D. Heckerman and R. Shachter. Decisiontheoretic foundations for causal reasoning. Journal of Artificial Intelligence Research, 3:405--430, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... primary event at time t (i.e. P (C = faulty) t) 1 Gamma e Gamma C t ) It should be clear that from the above conversion non root nodes of the BN are actually deterministic nodes, i.e. special chance (random) nodes with associated a deterministic function for their value determination [8]. Figure 4 shows the structure of the BN for the PLC system of figure 2 and derived from the FT of figure 3. Random variable nodes (i.e. root nodes) are shown as gray ovals, while deterministic variable nodes are empty ovals. Notice that, as mentioned in section 2, events of type Inp actually ....

D. Heckerman and R. Shachter. Decisiontheoretic foundations for causal reasoning. Journal of Artificial Intelligence Research, 3:405--430, 1995.

....by row number; e.g. the third function from Z X , denoted by (1; 0) is given by g(z 1 ) x 2 and g(z 2 ) x 1 . is a partition of U into n l m n pieces. This partition, called response variables or mapping variables, has been used before to derive bounds for the causal effect of X on Y [1, 3]. When all variables are binary, there are 16 pairs in P that corresponds to the cross product of the sets of functions in Table 1. The collection of probability distributions compatible with the model are those that can be generated when assigning probabilities to the pairs in P. There are n l ....

D. Heckerman and R. Shachter. Decision-theoretic foundations for causal reasoning. Journal of Arti- cial Intelligence Research, Volume 3, pages 405-430, 1995.

.... response behavior of a subject through the mapping: y = F Y #d; r#= 8 # # # # # # # # # # # # # # # # # # # # # : y 0 if r = r 0 y 0 if r = r 1 and d = d 0 y 1 if r = r 1 and d = d 1 y 1 if r = r 2 and d = d 0 y 0 if r = r 2 and d = d 1 y 1 if r = r 3 #3# Following Heckerman and Shachter #1995#, we call the response behavior r 0 , r 1 , r 2 and r 3 , respectively, neverrecover, helped, hurt and always recover. Let CR denote the variable whose state space is the cross product of the states of C and R. We use cr ij , with 0 # i; j # 3 to denote the state of CR corresponding to ....

....of CR corresponding to compliance behavior c i and response behavior r j . Figure 2 shows the graphical model that results from replacing U from Figure 1 by the 16 state variable CR. A state minimal variable like CR is called a response variable by Balke and Pearl #1994# and a mapping variable by Heckerman and Shachter #1995#, and its states correspond to the potential response vectors in Rubin s model #Rubin 1978#. Applying the de#nition of ACE#D Y # given in Equation 1, it follows that using the model of Figure 2wehave: ACE#D Y # = X i # cr i1 # , X i # cr i2 # #4# Z D CR Y CR cr ij ....

Heckerman, D., and Shachter, R. 1995. Decisiontheoretic foundations for causal reasoning. Journal of Arti#cial IntelligenceResearch 3:405#430.

....the directionality of the arcs (see Figure 1) Graphical models with both directed and undirected arcs are called chain graphs. In a BN, one can intuitively regard an arc from A to B as indicating the fact that A causes B. For a more formal treatment of causality in the context of BNs, see [HS95] Since evidence can be assigned to any subset of the nodes (i.e. any subset of nodes can be observed) BNs can be used for both causal reasoning (from known causes to unknown effects) an diagnostic reasoning (from known effects to unknown causes) or any combination of the two. The inference ....

D. Heckerman and R. Shachter. Decision-theoretic foundations for causal reasoning. J. of AI Research, 3:405--430, 1995.

....paper (see Eqs. 12) 14) require the evaluation of expressions of the form P (Y x 0 = y 0 jX = x; Y = y) with x and y 8 The connection between counterfactuals and local actions (sometimes resembling miracles ) is made in Lewis (1986) and is further elaborated in Balke and Pearl (1994) and Heckerman and Shachter (1995). incompatible with x 0 and y 0 , respectively. Eq. 4) allows the evaluation of this quantity as follows: P (Y x 0 = y 0 jX = x; Y = y) P (Y x 0 = y 0 ; X = x; Y = y) P (X = x; Y = y) X u P (Y x 0 (u) y 0 )P (ujx; y) 6) In other words, we first update P (u) to obtain ....

....is exactly the number of distinct realizations of PA Y . Moreover, it is easy to show that the matrix connecting p and q is invertible. We thus conclude that the probability of every counterfactual sentence 20 Balke and Pearl (1994) called these S variables response variables, and Heckerman and Shachter (1995) called them mapping variables. can be identified in any Markovian model composed of Noisy OR mechanisms, regardless of whether the exogenous variables in each family are mutually independent. The same holds of course for Noisy AND mechanisms or any combination thereof, including negating ....

D. Heckerman and R. Shachter. Decision-theoretic foundations for causal reasoning. Journal of Artificial Intelligence Research, 3:405--430, 1995.

....decision procedures is examined for all the languages and classes of models considered. 1 INTRODUCTION The important role of causal reasoning in prediction, explanation, and counterfactual reasoning has been argued eloquently in a number of recent papers and books [Chajewska and Halpern 1997; Heckerman and Shachter 1995; Henrion and Druzdzel 1990; Druzdzel and Simon 1993; Pearl 1995; Pearl and Verma 1991; Spirtes, Glymour, and Scheines 1993] If we are to reason about causality, then it is certainly useful to find axioms that characterize such reasoning. The way we go about axiomatizing causal reasoning depends ....

Heckerman, D. and R. Shachter (1995). Decisiontheoretic foundations for causal reasoning. Journal of Artificial Intelligence Research 3, 405--430.

....important features that we feel should constitute part of an approach to defining explanation. We suggest an approach that combines what we feel are the best features of these two definitions with some ideas from the more recent work on causality (Balke and Pearl 1994; Druzdzel and Simon 1993; Heckerman and Shachter 1995; Pearl 1995) One of the observations that falls naturally out of our approach is that we should expect different answers depending on whether we are asking for an explanation of beliefs or facts. For example, if the agent believes that it rained last night and we ask for an explanation for this ....

Heckerman, D. and R. Shachter (1995). Decisiontheoretic foundations for causal reasoning. Journal of Artificial Intelligence Research 3, 405--430.

....approach using a real world case study. 1 Introduction ABayesian network is a graphical model for probabilistic relationships among a set of variables. Over the last decade, the Bayesian network has become a popular representation for encoding uncertain expert knowledge in expert systems (Heckerman et al. 1995a) More recently, researchers have developed methods for learning Bayesian networks from data. The techniques that have been developed are new and still evolving, but they have been shown to be remarkably effective for some data analysis problems. In this paper, we provide a tutorial on Bayesian ....

....the assertions that Fraud is a direct cause of Gas,and Fraud, Age, and Sex are direct causes of Jewelry,we obtain the network structure in Figure 3. The causal semantics of Bayesian networks are in large part responsible for the success of Bayesian networks as a representation for expert systems (Heckerman et al. 1995a) In Section 15, we will see how to learn causal relationships from data using these causal semantics. In the final step of constructing a Bayesian network, we assess the local probability distribution(s) p(x i jpa i ) In our fraud example, where all variables are discrete, weassess one ....

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Heckerman, D. and Shachter, R. (1995). Decisiontheoretic foundations for causal reasoning. Journal of Artificial IntelligenceResearch, 3:405--430.

....is solved recursively through dynamic programming to determine an optimal policy, d # m (x I(dm ) for the latest decision, dm as a function of the information available at the time of the decision. Only the value nodes which are descendants of dm are a#ected by this policy, Vm = V #De(dm ) (Heckerman and Shachter 1995; Shachter and Peot 1992) This policy must satisfy E Vm d # m (x I(d m ) x I(d m ) max d E Vm d, x I(dm ) This suggests the use of the Bayes ball algorithm to determine the requisite sets. The decision dm can be replaced by the optimal policy to obtain the influence diagram ....

....problems. The new algorithm is linear time instead of O( number of decisions) graph size) and can exploit separable values. These algorithms recognize the special properties of deterministic relationships. Such models are becoming increasingly useful as new developments arise in causal models (Heckerman and Shachter 1995). An interesting extension of the deterministic model would be to represent determinism in more than one assessment order, such as representing when deterministic relationships are invertible. Another extension is to apply Bayes ball to cyclical networks (Pearl and Dechter 1996) Bayes ball can ....

Heckerman, D. and R. Shachter. "Decision-Theoretic Foundations for Causal Reasoning." Journal of Artificial Intelligence Research 3 (1995): 405-430.

....section, we describe a set of assumptions under which it is possible to identify an optimal sequence of observations and repair actions in time proportional to the number of components in the device, without explicitly constructing and rolling back a decision tree. The approach is described in Heckerman et al. 1995). Let us suppose that the device has n components c 1 ; c n and each component is in exactly one of a finite set of states. We assume 1 1 The appropriateness of these assumptions is discussed in Heckerman et al. 1995) 2 1. There is only one problem defining variable in the Bayesian ....

....and rolling back a decision tree. The approach is described in Heckerman et al. 1995) Let us suppose that the device has n components c 1 ; c n and each component is in exactly one of a finite set of states. We assume 1 1 The appropriateness of these assumptions is discussed in Heckerman et al. 1995). 2 1. There is only one problem defining variable in the Bayesian network for the device. This variable represents the functional status of the device. One of the states of this variable must correspond to normal operation. In Figure 1, the node labeled Printer Output is the problem defining ....

[Article contains additional citation context not shown here]

Heckerman, D. and Shachter, R. (1995). Decision-theoretic foundations for causal reasoning. Journal of Artificial Intelligence Research, 3:405--430.

....approach using a real world case study. 1 Introduction A Bayesian network is a graphical model for probabilistic relationships among a set of variables. Over the last decade, the Bayesian network has become a popular representation for encoding uncertain expert knowledge in expert systems (Heckerman et al. 1995a) More recently, researchers have developed methods for learning Bayesian networks from data. The techniques that have been developed are new and still evolving, but they have been shown to be remarkably effective for some data analysis problems. In this paper, we provide a tutorial on Bayesian ....

....assertions that Fraud is a direct cause of Gas, and Fraud, Age, and Sex are direct causes of Jewelry, we obtain the network structure in Figure 3. The causal semantics of Bayesian networks are in large part responsible for the success of Bayesian networks as a representation for expert systems (Heckerman et al. 1995a) In Section 15, we will see how to learn causal relationships from data using these causal semantics. In the final step of constructing a Bayesian network, we assess the local probability distribution(s) p(x i jpa i ) In our fraud example, where all variables are discrete, we assess one ....

[Article contains additional citation context not shown here]

Heckerman, D. and Shachter, R. (1995). Decisiontheoretic foundations for causal reasoning. Journal of Artificial Intelligence Research, 3:405--430.

No context found.

D. Heckerman and R. Shachter. Decisiontheoretic foundations for causal reasoning. Journal of Artificial Intelligence Research, 3:405--430, 1995.

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Heckerman, D. and Shachter, R.D., 1995. Decision-Theoretic Foundations for Causal Reasoning. Journal of Artificial Intelligence Research, 3: 405-430.

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D. Heckerman and R. Shachter. Decision-theoretic foundations for causal reasoning. Journal of Artificial Intelligence Research, 3(1995), pages 405--430.

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Heckerman D. & Shachter R. 1995 Decision-Theoretic Foundations for Causal Reasoning. Journal of Artificial Intelligence Research, 3, 405-430.

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