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The latter approach is to select a reasonable number of “good” models from all
the possible models, and pretend that these models are exhaustive. The questions
are: how to decide whether a model is “good” or not? How to search “good”
models? Whether precise result can be yielded when these approaches are
applied to Bayesian structure? There are some different definitions and
corresponding computational methods about “good” model. The last two
questions are hardly to be answered theoretically. Some research work had
demonstrated that using greedy algorithm to select single good model often leads
to precise prediction (Chickering,Heckerman, 1996). Applying Monte-Carlo
method to perform selective model averaging is sometime effective as well. It
may even result in better prediction. These results are somewhat largely
responsible for the great deal of recent interest in learning with Bayesian network
In 1995, Heckerman pointed out that under the precondition of parameter
independence, parameter modularity, likelihood equivalence, and so on, the
methods for learning Bayesian non-casual network can be applied to learning
casual network. In 1997, he suggested that under casual Markov condition, the
casual relationship could be deduced from conditional independence and
conditional correlation(Heckerman, 1997). This makes it possible that when
interference appears, corresponding effect can be predicted.
Below is a case study that Heckerman et al. used Bayesian network to
perform data mining and knowledge discovery. The data came from 10318
Wisconsin high school seniors (Sewell and Shah, 1968). Each student was
described by the following variables and corresponding states
Sex (SEX): male, female;
Socioeconomic Status (SES): low, lower middle, upper middle, high;
Intelligence Quotient (IQ): low, lower middle, upper middle, high;
Parental Encouragement (PE): low, high;
College Plans (CP): yes, no.
Table 6.3 Sufficient statistics
(male) 4 349 13 64 9 207 33 72 12 126 38 54 10 67 49 43
2 232 27 84 7 201 64 95 12 115 93 92 17 79 119 59
8 166 47 91 6 120 74 110 17 92 148 100 6 42 198 73
4 48 39 57 5 47 132 90 9 41 224 65 8 17 414 54
(female) 5 454 9 44 5 312 14 47 8 216 20 35 13 96 28 24
11 285 29 61 19 236 47 88 12 164 62 85 15 113 72 50
7 163 36 72 13 193 75 90 12 174 91 100 20 81 142 77
6 50 36 58 5 70 110 76 12 48 230 81 13 49 360 98
Our goal here is to discover the factors that affect the intention of high school
seniors to attend college, or to understand the possibly causal relationships
