Summary Transcription factor activities (TFAs), rather than expression levels, control gene expres- sion and provide valuable information for investigating TF-gene regulations. The underly- ing bimodal or switch-like patterns of TFAs may play important roles in gene regulation. Network Component Analysis (NCA) is a popular method to deduce TFAs and TF-gene control strengths from microarray data. However, it does not directly examine the bimodal- ity of TFAs and it needs the TF-gene connection topology to be a priori known. In this paper, we modify NCA to model gene expression regulation by Binary Factor Analysis (BFA), which directly captures switch-like patterns of TFAs. Moreover, sparse technique is employed on the mixing matrix of BFA, and thus the proposed sparse BYY-BFA al- gorithm, developed under Bayesian Ying-Yang (BYY) learning framework, can not only uncover the latent TFA profile’s switch-like patterns, but also be capable of automatically shutting off the unnecessary connections. Simulation study demonstrates the effectiveness of BYY-BFA, and a preliminary application to Saccharomyces cerevisiae cell cycle data and Escherichia coli carbon source transition data shows that the reconstructed binary pat- terns of TFAs by BYY-BFA are consistent with the ups and downs of TFAs by NCA, and that BYY-BFA also works well when the network topology is unknown.
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