Your problem here is not a discriminative problem in which you have two (or more) classes you want to recognize. If it had been the case - for example discriminate infant cry with recording of bird songs, you would have compared each MFCC vector from the incoming audio stream to a massive set of frames either labelled as "bird song" or "infant cry" depending on the recording from which they came from. Note that the datasets would have been absolutely massive if your training sets had more than seconds of audio.
Your problem consists in measuring how similar your data is to a given category; or how well it fits a model trained on the example data - it is a "one-class" problem. In a Bayesian framework, this is equivalent to evaluating the probability of the "infant cry" hypothesis given the MFCC frame as evidence. I recommend you to frame your problem in Bayesian terms because it is likely that for your application, there are probably different costs involved in a false alarms or in missing the detection of a cry; so you'd like to work with a method which can balance them. Working in a probabilistic frameworks implies that you'll need to pick a model for the distribution of MFCC vectors on your training data. The simplest, but most computationally expensive approach is to use Kernel density estimation - this is like a one-class, statistical cousin of k-NN (equally computationally intensive); but a more sensible approach given the amount of data would be gaussian mixture models.
