D. Heckerman. Bayesian networks for knowledge discovery. In Advances in Knowledge Discovery and Data Mining, pages 273--305, Cambridge, MA, 1996. MIT Press.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....information about one disease may require the protection of other probabilistically related records. In this paper, as in [CM02] a Bayesian net (network) representation is used to describe the probabilistic relationship. A corresponding Bayesian net representation is given in Figure 1 (see [He96] [SL90] SGS93] for details on how to construct a Bayesian net) which shows that AIDS may affect the consequence of both hepatitis and mental depression and also shows that a cause of AIDS is a blood transfusion. Table 2 shows the database that is considered for release to the ....

Heckerman, D. (1996) "Bayesian Networks for Knowledge Discovery," Advances in Knowledge Discovery and Data Mining, AAAI Press/MIT Press, pp. 273-305.

....on the Decision Maker s rules. If the inference is excessive, then the Parsimonious Downgrader will implement a protection plan to lessen the inference (i.e. decides to modify by deleting certain data from the database) The inference mechanism is based on a decision theoretical framework (e.g. [10][21] 23] 27] 28] It is the Bayesian network framework that will be used for our inference analysis in this paper. The output of the Rational Downgrader is the database to be released to Low. Our goal is to make modifications as parsimoniously as possible and thus avoid imposing unnecessary ....

....protect sensitive information about one disease may require the protection of other probabilistically related records. In this paper, we use a Bayesian network representation to describe the probabilistic relationship. A corresponding Bayesian network representation is given in Figure 1H (see [10][21]for details on how to construct a Bayesian network) which shows that AIDS may affect the consequence of both hepatitis and mental depression and a cause of AIDS is a (blood) transfusion. hepatitis depression AIDS transfusion Figure 1H. B net of the High. depression hepatitis ....

Heckerman, D. (1996) "Bayesian Networks for Knowledge Discovery," Advances in Knowledge Discovery and Data Mining, AAAI Press/MIT Press, pp. 273-305.

....publicly released data. To protect against such inference attacks, information that is probabilistically related to sensitive information must be examined and perhaps modified. The typical analysis of the probabilistic dependency relationships is carried out using Bayesian network theory [1] 2][3]. Pearl [1] 4] has shown how Bayesian networks model inference. We use the same technique to lessen inference. Specifically, we introduce a formal schema for database inference analysis, based upon a Bayesian network structure, which identifies critical parameters involved in the inference problem ....

.... several researchers offer different approaches to mitigating the database inference problem, e.g. 5] 6] 7] 8] 9] 10] 11] we are the first to use a Bayesian network approach ( 12] 13] In this paper we do not discuss how to construct a Bayesian network B n for a given database, see e.g. [3][14] The most common technique for protecting sensitive information is that of downgrading the non sensitive information in the database, also referred to as database sanitization. The result of downgrading is to mitigate, if not eradicate, the inference problem. We feel that it is important to ....

[Article contains additional citation context not shown here]

Heckerman, D. (1996) "Bayesian Networks for Knowledge Discovery," Advances in Knowledge Discovery and Data Mining, AAAI Press/MIT Press, pp. 273-305. 6

....of Combination of Attributes. A node represents an attribute. The dashed line denotes the combination and the straight line denotes the similarity relationship. 3. 2 Computation of Probabilistic Impact The analysis of the probabilistic dependency is based on a Bayesian net representation ([8][18] As shown in Figure 2, either AIDS or thyroid leads to mental depression , while hepatitis and mental depression support the diagnosis of AIDS . Thus, AIDS can be inferred from information about hepatitis and mental depression . Note that attributes about a person s background ....

....outside the dashed line are not included in the current database. 5.1 Restoration It is possible to (partially) restore hidden attribute values if the information of the underlying Bayesian network structures of the database are known this is the worst case to defend against. As in [2][8][12] the restoration approach primarily selects the set of instantiation x to the hidden values with respect to log Pr(Dm x Bn) for Dm. With data of Table 3, one could obtain the values of AIDS shown in Table 5. Note that the two blockings (i.e. data items 3 and 4) are also correctly restored ....

Heckerman D. (1996) "Bayesian Networks for Knowledge Discovery," Advances in Knowledge Discovery and Data Mining, AAAI Press/MIT Press, pp. 273-305.

.... based function [96, 97] the backpropagation algorithm for artificial neural networks (ANNs) 77, 111] decision tree construction algorithms utilizing various node decision criteria [29, 134, 5] spline methods for classification [165, 162] and probabilistic graphical dependency models [76, 32]. Evaluating an estimate g of g in terms of how well it performs on data not included in the training set, or how well g generalizes, is paramount. Often it is possible to allow a learning algorithm to construct g from a sufficiently complex function class so that g approximates g arbitrarily ....

.... to as batch and online k Mean clustering) Kohonen maps [87] and competitive learning [141] Probabilistic clustering methods include the COBWEB algorithm [60] AutoClass [39] the Expectation Maximization (EM) algorithm [50, 124] and, more recently, probabilistic graphical approaches [76, 32]. Hard clustering algorithms, such as k Mean, assign data items to a single cluster whereas soft clustering algorithms, such as EM, assign a given data point to all clusters with a certain probability of membership. Hard clustering algorithms can often be placed in the probabilistic framework ....

D. Heckerman. Bayesian networks for knowledge discovery. In Advances in Knowledge Discovery and Data Mining, pages 273--305, Menlo Park, CA, 1996. AAAI Press.

....database is available which includes information concerning the frequencies of occurrence of combinations of different variable values (the alarms) Therefore the problem is that of induction to induce or learn the structure from the data. Heckerman details a good description of the problem [14][15]. There has been a lot of research involved with the induction of probabilistic networks for example Cooper and Herskovits algorithm [16] Unfortunately the general problem is NP hard [17] For a given number of variables there is a very large number of potential graphical structures which can ....

D. Heckerman, "Bayesian Networks for Knowledge Discovery" (eds). Fayyad UM, Piatetsky-Shapiro G, Smyth P and Uthurusamy R, Advances in Knowledge Discovery and Data Mining, AAAI Press / The MIT Press, 1996 pp.273-305.

....known in advance, but there is a database of information concerning the frequencies of occurrence of combinations of different variable values (the alarms) In such a case the problem is that of induction to induce the structure from the data. Heckerman has a good description of the problem [20][21]. There has been a lot of work in the literature in the area, including that of Cooper and Herskovits[22] Unfortunately the general problem is NP hard [23] For a given number of variables there is a very large number of potential graphical structures which can be induced. To determine the best ....

Heckerman D, 1996. "Bayesian Networks for Knowledge Discovery" eds. Fayyad UM, Piatetsky-Shapiro G, Smyth P and Uthurusamy R, Advances in Knowledge Discovery and Data Mining, AAAI Press / The MIT Press, 273-305.

....not known in advance, but there is a database of information concerning the frequencies of occurrence of combinations of different variable values (the alarms) In such a case the problem is that of induction to induce the structure from the data. Heckerman has a good description of the problem[10]. There has been a lot of work in the literature in the area, including that of Cooper and Herskovits[11] Unfortunately the general problem is NP hard [12] For a given number of variables there is a very large number of potential graphical structures which can be induced. To determine the best ....

Heckerman D, 1996. "Bayesian Networks for Knowledge Discovery" In Fayyad UM, Piatetsky-Shapiro G, Smyth P and Uthurusamy R (Eds.), Advances in Knowledge Discovery and Data Mining, AAAI Press / The MIT Press, 273-305.

....known in advance, but there is a database of information concerning the frequencies of occurrence of combinations of different variable values (the alarms) In such a case the problem is that of induction to induce the structure from the data. Heckerman has a good description of the problem [8][9]. There has been a lot of work in the literature in the area, including that of Cooper and Herskovits [10] Unfortunately the general problem is NP hard [11] For a given number of variables there is a very large number of potential graphical structures which can be induced. To determine the best ....

Heckerman D, "Bayesian Networks for Knowledge Discovery" (eds). Fayyad UM, PiatetskyShapiro G, Smyth P and Uthurusamy R, Advances in Knowledge Discovery and Data Mining, AAAI Press / The MIT Press, (1996) 273-305.

....In many cases the structure of the graphical model is not known in advance, but there is a database of information concerning the frequencies of occurrence of combinations of different variable values. In such a case the problem is that of induction to induce the structure from the data. Heckerman (1996) has a good description of the problem. There has been a lot of work in the literature in the area, including that of Cooper and Herskovits (1992) Unfortunately the general problem is NP hard (Chickering and Heckerman, 1994) For a given number of variables there is a very large number of ....

Heckerman D, 1996. "Bayesian Networks for Knowledge Discovery" In Fayyad UM, Piatetsky-Shapiro G, Smyth P and Uthurusamy R (Eds.), {Advances in Knowledge Discovery and Data Mining} AAAI Press / The MIT Press, 273-305.

....classifiers and are computationally simplest and most efficient, but they sometimes lose accuracy because of the assumption they make that features appear independently in documents. More sophisticated categorization methods base the category ranks on groups of terms (Chakrabarti et al. 1997; Heckerman, 1996; Koller Sahami, 1996; Sahami, 1996; Yang, 1997) The methods that approach the problem hierarchically compute probabilities and make the categorization decision one level in the taxonomy at a time. We focus here on a categorization procedure that makes extensive use of the hierarchy. There are ....

Heckerman D. (1996). Bayesian Networks for Knowledge Discovery. Advances in Knowledge Discovery and Data Mining. Fayyad, Piatetsky-Shapiro, Smyth and Uthurusamy eds., MIT Press.

....the user s language and the data representation. This is clearly related to the earlier point on modelling statistical strategy as a whole, rather than focusing only on algorithmic details. Some promising approaches for building Bayesian (graphical) models from data are beginning to appear (see [19] for a survey) 3.5 Dealing with High Dimensionality Massiveness has two aspects to it: the number of data points and their dimensionality. Most traditional approaches in statistics and pattern recognition do not deal well with high dimensionality. From a classification viewpoint the key is ....

Heckerman, D. 1996. Bayesian Networks for Knowledge Discovery, pp. 273--306, Advances in Knowledge Discovery and Data Mining, U. Fayyad, G. Piatetsky-Shapiro, P. Smyth, & R. Uthurusamy (Eds.), Boston: MIT Press.

....This paper considers data sourced learning. The extraction of a Bayes net from data is a statistical problem. Intuitively, we want to find those structures that, based on the observed data, are well justified. For a review of the literature and tutorials on learning probabilistic networks see [6, 15, 16]. This paper presents a new method to extract structures from frequency data and to evaluate their probability. We select networks containing strong links and substantial deviance from independence. The critical level at which links are considered to be strong or weak, may vary and depend upon the ....

....known to me, and the same holds for frequentist confidence regions. The most prominent approach to the identification of Bayes nets is the Bayesian version of hypothesis testing introduced by Cooper Herskovits [11] and further investigated by Heckerman, Geiger, Chickering [17] and Heckerman [15]. A tutorial is provided by Heckerman [16] A treatment of Bayesian hypothesis testing from the perspective of Markov Chain Monte Carlo methods is given by Raftery [37] As the method proposed in this paper is Bayesian, though not Bayesian hypothesis testing but Bayesian interval judgment, we give ....

Heckerman, D. (1996). Bayesian networks for knowledge discovery. In Fayyad, U. M., Piatesky-Shapiro, G., Smyth, P., & Uthurusamy, R. (Eds.), Advances in Knowledge Discovery and Data Mining. Menlo Park: AAAI Press/The MIT Press, 273--305.

....52 probabilities will need to be specified, according to table 4.3. This represents a substantial reduction in relation to the 256 probabilities required by the conditional distribution. Steps for the Construction of a Bayesian Network Three steps are necessary to construct a Bayesian network [Heckerman, 1996]: a) To choose the variables and the states of each one of them; 89 Parent Nodes Probabilities P (PD = F jTO = F ) P (PD = F jTO = AC) P (PD = F jTO = A) P (PD = F jTO = N) Transparent P (PD = ACjTO = F ) P (PD = ACjTO = AC) P (PD = ACjTO = A) P (PD = ACjTO = N) Optical P (PD = AjTO = F ) P ....

David Heckerman. Bayesian Networks for Knowledge Discovery, pages 273--305. In Fayyad et al. [1996], 1996.

....655721, fax: 44 (1908) 653169, email: M.Ramoni open.ac.uk, url: http: kmi.open.ac.uk marco. Discovering Bayesian Networks in Incomplete Databases 1. Introduction Bayesian Belief Networks (bbns) are becoming increasingly popular in the Knowledge Discovery and Data Mining (kdd) community [2, 9]. bbns are a successful knowledge representation and reasoning formalism based on probability theory. A bbn [12] is defined by a graphical structure of conditional dependencies among the domain variables and a set of probability distributions defining these dependencies. In this way, bbns provide ....

D. Heckerman. Bayesian networks for knowledge discovery. In Advances in Knowledge Discovery and Data Mining, pages 153--180. MIT Press, Cambridge, MA, 1996.

....determining influences on patient risk factors, treatment, and outcomes. The result of the data mining expert s efforts is a model of the variables, accessible through databases, which influence choice of treatment, outcomes of treatment, and patient risk factors. Unlike Bayesian networks [8], the current version of the system makes no assumptions about the statistical independence of these variables. Although it may be necessary to move toward a system with such simplifying assumptions, the present approach assumes that a very large amount of data will be available through ....

Heckerman D. Bayesian Networks for Knowledge Discovery, chapter 11, pages 273--306. AAAI Press/ MIT Press, 1996.

....and the local maxima are usually sufficient. However, it deals only with simple values. The use of Bayesian networks (Directed Acyclic Graph or DAG) for the discovery of causal relationships among objects is proposed for KDD by Buntine [11, 12] Spirtes et al. 103] and Hackerman et al. [54, 55]. Nodes in a Bayesian network represent variables or states, and arcs represent the dependencies between nodes, directed from the cause to the effect. Figure 2.1 gives a very simple Bayesian network for medical problems [11] CHAPTER 2. RELATED WORK IN KDD 18 Age Occupation Climate Symptoms ....

....DAG, i.e. the dependencies among the nodes in terms of probability distributions. Usually the first step is performed by user or domain expert. Buntine and Hackerman et al. used Bayesian metrics, such as maximum a posteriori probability, and heuristic search to find the structure and parameters [12, 54]. Starting from a given or randomly generated network, the algorithms search for a better network (based on the metrics) until a local optimum is found. Spirtes et al. 103] used conditional independence tests in their TETRED system to find the optimal network. Bayesian networks are powerful tools ....

D. Heckerman. Bayesian networks for knowledge discovery. In U.M. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy, editors, Advances in Knowledge Discovery and Data Mining, pages 273--306. AAAI/MIT Press, 1996.

.... from classification, to clustering, neural networks, and learning of Bayesian Belief Networks (bbns) This paper will focus on bbns as they have been proved to be general enough to encompass a variety of models, including classification models (Friedman Goldsmidth, 1996) clustering methods (Heckerman, 1996), and feed forward neural networks (Buntine, 1994) so that the results here presented can easily be applied to other domains. A Bayesian Belief Network (bbn) is defined by a set of variables X = fX 1 ; X I g and a directed acyclic graph defining a model M of conditional dependencies among ....

Heckerman, D. (1996). Bayesian networks for knowledge discovery. In Advances in Knowledge Discovery and Data Mining, pp. 153--180. MIT Press, Cambridge, MA.

....said to be equivalent if they have the same set of probability distributions. The existing knowledge of an expert or set of experts is encoded into a Bayesian network, then a database is used to update the knowledge, and thus creates one or several new networks. Bayesian Networks are described in [7], 13] 15] and [1] In Fig 3.3, a Bayesian network is illustrated. A disease is dependent on age, work and environment. A symptom is again dependent on a disease. Figure 3.1: A Bayesian Network example. Chapter 3. Methods for Data Mining 3.3.1 Theoretical Overview In probability theory, P (A) ....

....reason on a structure that is already known. One Variable With only one variable, the task is to compute a distribution for the variable given any database. For instance, if we want to compute the probability distribution for a coin that is flipped, the distribution for the variable would be: [7]) p( j h heads; t tails; c h (1 Gamma ) t p( j ) 3.5) Where denote the background knowledge of the model, h denotes the number of heads and t the number of tails. This result is only dependent on the data in the database. In general, for a variable that can have more outcomes, ....

David Heckerman. Bayesian networks for knowledge discovery. In Advances in Knowledge Discovery and Data Mining. AAAI/MIT Press, 1996.

....nodes in the causal graph. B, and event B, and then apply the following equation. P rob(AjB) freq(AandB) freq(B) Alternatively, when the data sources do not contain enough data to reliably count the frequency of a very complex event, the algorithm could follow a Bayesian network approach (Heckerman, 1996), in which assumptions about the independence of variables, and knowledge of the frequencies of less complex events, reduce the need to know the frequencies of these very complex events. These alternative algorithms satisfy essentially the same goal, with respect to the application domain model, ....

D. Heckerman (1996) Bayesian networks for knowledge discovery. in U. Fayyad, G. Piatetsky-Shapiro, P. Smyth, and R. Uthurusamy (Editors) Advances in Knowledge Discovery and Data Mining. AAAI Press/The MIT Press: Cambridge, Mass.

....personal acknowledgement is also needed. This has been brought to the beginning of the paper in order to be clear about the lineage of this tutorial from the outset. This paper initially started as a joint effort between myself and David Heckerman. Because of this I have drawn on David s tutorials [36] and [37] at several points. In addition David has provided extensive comments on three early versions. However, at several points in this paper I put forward my own perspective of subjective probabilities as expert judgements of a true, physical, probability, rather than as a degree of belief. ....

....for 2 of 38 helpful comments on earlier drafts would be a poor acknowledgement of his help and support; I simply could not have produced a paper that was worthy of submission without this help. Good discussions of subjective probabilities as degrees of belief can be found in, for example, 7] [36] and [37] and again I emphasise that this paper is necessarily but a first step on the road to understanding this subject. Look upon it as an exercise in scientific journalism. 2. Aims of the paper During the last two decades there has been a steadily expanding interest in the use of rigorous ....

[Article contains additional citation context not shown here]

Heckerman D. 1996a Bayesian Networks for Knowledge Discovery. In: Fayyad U.M., Piatetsky-Shapiro G., Smyth P and Uthurusamy R. (eds), Advances in Knowledge Discovery and Data Mining. Cambridge, MA: MIT Press, 273-305.

.... to include the dependent case: p(ffl m jn; e m ) p(e m jn; ffl m ) p(8 1im e m;i e m jn; ffl m ) Gammap(8 1im e m;i e m jn; ffl m ) 11) Evaluating this expression when high order dependencies are present will generally not be feasible, but the standard Bayesian network approach (Heckerman, 1996) is applicable here: the number of training errors e m;i of each hypothesis h m;i generated by Lm can be viewed as a node in a Bayesian network, whose parents are the training errors of the hypotheses h m;j it is primarily dependent on. For example, in many greedy search processes (e.g. standard ....

Heckerman, D. (1996). Bayesian networks for knowledge discovery. In U. M. Fayyad, G. PiatetskyShapiro, P. Smyth, & R. Uthurusamy (Eds.), Advances in Knowledge Discovery and Data Mining (pp. 273--305). Menlo Park, CA: AAAI Press.

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D. Heckerman. Bayesian networks for knowledge discovery. In Advances in Knowledge Discovery and Data Mining, pages 273--305, Cambridge, MA, 1996. MIT Press.

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Heckerman, D. 1996. "Bayesian Networks for Knowledge Discovery." In Advances in Knowledge Discovery and Data Mining. Fayyad, U. M., Piatetsky-Shapiro, G., Smyth, P., and Uthurusamy, R., Eds. AAAI press/MIT press.

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, Advances in Knowledge Discovery and Data Mining, AAAI Press, 1996, pp. 273-305.

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