Figure 2: The architecture and workflow of METRIC to infer true nutrient profiles.

For simplicity, we used a hypothetical example with n=3 training samples and 2 samples in the test set. For each sample, there are N. microbial species and N_n nutrients. Across panels, microbial species and their relative abundances are colored blue. Nutrients and their amounts are colored red. The corrupted nutrient profiles are created by adding different types of random noise (i.e., Gaussian, Uniform, etc.) to the assessed nutrient profiles. Icons associated with assessed/corrupted nutrient profiles are bounded by solid black/dashed lines. Icons associated with true nutrient profiles are bounded by solid green lines. a, During the training of METRIC, the method takes corrupted nutrient profiles and microbial compositions as the input and learns to infer assessed nutrient profiles. b, Similar to multilayer perceptrons, METRIC has several hidden layers in the middle. The skip connection provides the corrupted nutrient profile directly to one layer before the final output, enabling it to skip the propagation through the hidden layers. The skipped corrupted nutrient profile multiplied by the weight parameter α and the final hidden layer (the bottom grey nodes) multiplied by (1 − α) add up as the final output (the bottom red nodes). c, The well-trained METRIC is applied to the test set to generate predictions for nutrient profiles whose values are compared to true nutrient profiles.