Pruned Argumentative Probability Tree Sample Clauses

Pruned Argumentative Probability Tree. ‌ In this paper, we aim to explain a whole scenario in the form of the MPE solution or alternatives of that. However, explaining every parent for every node can result in long and complex explanations, especially in larger BNs. Therefore pruning the tree can be a solution, such that information which is not important for the scenario does not have to be explained. In Sect. 3.1, d-separated nodes are already omitted. In this section we will filter for parent nodes, which have a significant impact on its child nodes. Only such parents will be used in the explanation. To calculate the threshold of significance we use the likelihood ratio, which has been used before in related literature [11, 12]. Typically, binary-valued xxxx- xxxxx are used. Here we generalize this to multinomial distributions. Suppose that we are interested in the effect of a set of nodes x on Y = yi. We define the strength as the likelihood ratio, i.e. Σ (y , x) = P (yi | x) s i i P (yj | x) ≤ One reasonable threshold th is th = 1, such that all node pairs with a strength th s(yi, x) are not explained, because there it is unlikely that xx follows from x. For example, the strength of food intake(true) given glycaemia(hyper) is 3.81, whereas quality of beta cells(high) given glycaemia(hyper) has the strength 0.72, therefore glycaemia(hyper) is not considered in the explanation of quality of beta cells(high). A related method to calculate the threshold of significance was recently intro- duced by Xxxxxx et al. [7]. The main difference is that Xxxxxx et al. aims at finding the most significant evidence for a variable of interest. However, in our case, evidence is given, and the most related variables are selected, which can be seen as the reverse problem. However, we also borrow the idea by Xxxxxxx [7] to perform a conflict analysis. This analysis aims to examine if every premise in a rule has the same direction in creating the overall change in a variable of interest, i.e., a positive or negative influence to the conclusion. We will explain a node with significant parent nodes which are contributing to the observed value of the node. For example, in the diabetes example glycaemia(hyper) and food intake(true) cause the same direction of change when they are observed on all other variables, for example quality of beta cells(high) is decreasing. A different direction of change is caused by the observation diabetes(f alse), because the probability of quality of beta cells(high) is now increased. Since the ove...
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