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Similar separations, as well as the fact that random oracles separate classes with probability 0 or 1 (as a consequence of the Kolmogorov's zero–one law), led to the creation of the Random Oracle Hypothesis, that two "acceptable" complexity classes C 1 and C 2 are equal if and only if they are equal (with probability 1) under a random oracle ...
One example is the "Rank–rank hypergeometric overlap" approach, [2] which is designed to compare ranking of the genes that are at the "top" of two ordered lists of differentially expressed genes. A similar approach is taken by the "Rank Biased Overlap (RBO)", [ 3 ] which also implements an adjustable probability, p, to customize the weight ...
The following example uses data from Chambers et al. [17] on daily readings of ozone for May 1 to September 30, 1973, in New York City. The data are in the R data set airquality, and the analysis is included in the documentation for the R function kruskal.test. Boxplots of ozone values by month are shown in the figure.
The analysis is conducted on pairs, defined as a member of one group compared to a member of the other group. For example, the fastest runner in the study is a member of four pairs: (1,5), (1,7), (1,8), and (1,9). All four of these pairs support the hypothesis, because in each pair the runner from Group A is faster than the runner from Group B.
Conover and Iman provided a review of the four main types of rank transformations (RT). [1] One method replaces each original data value by its rank (from 1 for the smallest to N for the largest). This rank-based procedure has been recommended as being robust to non-normal errors, resistant to outliers, and highly efficient for many distributions.
As an example, consider a random sample of size 6. In that case, the sample median is usually defined as the midpoint of the interval delimited by the 3rd and 4th order statistics. However, we know from the preceding discussion that the probability that this interval actually contains the population median is [clarification needed]
An oracle machine can perform all of the usual operations of a Turing machine, and can also query the oracle to obtain a solution to any instance of the computational problem for that oracle. For example, if the problem is a decision problem for a set A of natural numbers, the oracle machine supplies the oracle with a natural number, and the ...
Query-independent methods attempt to measure the estimated importance of a page, independent of any consideration of how well it matches the specific query. Query-independent ranking is usually based on link analysis; examples include the HITS algorithm, PageRank and TrustRank. Query-dependent methods attempt to measure the degree to which a ...