### Table 1 illustrates this by means of some examples. (0, 1) and (1, 0) are respectively the smallest and the biggest element of L , corresponding to full distrust and full trust; obviously in these situations there is no hesitation. In the case of no knowledge, namely (0, 0), the hesitation is 1. The most wide spread approach (see column 2) only takes into account the degree of trust, and can not make the distinction between a case of full distrust and a case of no knowledge. In [4] the distrust degree d is subtracted from the trust degree t, giving rise to a trust value on a scale from -1 to 1. The examples (0.2, 0) and (0.6, 0.4) illustrate that valuable information is lost in this mapping process. Indeed (0.6, 0.4) expresses a strong opinion to trust a source to degree 0.6 but not more, while (0.2, 0) suggests to trust to degree 0.2 but possibly more because there is a lot of doubt in this case (the hesitation degree is 0.8). In [4], both cases are mapped to the same value, namely 0.2.

"... In PAGE 4: ... Table1 . Examples of trust values 3 Propagation of Trust and Distrust As recalled in the introduction, in a probabilistic framework, trust is propa- gated by means of the multiplication operation.... ..."

### Table 3 Comparison of propositional rule sets and probabilistic rule sets refined by a BPF framework. The complexity measure is the number of premises of the model. For data sets where cross-validation was applied, the results were averaged over the 10 trials. Numbers in italic represent the standard variation of these results. Accuracy results were given to provide evidence that this approach is able to effectively reduce the complexity of the rule sets while maintaining similar classification power in nearly all data sets

in IOS Press

2000

"... In PAGE 9: ...5RULES were much larger than those reported on this section. All accuracy results on Table3 were measured with respect to pruned rule sets. The BPF variations were initialized by a remapping of the final models obtained using PRIM and C4.... ..."

### Table 1: Probabilistic Relevance Propagation Algorithms Method k Neighbors is pis

"... In PAGE 3: ... In particular, the framework can recover most existing link-based algorithms. Table1 shows a family of relevance propagation algorithms which are covered by our general framework. As can be seen from the table, PageRank and its extensions are special cases of the framework.... ..."

Cited by 2

### Table 5: Parameters and Training Time stricted to probabilistic context-free grammars. Af- ter completing the implementation of our move set, we plan to explore the modeling of context- sensitive phenomena. This work demonstrates that Solomono apos;s elegant framework deserves much fur- ther consideration.

1995

"... In PAGE 6: ...7% Table 3: Wall Street Journal-like arti cial grammar Inside-Outside algorithm in the rst two domains, while in the part-of-speech domain we are outper- formed by n-gram models but we vastly outperform the Inside-Outside algorithm. In Table5 , we display a sample of the number of parameters and execution time (on a Decstation 5000/33) associated with each algorithm. We choose n to yield approximately equivalent performance for each algorithm.... ..."

Cited by 42

### Table 2. Comparison between deterministic reasoning and probabilistic inferring with test data Deterministic Probabilistic Sequence Ground

"... In PAGE 14: ... Wc, Wp, Wt and Wz are scaling factors used for normalizing different scales between audio and motion representations. Table2 shows the detailed results for comparison performed on test data set. Again, in order to have a fair comparison and to exclude any impacts from audio-visual features or other issues, we use the same audio and motion representations proposed in Section 2 to implement the deterministic method.... In PAGE 14: ...epresentations. Table 2 shows the detailed results for comparison performed on test data set. Again, in order to have a fair comparison and to exclude any impacts from audio-visual features or other issues, we use the same audio and motion representations proposed in Section 2 to implement the deterministic method. In Table2 , the proposed HMM-based framework once again outperforms the deterministic method. Figure 9 is the detection result using deterministic method with test sequence T0, and this result demonstrates that it is quite difficult to judge highlight segments based on the deterministic method, since occurrence of likelihood peaks is very noisy.... ..."

Cited by 1

### Table 1: Algorithmic framework for a general probabilistic population-based EA. Initially, construct a probability density p0(x) that represents the model of the search space (or where it is believed that good solutions are distributed in IRn). This initial density may be quite general, or it may be tailored to the speci cs of a given problem, through the incorporation of any available prior knowledge. At each iteration (generation) t of the algorithm, a set D of k solutions is generated for the optimization problem by sampling k times from the probability density pt(x) D(k) t

### Table 1. As an example of this framework, consider the following iterative improve- ment (ItIm) algorithm

"... In PAGE 3: ...Initialize probability model p0(x); t = 0 Step 2: Sample from pt(x) D(k) = fx1; : : : ; xkg Step 3: Evaluate F(k) = ff(x1); : : : ; f(xk)g Step 4: Update probability model : pt(x) ! pt+1(x) Step 5: Increment time t = t + 1 Step 6: Goto Step 2 (until termination condition) Table1 : Algorithmic framework for a general probabilistic population-based EA. Initially, construct a probability density p0(x) that represents the model of the search space (or where it is believed that good solutions are distributed in IRn).... ..."

### Table 1. Debt Sustainability Analysis (DSA) and Risk Assessment Deterministic Bound Testing Probabilistic Approach

2006

"... In PAGE 6: ... Deviations of actual policies from the benchmark provided by the estimated reaction function may prove useful in assessing such effort, and thereby assessing the room for fiscal adjustment (Abiad and Ostry, 2005; and Debrun, 2005a). Table1 summarizes some key differences between the usual DSA framework and the extended DSA proposed in this paper. 4Our simulation tool can, however, accommodate any normative policy scenario, including the constant ... ..."

Cited by 1

### Table 1. Probabilistic techniques.

1994

Cited by 192

### Table 1: Probabilistic Approaches

"... In PAGE 2: ...3 Word-based, Probabilistic Approaches The third category assumes at most whitespace and punctuation knowledge and attempts to infer MWUs using word combination probabilities. Table1 (see next page) shows nine commonly-used probabilistic MWU-induction approaches. In the table, f and P signify frequency and probability XX of a word X.... ..."