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Bias aware probabilistic Boolean matrix factorization

Boolean matrix factorization (BMF) is a combi-natorial problem arising from a wide range of applications including recommendation system, col-laborative ﬁltering, and dimensionality reduction. Currently, the noise model of existing BMF methods is often assumed to be homoscedastic; however, in real world data scenarios, the deviations of observed data from their true values are almost surely diverse due to stochastic noises, making each data point not equally suitable for ﬁtting a model. In this case, it is not ideal to treat all data points as equally distributed. Motivated by such observations, we introduce a probabilistic BMF model that recognizes the object- and feature-wise bias distribution respectively, called bias aware BMF (BABF). To the best of our knowledge, BABF is the ﬁrst approach for Boolean decomposition with consideration of the feature-wise and object-wise bias in binary data. We conducted experiments on datasets with different levels of background noise, bias level, and sizes of the signal patterns, to test the effectiveness of our method in various scenarios. We demonstrated that our model outperforms the state-of-the-art factorization methods in both accuracy and efﬁciency in recovering the original datasets, and the inferred bias level is highly sig-niﬁcantly correlated with true existing bias in both simulated and real world datasets.