MAP Estimation With Bernoulli Randomness, and Its Application to Text Analysis and Recommender Systems

MAP estimation plays an important role in many probabilistic models. However, in many cases, the MAP problem is non-convex and intractable. In this work, we propose a novel algorithm, called BOPE, which uses Bernoulli randomness for Online Maximum a Posteriori Estimation. We show that BOPE has a fast convergence rate. In particular, BOPE implicitly employs a prior which plays as regularization. Such a prior is different from the one of the MAP problem and will be vanishing as BOPE does more iterations. This property of BOPE is significant and enables to reduce severe overfitting for probabilistic models in ill-posed cases, including short text, sparse data, and noisy data. We validate the practical efficiency of BOPE in two contexts: text analysis and recommender systems. Both contexts show the superior of BOPE over the baselines.