@article{7141,
  abstract     = {                  This tutorial provides a comprehensive and intuitive journey through the evolution of deep generative models, tracing a clear path from the foundations of Principal Component Analysis (PCA) to modern Variational Autoencoders (VAEs), showing how each method solves the limitations of the previous one. We begin with PCA, a linear tool for reducing data dimensions. Its inability to model non-linear patterns motivates the use of Autoencoders (AEs), which use neural networks to learn flexible, compressed representations. However, AEs lack a probabilistic framework, preventing them from generating new data. VAEs address this by treating the latent space as a probability distribution, enabling data generation. We compare the three methods through theoretical analysis, experiments, and step-by-step numerical examples that show exactly how each model compresses data—a detail often missing elsewhere. Unlike resources that treat these topics separately, we connect them into a single narrative, building intuition progressively from linear to probabilistic deep generative models.
                },
  author       = {Tharwat, Alaa and Eid, Mahmoud M.},
  issn         = {2571-905X},
  journal      = {Stats},
  number       = {2},
  publisher    = {MDPI AG},
  title        = {{The Path from PCA to Autoencoders to Variational Autoencoders: Building Intuition for Deep Generative Modeling}},
  doi          = {10.3390/stats9020023},
  volume       = {9},
  year         = {2026},
}