2019, 40(11): 1179-1203.
doi: 10.21656/1000-0887.400245
Abstract:
In the era of big data and artificial intelligence, it is a common challenge for applied mathematics, statistics and computer science to extract valuable information and knowledge from complex data and models. Generative models are a class of powerful models which can potentially handle the above difficulty. From a macro point of view, the differential equations and dynamic systems in applied mathematics, the probability distribution in statistical models, and the typical generative models (generative adversarial networks and variational auto-encoders) in computer science could be considered as generalized generative models. Along with larger and larger-size data, the structure of data becomes more and more complicated simultaneously. Therefore, more powerful generative models are essential to process real problems. It is a challenge to describe mathematical structures of these generative models. It poses a natural question of how to analyze such generative models without analytic forms (or hard to obtain their analytic forms). Originated from the Bayesian inference, the approximate Bayesian computation, as a likelihood-free technique, plays an important role in processing complex statistical models and generative models. Based on the classic approximate Bayesian computation, the development and recent advance of approximate Bayesian computation were systematically reviewed. Finally, the application of the approximate Bayesian computation to complex data and the deep connection between the approximate Bayesian computation and cutting-edge artificial intelligence methods were discussed.
