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【正文】 ent since they both cause Alarm. 9 Independencies in Bayes Nets ? If removing a subset of nodes S from the work renders nodes Xi and Xj disconnected, then Xi and Xj are independent given S, . P(Xi | Xj, S) = P(Xi | S) ? However, this is too strict a criteria for conditional independence since two nodes will still be considered independent if their simply exists some variable that depends on both. – For example, Burglary and Earthquake should be considered independent since they both cause Alarm. P(Xi | Xj, S) = P(Xi | S) , is equivalent to P(Xi , Xj | S) = P(Xi | S) P(Xj | S) How to prove? 10 Independencies in Bayes Nets ? If removing a subset of nodes S from the work renders nodes Xi and Xj disconnected, then Xi and Xj are independent given S, . P(Xi | Xj, S) = P(Xi | S) ? However, this is too strict a criteria for conditional independence since two nodes will still be considered independent if their simply exists some variable that depends on both. – For example, Burglary and Earthquake should be considered independent since they both cause Alarm. 11 Independencies in Bayes Nets (cont.) ? Unless we know something about a mon effect of two “independent causes” or a descendent of a mon effect, then they can be considered independent. – For example, if we know nothing else, Earthquake and Burglary are independent. ? However, if we have information about a mon effect (or descendent thereof) then the two “independent” causes bee probabilistically linked since evidence for one cause can “explain away” the other. – For example, if we know the alarm went off that someone called about the alarm, then it makes earthquake and burglary dependent since evidence for earthquake decreases belief in burglary. and vice versa. 12 Bayes Net Inference ? Given known values for some evidence variables, determine the posterior probability of some query variables. ? Example: Given that John calls, what is the probability that there is a Burglary? Burglary Earthquake Alarm JohnCalls MaryCalls ??? John calls 90% of the time there is an Alarm and the Alarm detects 94% of Burglaries so people generally think it should be fairly high. However, this ignores the prior probability of John calling. 1
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