Finding the state sequence maximizing P(O; I|λ) on distributed HMMs with Privacy

Hidden Markov models (HMMs) are widely used by many applications for forecasting purposes. They are increasingly becoming popular models as part of prediction systems in finance, marketing, bio-informatics, speech recognition, signal processing, and so on. Given an HMM, an application of HMMs is to choose a state sequence so that the joint probability of an observation sequence and a state sequence given the model is maximized. Although this seems an easy task if the model is given, it becomes a challenge when the model is distributed between various parties. Due to privacy, financial, and legal reasons, the model owners might not want to integrate their split models. In this paper, we propose schemes to select a state sequence so that the joint probability of an observation sequence and a state sequence given the model is maximized when the model is horizontally or vertically distributed between two parties while preserving their privacy. We then analyze the proposed schemes in terms of privacy, accuracy, and additional overhead costs. Since privacy, accuracy, and performance are conflicting goals, our proposed methods are able to achieve an equilibrium among them.