Generative models have been in existence for many decades. In the field of machine learning, we come across many scenarios when directly learning a target is intractable through discriminative models, and in such cases the joint distribution of the target and the training data is approximated and generated. These generative models help us better represent or model a set of data by generating data in the form of Markov chains or simply employing a generative iterative process to do the same. With the recent innovation of Generative Adversarial Networks (GANs), it is now possible to make use of AI to generate pieces of art, music, etc. with a high extent of realism. In this paper, we review and analyse critically all the generative models, namely Gaussian Mixture Models (GMM), Hidden Markov Models (HMM), Latent Dirichlet Allocation (LDA), Restricted Boltzmann Machines (RBM), Deep Belief Networks (DBN), Deep Boltzmann Machines (DBM), and GANs. We study their algorithms and implement each of the models to provide the reader some insights on which generative model to pick from while dealing with a problem. We also provide some noteworthy contributions done in the past to these models from the literature.

生成模型已经存在了数十年。在机器学习领域，我们遇到了许多情况，其中通过判别模型难以直接学习目标，并且在这种情况下，目标和训练数据的联合分布是近似的并生成。这些生成模型通过生成以马尔可夫链形式的数据或简单地使用生成迭代过程来完成数据，从而帮助我们更好地表示或建模一组数据。借助对抗性生成网络（GANs）的最新创新，现在可以利用AI生成具有高度真实感的艺术品，音乐等。在本文中，我们严格审查和分析了所有生成模型，即高斯混合模型（GMM），隐马尔可夫模型（HMM），潜在狄利克雷分配（LDA），受限玻尔兹曼机（RBM），深层信任网络（DBN），深层玻尔兹曼机（DBM）和GAN。我们研究了他们的算法并实现了每个模型，以为读者提供一些有关在处理问题时从中选择生成模型的见解。我们还提供了过去文献中对这些模型所做的一些值得注意的贡献。