A generative model is a mathematical formulation that generates a sample similar to real data. Many such models have been proposed using machine learning methods, including deep learning. Study of a good model serves to characterize the nature of a system and also to clarify the potential of machine learning. We study various time series models including classical Markov models, grammatical models, Simon processes, random walks on a network, neural models, autoencoders, and adversarial methods. The fundamental properties of generative models are studied in terms of whether they can generate samples resembling real data.

Taylor’s law for linguistic sequences and random walk models. Kumiko Tanaka-Ishii and Tatsuru Kobayashi. Journal of Physics Communications, 2018.

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