The olfactory system, like other sensory systems, can detect specific stimuli of interest amidst complex, varying backgrounds. To gain insight into the neural mechanisms underlying this ability, we imaged responses of mouse olfactory bulb glomeruli to mixtures. We used this data to build a model of mixture responses that incorporated nonlinear interactions and trial-to-trial variability and explored potential decoding mechanisms that can mimic mouse performance when given glomerular responses as input. We find that a linear decoder with sparse weights could match mouse performance using just a small subset of the glomeruli (∼15). However, when such a decoder is trained only with single odors, it generalizes poorly to mixture stimuli due to nonlinear mixture responses. We show that mice similarly fail to generalize, suggesting that they learn this segregation task discriminatively by adjusting task-specific decision boundaries without taking advantage of a demixed representation of odors.