Probabilistic sparse matrix factorization with an application to discovering gene functions in mouse mRNA expression data
We address the problem of sparse matrix factorization using a generative model. Our algorithm, probabilistic sparse matrix factorization (PSMF), is a probabilistic extension of a previous hard-decision algorithm for this problem (Srebro and Jaakkola 2001). PSMF allows for varying levels of sensor noise in the data, uncertainty in the hidden prototypes used to explain the data, and uncertainty as to which prototypes are selected to explain each data vector. We present experimental results demonstrating that our method can better recover functionally relevant clusterings in mRNA expression data than standard clustering techniques, and we show that by computing probabilities instead of point estimates, our method avoids converging to poor solutions.