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To estimate the effect of the smaller set, we prepared hundred random set, by removing 61 proteins randomly from the Structure benchmark set, and tested the accuracy on these random sets as well.
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In the first case, the upper probability is computed as the supremum of the probabilities that g(Xλ) lies in B. In the second case, one considers the random set generated by all g(Xλ), λ∈Λ, e.g. by transforming Xλ to standard normal as a common probability space, and computes the corresponding upper probability.
The expectation of a fuzzy random set, denoted by is an element in such that for each (2.8).
Each of the 1000 sequences in a given random set is generated by a 0th order Markov model based on a GC content chosen from a normal distribution.
Each random set is produced by randomly picking out the same number of genes as are in the small set from the large set of genes.
Hence, we tested whether a specific set of TF expression profiles predicts a specific target gene's expression better than a random set of TFs by comparing the R from our gene expression models to the Rfrom null models.
The statistical significance of the difference between the observed and the random set was assessed by applying a chi-squared test (degree of freedom = 1) to the resulting 2 × 2 contingency matrix [ 44].
It is proved theoretically and by means of numerical experiments, that the latter method provides tighter bounds on the probability of failure than those estimated by random set theory.
In Figure 6 we show two postures corresponding to frames 10 and 40 from the learnt mean performance and a random set of accepted postures by the action model.
The microarray findings were independently corroborated for a random set of 14 mRNAs by RT-PCR analysis.
For each random set, the expectation of, denoted by is defined by (2.5).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com