The paper "Semi-supervised Learning with Deep Generative Models" by Diederik P. Kingma, Danilo J. Rezende, Shakir Mohamed, and Max Welling revisits the approach to semi-supervised learning using generative models and develops new models that allow for effective generalization from small labeled datasets to large unlabeled ones. The authors argue that existing generative approaches have been inflexible, inefficient, or non-scalable, but show that deep generative models and approximate Bayesian inference, leveraging recent advances in variational methods, can significantly improve performance, making generative approaches highly competitive for semi-supervised learning. The paper introduces a new framework for semi-supervised learning with generative models, employing rich parametric density estimators formed by the fusion of probabilistic modeling and deep neural networks. It also presents a stochastic variational inference algorithm that allows for joint optimization of both model and variational parameters, and demonstrates the approach's effectiveness on various datasets, achieving state-of-the-art results on benchmark problems. The authors propose two main models: a latent-feature discriminative model (M1) and a generative semi-supervised model (M2). M1 provides an embedding or feature representation of the data, while M2 describes the data as generated by a latent class variable and a continuous latent variable. The stacked generative semi-supervised model (M1+M2) combines these two approaches, learning a new latent representation using M1 and then applying M2 to this representation. The paper also discusses scalable variational inference, including the lower bound objective and optimization strategies. The computational complexity of the algorithms is analyzed, showing that the approach is efficient and comparable to other competitive methods. Experimental results on datasets like MNIST, SVHN, and NORB demonstrate the effectiveness of the proposed models, achieving superior performance compared to existing semi-supervised learning methods.The paper "Semi-supervised Learning with Deep Generative Models" by Diederik P. Kingma, Danilo J. Rezende, Shakir Mohamed, and Max Welling revisits the approach to semi-supervised learning using generative models and develops new models that allow for effective generalization from small labeled datasets to large unlabeled ones. The authors argue that existing generative approaches have been inflexible, inefficient, or non-scalable, but show that deep generative models and approximate Bayesian inference, leveraging recent advances in variational methods, can significantly improve performance, making generative approaches highly competitive for semi-supervised learning. The paper introduces a new framework for semi-supervised learning with generative models, employing rich parametric density estimators formed by the fusion of probabilistic modeling and deep neural networks. It also presents a stochastic variational inference algorithm that allows for joint optimization of both model and variational parameters, and demonstrates the approach's effectiveness on various datasets, achieving state-of-the-art results on benchmark problems. The authors propose two main models: a latent-feature discriminative model (M1) and a generative semi-supervised model (M2). M1 provides an embedding or feature representation of the data, while M2 describes the data as generated by a latent class variable and a continuous latent variable. The stacked generative semi-supervised model (M1+M2) combines these two approaches, learning a new latent representation using M1 and then applying M2 to this representation. The paper also discusses scalable variational inference, including the lower bound objective and optimization strategies. The computational complexity of the algorithms is analyzed, showing that the approach is efficient and comparable to other competitive methods. Experimental results on datasets like MNIST, SVHN, and NORB demonstrate the effectiveness of the proposed models, achieving superior performance compared to existing semi-supervised learning methods.