Author: Marcus Ludwig; Louis-Félix Nothias; Kai Dührkop; Irina Koester; Markus Fleischauer; Martin A. Hoffmann; Daniel Petras; Fernando Vargas; Mustafa Morsy; Lihini Aluwihare; Pieter C. Dorrestein; Sebastian Böcker
Title: ZODIAC: database-independent molecular formula annotation using Gibbs sampling reveals unknown small molecules Document date: 2019_11_16
ID: 03uonbrv_61
Snippet: Here, P(u, v | true ) is the prior probability that two compounds with molecular formulas u, v cooccur in the dataset; analogously, P(u, v | false ) if u, v do not co-occur. To simplify our calculations, we introduce a mapping c : V → C that maps any molecular formula to the compound it belongs to: c(v) = c for all v ∈ V (c), for c ∈ C. Note that c(a(c)) = c for all c ∈ C. Now, unfortunately, we will see that this is not easy, as the unde.....
Document: Here, P(u, v | true ) is the prior probability that two compounds with molecular formulas u, v cooccur in the dataset; analogously, P(u, v | false ) if u, v do not co-occur. To simplify our calculations, we introduce a mapping c : V → C that maps any molecular formula to the compound it belongs to: c(v) = c for all v ∈ V (c), for c ∈ C. Note that c(a(c)) = c for all c ∈ C. Now, unfortunately, we will see that this is not easy, as the underlying computational problem is NPcomplete. Another natural question is to sample from the posterior distribution; this will be addressed below.
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