Divergence Family Attains Blockchain Applications via α-EM Algorithm

We present a path starting from generalized information measures to blockchain applications. In the middle of these two endpoints, we derive the alpha-EM algorithm and the traditional log-EM algorithm simultaneously from a sole divergence. Thus, there are three subjects. The first part discusses the relationship between the Bregman divergence and the probabilistic alpha-divergence. There, a new alpha-divergence is derived from the Bregman divergence by skewing the probability space. In the second part, both the alpha-EM algorithm and the traditional log-EM algorithm are derived simultaneously from this single divergence. The third part is on the applications to the blockchain. The EM families are effective in statistical machine learning that can be incorporated in miners of blockchains for evaluating the data sent from clients. Any miner appreciates the speed in order to contest with other miners. The alpha-EM matches this purpose because of its faster speed than the log-EM. As a concrete application, we present the wine sommelier evaluation. This formulation using the multinomial mixture distribution can be applicable to a wider class of IoT data that fly on the network.