1. A method for analyzing a hidden dynamic of a set of sources in an infrastructure, the method comprising: with a computer, acquiring discrete observations from a set of sources of the observations, each discrete observation having an observed value selected from two or more different discrete values; constructing a factorial hidden Markov model (FHMM) relating the discrete observations to a plurality of hidden dynamics of the set of sources, wherein each of the hidden dynamics is able to assume any one of a number of states at a time, a contribution of the state of each hidden dynamic to the discrete observation being represented in the FHMM as an observational parameter which scales at least one nominal parameter which is derived from a nominal distribution of the observations, including deriving the parameters of the model by training a variational expectation maximization algorithm; and inferring states of the hidden dynamics from the discrete observations based on the FHMM, including applying the variational expectation maximization algorithm to a new set of the discrete observations by an approximation based on minimizing the Kullback-Leibler (KL) divergence between a true conditional distribution of the parameters and hidden states given the observations and a set of target distributions where the parameters and hidden states are forced to be independent; and outputting information corresponding to at least one inferred state of at least one of the hidden dynamics corresponding to a hidden state of one of the sources in the set of sources.