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_96
Snippet: To apply Gibbs sampling in practice, the critical point is to quickly reach a large number of samples, so that probability estimates become reliable. To further decrease running time, we assume that we have, at any step, knowledge about all (log) conditional probabilities, for all nodes v ∈ V (c) and all colors c ∈ C. We assume that conditional probabilities are not normalized; to sample a new active node, we uniformly draw a random number be.....
Document: To apply Gibbs sampling in practice, the critical point is to quickly reach a large number of samples, so that probability estimates become reliable. To further decrease running time, we assume that we have, at any step, knowledge about all (log) conditional probabilities, for all nodes v ∈ V (c) and all colors c ∈ C. We assume that conditional probabilities are not normalized; to sample a new active node, we uniformly draw a random number between zero and the sum of conditional probabilities, over all nodes with this color. To improve the sampling speed, we want to estimate conditional probabilities without performing a full calculation using (9). Lemma 2. One step of the Gibbs sampler, exchanging some node u by another node v with the same color c := c(u) = c(v), can be carried out in O |V (c)| + deg(u) + deg(v) time.
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