This paper presents a new framework for semi-supervised learning using deep generative models. The authors propose two models: a latent-feature discriminative model (M1) and a generative semi-supervised model (M2), which are combined into a stacked generative semi-supervised model (M1+M2). These models use deep neural networks to learn latent representations of data, which are then used for classification. The authors also develop a scalable variational inference algorithm that allows for joint optimization of model and variational parameters, making the approach suitable for large datasets. The models are evaluated on benchmark datasets, including MNIST, SVHN, and NORB, and show state-of-the-art results. The models are also shown to be effective at generating analogies between data points, demonstrating their ability to separate class-specific features from style variations. The authors conclude that their approach is highly competitive for semi-supervised learning and that further research on generative models for this task is promising.This paper presents a new framework for semi-supervised learning using deep generative models. The authors propose two models: a latent-feature discriminative model (M1) and a generative semi-supervised model (M2), which are combined into a stacked generative semi-supervised model (M1+M2). These models use deep neural networks to learn latent representations of data, which are then used for classification. The authors also develop a scalable variational inference algorithm that allows for joint optimization of model and variational parameters, making the approach suitable for large datasets. The models are evaluated on benchmark datasets, including MNIST, SVHN, and NORB, and show state-of-the-art results. The models are also shown to be effective at generating analogies between data points, demonstrating their ability to separate class-specific features from style variations. The authors conclude that their approach is highly competitive for semi-supervised learning and that further research on generative models for this task is promising.