| M. Ramoni and P. Sebastiani, "Parameter estimation in Bayesian networks from incomplete databases," Technical Report KMi-TR-57, Knowledge Median Institute, The Open University, November 1997. |
....According to [40] the BC EM method exhibits a faster convergence rate, and more e ective and robust behavior than the EM algorithm. That is why the BC EM method is used in our experimental evaluation of RBMNs. Basically, the BC EM method alternates between the Bound and Collapse (BC) method [45, 46] and the EM algorithm. The BC method is a deterministic method to estimate conditional probabilities from databases with missing entries. It bounds the set of possible estimates consistent with the available information by computing the minimum and the maximum estimate that would be obtained from ....
Ramoni, M., & Sebastiani, P. (1998). Parameter Estimation in Bayesian Networks from Incomplete Databases. Intelligent Data Analysis, 2. 27
....search of the MAP parameters. The BC EM method is presented in [19,20] as an alternative approach to carry out the task of the EM algorithm when working with discrete variables (as is our present case) The key idea of the BC EM method is to alternate between the Bound and Collapse (BC) method [21,22] and the EM algorithm [4,14] The BC method is a deterministic method to estimate conditional probabilities from incomplete databases. It bounds the set of possible estimates consistent with the available information by computing the minimum and the maximum estimate that would be obtained from ....
....and the maximum estimate that would be obtained from all possible completions of the database. These bounds that determine a probability interval are then collapsed into a unique value via a convex combination of the extreme points with weights depending on the assumed pattern of missing data (see [22] for further details) This method presents all the advantages of a deterministic method and a dramatic gain in efficiency when compared with the EM algorithm. The BC is described to be used in the presence of missing data, but it is not useful when there is a hidden variable as in the data ....
M. Ramoni and P. Sebastiani, Parameter Estimation in Bayesian Networks from Incomplete Databases, Intelligent Data Analysis 2 (1) (1998).
....an alternative technique to perform the parameter search step in discrete domains. It exhibits a faster convergence rate as well as a more effective and robust behaviour than the EM algorithm. Basically,the BC EM method is comprised of an alternation between the Bound and Collapse method (Ramoni and Sebastiani 1998, 1999) and the EM algorithm. To completely specify the BS EM and BS BC EM algorithms, we havetodecide on the structural search procedure (step 2 in Figure 1) The usual approach is to perform a greedy hill climbing searchover model structures considering all possible additions, removals and ....
M. Ramoni and P. Sebastiani (1998). Parameter Estimation in Bayesian Networks from Incomplete Databases. Intelligent Data Analysis 2.
....in which case missingness should be modeled as an ordinary data value. Then the problem has been internalized, and the analysis can proceed as usual, with the important di erence that the missing values are not available for analysis. A more sceptical approach was developed by Ramoni and Sebastiani[27], who consider an option to regard the missing values as adversaries (the conclusions on dependence would then be true no matter what the missing values are) The other possibility is that missingness is known to have nothing to do with the objectives of the analysis. For example, in a medical ....
M. Ramoni and P. Sebastiani. Parameter estimation in Bayesian networks from incomplete databases. Intelligent Data Analysis, 2, 1998.
....completing the database. Therefore, a score criterion that is both in closed and factorable form can be used. In addition, we propose an alternative approach to fulfill the task of the EM algorithm which reveals a faster and more effective method: an alternation of the Bound and Collapse method [20,21] and the EM algorithm. We also consider the possibility of interleaving one of these two methods (the EM algorithm or the alternative approach) after each structural change to improve the set of parameter values for the new structure. The remaining part of this paper is structured as follows. In ....
....convergence rate of the EM algorithm is painfully slow, we present an alternative approach to carry out the task of the EM algorithm. In the remaining part of this paper we refer to this method as BC EM as it alternates between the Bound and Collapse (BC) method and the EM algorithm. The BC method [20,21] is a deterministic method to estimate conditional probabilities from incomplete databases. It bounds the set of possible estimates consistent with the available information by computing the minimum and the maximum estimate that would be obtained from all possible completions of the database. ....
[Article contains additional citation context not shown here]
M. Ramoni and P. Sebastiani, Parameter Estimation in Bayesian Networks from Incomplete Databases, Intelligent Data Analysis 2 (2) (1998).
....M, we are challenged by modeling and computational problems. The typical assumptions that ensure the ignorability of the missing data mechanism for statistical estimation do not yield ignorability for model selection as we need to distinguish between total and partial ignorability (Sebastiani and Ramoni, 1998). The former implies the ignorability of the missing data mechanism for every model considered in the selection process and holds, for instance, when data are missing completely at random so that the probability that the value of a variable is not observed is independent of the other variables ....
....has the advantage of being computationally very efficient at the price of producing rgms slightly more connected than those generating the data. The basic idea of this method is to use estimates of the parameters quantifying the dependency structure of a rgm by using the Bound and Collapse method (Ramoni and Sebastiani, 1998), and to use these estimates to create an expected completion of the data set on which to evaluate the marginal likelihood of the rgm itself. This paper extends further this idea, by introducing an iterative procedure to estimate the marginal likelihood of a rgm from an incomplete data set. The ....
Ramoni, M., and Sebastiani, P. (1998). Parameter estimation in Bayesian networks from incomplete databases. Intelligent Data Analysis Journal, 2.
....can dramatically decrease. Finally, the computational cost of these methods heavily depends on the absolute number of missing data, and this can prevent their scalability to large databases. This situation motivated the recent development of a deterministic method, called Bound and Collapse (bc) (Ramoni Sebastiani, 1998) to estimate conditional probability distributions from possibly incomplete databases. bc was proved to be extremely scalable, as the complexity of the algorithm does not depend on the number of missing data. This paper presents an experimental comparison of em, gs and bc on a real world ....
....method. have been exploited by bc to achieve a better performance. The main difference among the three methods highlighted by the experiments is the execution time and, most of all, the shape of its growth curve, showing that the execution time of bc is independent of the number of missing data (Ramoni Sebastiani, 1998). Table 2 shows the execution time for all eight databases generated during the experiments. The first column reports the absolute number of missing entries from the original entries of the complete database. Results are in hours:minutes:seconds format. 4. CONCLUSIONS The first character of bc is ....
Ramoni, M., & Sebastiani, P. (1998). Parameter estimation in bayesian networks from incomplete databases. Intelligent Data Analysis Journal, 2 (1).
No context found.
M. Ramoni and P. Sebastiani, "Parameter estimation in Bayesian networks from incomplete databases," Technical Report KMi-TR-57, Knowledge Median Institute, The Open University, November 1997.
No context found.
Ramoni, M. and Sebastiani, P. (1998). Parameter estimation in Bayesian networks from incomplete databases. Journal of Intelligent Data Analysis, Vol. 2.
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