Feedback is a common problem in teleconferencing systems. Typical usage of an adaptive filter can be effective for feedback reduction but it relies on the presence of such a filter on the side of the far speaker in order to reduce feedback on the side of the near speaker. In order to avoid this reliance on the far speaker's setup, we can use an adaptive filter on the side of the near speaker. Unfortunately, due to non-linear speech coding typically used during speech transmission, these filters perform poorly in this situation. In this paper, we present a novel probabilistic method, using a non-negative convolutive decomposition of spectrogram data to perform feedback reduction by posing the problem as a source separation problem. Our method is robust to non-linear speech coding as well as continuous double-talk, which often presents a challenge to adaptive filters. We compare our method to the use of an adaptive filter and show superior results with respect to standard source separation metrics.