BORG (Bayesian Origin Reconstruction from Galaxies) is an inference engine that derives the initial conditions given a cosmological model and the survey data, and produces physical reconstructions of the underlying large-scale structure by assimilating the data into the model. Building upon the application of BORG to the Sloan Digital Sky Survey data, Florent will present detailed characterizations of dynamic cosmic web type environments. These developments naturally bring in a connection between cosmic web analysis and information theory. He will discuss the Shannon entropy of structure-type probability distributions and the information gain due to Sloan Digital Sky Survey galaxies, propose a decision criterion for classifying structures in the presence of uncertainty, and introduce utility functions for the optimal choice of a cosmic web classifier, specific to the application of interest. As showcases, Florent will discuss the discrimination of dark energy models from the cosmic web and an approach inspired by supervised machine learning for predicting galaxy colours given their large-scale environment.