Protein-protein interactions are important events in cellular and biochemical processes within a cell. Several researchers have undertaken the task of analyzing protein-protein interactions covering all genes of an organism by using yeast two-hybrid assays. Protein-protein interactions involve physical interactions between protein domains. Therefore, understanding protein interactions at the domain level gives a global view of the protein interaction network, and possibly extends functions of proteins. In this study, we present a Maximum Likelihood approach to infer domain-domain interactions from the 5719 yeast protein-protein interactions obtained in the high throughput two-hybrid experiments by Uetz et al., 2000 and Ito et al., 2001. The accuracies of our predictions are measured at the protein level. Our study includes the following three results: (1) using the inferred domain-domain interactions, we predict interactions between proteins and achieve 39.0% specificity and 79.7% sensitivity; (2) our predicted protein-protein interactions have a significant overlap with the MIPS(http://mips.gfs.de) protein-protein interactions obtained by methods other than the two-hybrid systems; and (3) the mean correlation coefficient of the gene expression profiles for our predicted interacting pairs is significantly higher than that for random pairs as well as that of interacting pairs in Uetz's and Ito's experimental data. Our method has shown robustness in analyzing incomplete data sets and dealing with various experimental errors. We find several novel protein-protein interactions such as RPS0A interacting with APG17 and TAF40 interacting with SPT3, which are consistent with the functions of the proteins.