An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> This paper presents a Bayesian method for constructing probabilistic networks from databases. In particular, we focus on constructing Bayesian belief networks. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of probabilistic expert systems. We extend the basic method to handle missing data and hidden (latent) variables. We show how to perform probabilistic inference by averaging over the inferences of multiple belief networks. Results are presented of a preliminary evaluation of an algorithm for constructing a belief network from a database of cases. Finally, we relate the methods in this paper to previous work, and we discuss open problems. <s> BIB001 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> Data products (macrodata or tabular data and micro-data or raw data records), are designed to inform public or business policy, and research or public information. Securing these products against unauthorized accesses has been a long-term goal of the database security research community and the government statistical agencies. Solutions to this problem require combining several techniques and mechanisms. Recent advances in data mining and machine learning algorithms have, however, increased the security risks one may incur when releasing data for mining from outside parties. Issues related to data mining and security have been recognized and investigated only recently. This paper deals with the problem of limiting disclosure of sensitive rules. In particular it is attempted to selectively hide some frequent itemsets from large databases with as little as possible impact on other non-sensitive frequent itemsets. Frequent itemsets are sets of items that appear in the database "frequently enough" and identifying them is usually the first step toward association/correlation rule or sequential pattern mining. Experimental results are presented along with some theoretical issues related to this problem. <s> BIB002 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models without access to precise information in individual data records? We consider the concrete case of building a decision-tree classifier from training data in which the values of individual records have been perturbed. The resulting data records look very different from the original records and the distribution of data values is also very different from the original distribution. While it is not possible to accurately estimate original values in individual data records, we propose a novel reconstruction procedure to accurately estimate the distribution of original data values. By using these reconstructed distributions, we are able to build classifiers whose accuracy is comparable to the accuracy of classifiers built with the original data. <s> BIB003 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> Motivated by the application of private statistical analysis of large databases, we consider the problem of selective private function evaluation (SPFE). In this problem, a client interacts with one or more servers holding copies of a database x = x 1 , … , x n in order to compute f(x i 1 , … , x i m ), for some function f and indices i = i 1 , … , i m chosen by the client. Ideally, the client must learn nothing more about the database than f(x i , … , x i m ), and the servers should learn nothing. Generic solutions for this problem, based on standard techniques for secure function evaluation, incur communication complexity that is at least linear in n, making them prohibitive for large databases even when f in relatively simple and m is small. We present various approaches for constructing sublinear-communication SPFE protocols, both for the general problem and for special cases of interest. Our solutions not only offer sublinear communication complexity, but are also practical in many scenarios. <s> BIB004 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> The growth of the Internet opens up tremendous opportunities for cooperative computation, where the answer depends on the private inputs of separate entities. Sometimes these computations may occur between mutually untrusting entities. The problem is trivial if the context allows the conduct of these computations by a trusted entity that would know the inputs from all the participants; however if the context disallows this then the techniques of secure multiparty computation become very relevant and can provide useful solutions. Statistical analysis is a widely used computation in real life, but the known methods usually require one to know the whole data set; little work has been conducted to investigate how statistical analysis could be performed in a cooperative environment, where the participants want to conduct statistical analysis on the joint data set, but each participant is concerned about the confidentiality of its own data. We have developed protocols for conducting the statistical analysis in such a cooperative environment based on a data perturbation technique and cryptography primitives. <s> BIB005 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> Privacy considerations often constrain data mining projects. This paper addresses the problem of association rule mining where transactions are distributed across sources. Each site holds some attributes of each transaction, and the sites wish to collaborate to identify globally valid association rules. However, the sites must not reveal individual transaction data. We present a two-party algorithm for efficiently discovering frequent itemsets with minimum support levels, without either site revealing individual transaction values. <s> BIB006 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> Privacy and security concerns can prevent sharing of data, derailing data mining projects. Distributed knowledge discovery, if done correctly, can alleviate this problem. The key is to obtain valid results, while providing guarantees on the (non)disclosure of data. We present a method for k-means clustering when different sites contain different attributes for a common set of entities. Each site learns the cluster of each entity, but learns nothing about the attributes at other sites. <s> BIB007 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> The problem of secure distributed classification is an important one. In many situations, data is split between multiple organizations. These organizations may want to utilize all of the data to create more accurate predictive models while revealing neither their training data / databases nor the instances to be classified. The Naive Bayes Classifier is a simple but efficient baseline classifier. In this paper, we present a privacy preserving Naive Bayes Classifier for horizontally partitioned data. <s> BIB008 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> The problem of secure distributed classification is an important one. In many situations, data is split between multiple organizations. These organizations may want to utilize all of the data to create more accurate predictive models while revealing neither their training data / databases nor the instances to be classified. The Naive Bayes Classifier is a simple but efficient baseline classifier. In this paper, we present a privacy preserving Naive Bayes Classifier for horizontally partitioned data. <s> BIB009 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> Data mining can extract important knowledge from large data collections ut sometimes these collections are split among various parties. Privacy concerns may prevent the parties from directly sharing the data and some types of information about the data. We address secure mining of association rules over horizontally partitioned data. The methods incorporate cryptographic techniques to minimize the information shared, while adding little overhead to the mining task. <s> BIB010 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> We consider the problem of computing the intersection of private datasets of two parties, where the datasets contain lists of elements taken from a large domain. This problem has many applications for online collaboration. We present protocols, based on the use of homomorphic encryption and balanced hashing, for both semi-honest and malicious environments. For lists of length k, we obtain O(k) communication overhead and O(k In In k) computation. The protocol for the semi-honest environment is secure in the standard model, while the protocol for the malicious environment is secure in the random oracle model. We also consider the problem of approximating the size of the intersection, show a linear lower-bound for the communication overhead of solving this problem, and provide a suitable secure protocol. Lastly, we investigate other variants of the matching problem, including extending the protocol to the multi-party setting as well as considering the problem of approximate matching. <s> BIB011 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> This study presents a holistic method for constructing a Bayesian network (BN) model for estimating system reliability. BN is a probabilistic approach that is used to model and predict the behavior of a system based on observed stochastic events. The BN model is a directed acyclic graph (DAG) where the nodes represent system components and arcs represent relationships among them. Although recent studies on using BN for estimating system reliability have been proposed, they are based on the assumption that a pre-built BN has been designed to represent the system. In these studies, the task of building the BN is typically left to a group of specialists who are BN and domain experts. The BN experts should learn about the domain before building the BN, which is generally very time consuming and may lead to incorrect deductions. As there are no existing studies to eliminate the need for a human expert in the process of system reliability estimation, this paper introduces a method that uses historical data about the system to be modeled as a BN and provides efficient techniques for automated construction of the BN model, and hence estimation of the system reliability. In this respect K2, a data mining algorithm, is used for finding associations between system components, and thus building the BN model. This algorithm uses a heuristic to provide efficient and accurate results while searching for associations. Moreover, no human intervention is necessary during the process of BN construction and reliability estimation. The paper provides a step-by-step illustration of the method and evaluation of the approach with literature case examples. <s> BIB012 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> In this paper we discuss different architectures for reasoning under uncertainty related to our ongoing research into building a medical decision support system. The uncertainty in the medical domain can be divided into a well understood part and a less understood part. This motivates the use of a hybrid decision support system, and in particular, we argue that a Bayesian network should be used for those parts of the domain that are well understood and can be explicitly modeled, whereas a case-based reasoning system should be employed to reason in parts of the domain where no such model is available. Four architectures that combine Bayesian networks and case-based reasoning are proposed, and our working hypothesis is that these hybrid systems each will perform better than either framework will do on its own. <s> BIB013 </s> An Overview of Bayesian Network Applications in Uncertain Domains <s> A. Bayesian Network Representation <s> In the privacy preservation of association rules, sensitivity analysis should be reported after the quantification of items in terms of their occurrence. The traditional methodologies, used for preserving confidentiality of association rules, are based on the assumptions while safeguarding susceptible information rather than recognition of insightful items. Therefore, it is time to go one step ahead in order to remove such assumptions in the protection of responsive information especially in XML association rule mining. Thus, we focus on this central and highly researched area in terms of generating XML association rule mining without arguing on the disclosure risks involvement in such mining process. Hence, we described the identification of susceptible items in order to hide the confidential information through a supervised learning technique. These susceptible items show the high dependency on other items that are measured in terms of statistical significance with Bayesian Network. Thus, we proposed two methodologies based on items probabilistic occurrence and mode of items. Additionally, all this information is modeled and named PPDM (Privacy Preservation in Data Mining) model for XARs. Furthermore, the PPDM model is helpful for sharing markets information among competitors with a lower chance of generating monopoly. Finally, PPDM model introduces great accuracy in computing sensitivity of items and opens new dimensions to the academia for the standardization of such NP-hard problems. <s> BIB014
In system behavior, probabilistic relationships among system components are assessed with the help of Conditional Probability Table (CPT). The components CPT can be obtained from () P X S ; where S is the set of X's parents. Each member in the set of parents in CPT of X's is instantiated as either "Success" or "Failure". PPDM is introduced in BIB001 , BIB003 which refers to protecting fragments of the original data. This is a BN-based NP-hard problem  as argued in BIB002 . A variety of PPDM algorithms are proposed for association rules BIB010 , BIB006 and XML Association rules BIB014 , BIB006 , clustering BIB007 , naive Bayes classifiers BIB008 , BIB009 , statistical analysis BIB004 , BIB005 , and discovering common elements BIB013 BIB011 ,  . Amongst such a variety of PPDM research areas, we focused on application of BN for system reliability analysis and estimation  , BIB012 , and PPDM in XML association rule mining BIB014 .