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This paper describes a framework for the development of an integrative cognitive system based on probabilistic generative models (PGMs) called Neuro-SERKET. Neuro-SERKET is an extension of SERKET, which can compose elemental PGMs developed in a distributed manner and provide a scheme that allows the composed PGMs to learn throughout the system in an unsupervised way. In addition to the head-to-tail connection supported by SERKET, Neuro-SERKET supports tail-to-tail and head-to-head connections, as well as neural network-based modules, i.e., deep generative models. As an example of a Neuro-SERKET application, an integrative model was developed by composing a variational autoencoder (VAE), a Gaussian mixture model (GMM), latent Dirichlet allocation (LDA), and automatic speech recognition (ASR). The model is called VAE+GMM+LDA+ASR. The performance of VAE+GMM+LDA+ASR and the validity of Neuro-SERKET were demonstrated through a multimodal categorization task using image data and a speech signal of numerical digits., Comment: New Gener. Comput. (2020)