Assigning functions to novel proteins is one of the most important problems in the post-genomic era. Several approaches have been applied to this problem, including analyzing gene expression patterns, phylogenetic profiles, protein fusions and protein-protein interactions. We develop a novel approach that applies the theory of Markov random fields to infer a protein's functions using protein-protein interaction data and the functional annotations of its interaction protein partners. For each function of interest and a protein, we predict the probability that the protein has that function using Bayesian approaches. Unlike in other available approaches for protein annotation where a protein has or does not have a function of interest, we give a probability for having the function. This probability indicates how confident we are about the prediction. We apply our method to predict cellular functions (43 categories including a category "others") for yeast proteins defined in the Yeast Proteome Database (YPD), using the protein-protein interaction data from the Munich Information Center for Protein Sequences (MIPS, http://mips.gsf.de). We show that our approach outperforms other available methods for function prediction based on protein interaction data.