Explore a comprehensive lecture on identifiable deep generative models through sparse decoding. Delve into the development of the sparse VAE for unsupervised representation learning on high-dimensional data. Understand how this model learns latent factors summarizing associations in observed data features, with each feature depending on a small subset of latent factors. Examine real-world applications in ratings data, text analysis, and genomics. Learn about the model's identifiability and its ability to recover true model parameters with infinite data. Investigate empirical studies using simulated and real data, showcasing the sparse VAE's effectiveness in recovering meaningful latent factors and achieving smaller holdout reconstruction errors compared to related methods. Follow the lecture's structure, covering introduction and background, sparse variational autoencoder, identifiability, estimation, experiments, summary, and concluding with an insightful discussion.