions. The nonimpeding noisyAND (NINAND) tree is the first causal model that explicitly expresses reinforcement, undermining, and their mixture. It has linear complexity, but requires elicitation of a tree topology for types of causal interactions. We study their topology space and develop two novel techniques for more effective elicitation. 1
Knowledge Intensive Learning: Combining Qualitative Constraints with Causal Independence for Parameter Learning in Probabilistic Models
"... Abstract. In Bayesian networks, prior knowledge has been used in the form of causal independencies between random variables or as qualitative constraints such as monotonicities. In this work, we extend and combine the two different ways of providing domain knowledge. We derive an algorithm based on ..."
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Cited by 3 (0 self)
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Abstract. In Bayesian networks, prior knowledge has been used in the form of causal independencies between random variables or as qualitative constraints such as monotonicities. In this work, we extend and combine the two different ways of providing domain knowledge. We derive an algorithm based on gradient descent for estimating the parameters of a Bayesian network in the presence of causal independencies in the form of NoisyOr and qualitative constraints such as monotonicities and synergies. NoisyOr structure can decrease the data requirements by separating the influence of each parent thereby reducing greatly the number of parameters. Qualitative constraints on the other hand, allow for imposing constraints on the parameter space making it possible to learn more accurate parameters from a very small number of data points. Our exhaustive empirical validation conclusively proves that the synergy constrained NoisyOR leads to more accurate models in the presence of smaller amount of data. 1
Acquisition and Computation Issues with NINAND Tree Models
"... Most techniques to improve efficiency of conditional probability table (CPT) acquisition for Bayesian network (BN) can only represent reinforcing causal interactions. The nonimpeding noisyAND (NINAND) tree is the first causal model that explicitly expresses reinforcement, undermining, and their mi ..."
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Cited by 2 (2 self)
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Most techniques to improve efficiency of conditional probability table (CPT) acquisition for Bayesian network (BN) can only represent reinforcing causal interactions. The nonimpeding noisyAND (NINAND) tree is the first causal model that explicitly expresses reinforcement, undermining, and their mixture, while its acquisition is of linear complexity. We address three issues on acquisition and computation with these models. In particular, we propose methods to improve computation of conditional probability from a model, to improve the efficiency of CPT computation from these models, and to address NINAND tree acquisition by elicitation of pairwise causal interactions. 1
Indirect elicitation of NINAND trees in causal model acquisition
 INTER. CONF. ON SCALABLE UNCERTAINTY MANAGEMENT (SUM 2011), LNCS 6929, SPRINGERVERLAG
, 2011
"... To specify a Bayes net, a conditional probability table, often of an effect conditioned on its n causes, needs to be assessed for each node. Its complexity is generally exponential in n and hence how to scale up is important to knowledge engineering. The nonimpeding noisyAND (NINAND) tree causa ..."
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Cited by 2 (2 self)
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To specify a Bayes net, a conditional probability table, often of an effect conditioned on its n causes, needs to be assessed for each node. Its complexity is generally exponential in n and hence how to scale up is important to knowledge engineering. The nonimpeding noisyAND (NINAND) tree causal model reduces the complexity to linear while explicitly expressing both reinforcing and undermining interactions among causes. The key challenge to acquisition of such a model from an expert is the elicitation of the NINAND tree topology. In this work, we propose and empirically evaluate two methods that indirectly acquire the tree topology through a small subset of elicited multicausal probabilities. We demonstrate the effectiveness of the methods in both humanbased experiments and simulationbased studies.
Modelling the Interactions between Discrete and Continuous Causal Factors in Bayesian Networks
"... The theory of causal independence is frequently used to facilitate the assessment of the probabilistic parameters of discrete probability distributions of complex Bayesian networks. Although it is possible to include continuous parameters in Bayesian networks as well, such parameters could not, so f ..."
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The theory of causal independence is frequently used to facilitate the assessment of the probabilistic parameters of discrete probability distributions of complex Bayesian networks. Although it is possible to include continuous parameters in Bayesian networks as well, such parameters could not, so far, be modelled by means of causal independence theory, as a theory of continuous causal independence was not available. In this paper, such a theory is developed and generalised such that it allows merging continuous with discrete parameters based on the characteristics of the problem at hand. This new theory is based on the discovered relationship between the theory of causal independence and convolution in probability theory, discussed for the first time in this paper. It is also illustrated how this new theory can be used in connection with special probability distributions. 1
Nonimpeding NoisyAND Tree Causal Models Over Multivalued Variables
"... To specify a Bayesian network (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, must be assessed for each node. Its complexity is generally exponential in n. NoisyOR and a number of extensions reduce the complexity to linear, but can only represent reinfor ..."
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To specify a Bayesian network (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, must be assessed for each node. Its complexity is generally exponential in n. NoisyOR and a number of extensions reduce the complexity to linear, but can only represent reinforcing causal interactions. Nonimpeding noisyAND (NINAND) trees are the first causal models that explicitly express reinforcement, undermining, and their mixture. Their acquisition has a linear complexity, in terms of both the number of parameters and the size of the tree topology. As originally proposed, however, they allow only binary effects and causes. This work generalizes binary NINAND tree models to multivalued effects and causes. It is shown that the generalized NINAND tree models express reinforcement, undermining, and their mixture at multiple levels, relative to each active value of the effect. The model acquisition is still efficient. For binary variables, they degenerate into binary NINAND tree models. Hence, this contribution enables CPTs of discrete BNs of arbitrary variables (binary or multivalued) to be specified efficiently through the intuitive concepts of reinforcement and undermining. Key words: Bayesian networks, causal probabilistic models, conditional probability distributions, knowledge acquisition.
1Acquisition of Causal Models for Local Distributions in Bayesian Networks
"... Abstract—To specify a Bayesian network, a local distribution in the form of a conditional probability table, often of an effect conditioned on itsn causes, needs to be acquired, one for each nonroot node. Since the number of parameters to be assessed is generally exponential in n, improving the eff ..."
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Abstract—To specify a Bayesian network, a local distribution in the form of a conditional probability table, often of an effect conditioned on itsn causes, needs to be acquired, one for each nonroot node. Since the number of parameters to be assessed is generally exponential in n, improving the efficiency is an important concern in knowledge engineering. Nonimpeding noisyAND (NINAND) tree causal models reduce the number of parameters to being linear inn, while explicitly expressing both reinforcing and undermining interactions among causes. The key challenge in NINAND tree modeling is the acquisition of the NINAND tree structure. In this work, we formulate a concise structure representation and an expressive causal interaction function of NINAND trees. Building on these representations, we propose two structural acquisition methods, which are applicable to both elicitationbased and machine learningbased acquisitions. Their accuracy is demonstrated through experimental evaluations. F 1
Bayesian Network Inference With NINAND Tree Models
"... Nonimpeding noisyAND (NINAND) tree models were developed to improve efficiency and expressiveness in acquisition of conditional probability tables (CPTs) when constructing Bayesian networks (BNs). To take advantage of these models in the BN inference, we propose a multiplicative factorization of ..."
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Nonimpeding noisyAND (NINAND) tree models were developed to improve efficiency and expressiveness in acquisition of conditional probability tables (CPTs) when constructing Bayesian networks (BNs). To take advantage of these models in the BN inference, we propose a multiplicative factorization of these models and a compilation of NINAND tree modeled BNs for lazy propagation (LP). Soundness of the method and its efficiency improvement are shown.