Fig 1.
Schematic of the SigMoiD approach.
Probabilities πsi for binary variables i in samples s are generated according to a Gibbs-Boltzmann distribution with energies (features) E and inverse temperatures (latents) β. The observed data (samples) is assumed to have arisen from Bernoulli trials based on the model probabilities. SiGMoiD infers the parameters E and β using maximum likelihood inference.
Fig 2.
Comparison of SiGMoiD with max ent modeling.
(A) the frequencies of individual configurations estimated from the samples (x-axis) and from the two models (y-axis), (red: max ent, blue: SiGMoiD). Only the frequencies of the 1442 configurations observed at least once in the samples are shown. (B) the probability that n neurons fire in any given configuration as estimated from samples (black), the max ent model (red), and SiGMoiD (blue), (C) and (D) comparison between the absolute values of three variable correlations 〈δσiδσjδσk〉 estimated from data (x-axis) and those using the models (y-axis). There are such correlations.
Fig 3.
SiGMoiD models bacterial co-occurrences and interactions.
(A) the probabilities of co-occurrence of multiple OTUs in a single particle. Black circles represent the data, the blue line and shaded blue region represents the SiGMoiD predictions and standard deviations around the predictions, and the red line represents a prediction based on mean occupancies of OTUs. (B) Clustergram showing similarity in features between OTUs. The identified outgroup is marked red. (C) PCA of 3 clusters identified using particle-specific latents βs. (d) (upper half) Co-occurrence frequencies of 10 OTUs whose occurrence frequency was most significantly different in cluster 3 compared to the baseline co-occurrence frequencies of the same OTUs (bottom half).
Fig 4.
SiGMoiD predicts the presence/absence of metabolic reactions.
(A) Receiver operating characteristic (ROC) curve for SiGMoiD-based prediction of missing metabolic reactions. Different lines represent metabolic models with different fractions of known reactions. (B) The mean Jaccard index between the set of predicted metabolic reactions and the actual metabolic reactions in any species (y-axis) vs. the relative size of the predicted network to the actual network (x-axis).