---
res:
  bibo_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.\r\n                @eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Alaa
      foaf_name: Tharwat, Alaa
      foaf_surname: Tharwat
      foaf_workInfoHomepage: http://www.librecat.org/personId=238549
  - foaf_Person:
      foaf_givenName: Mahmoud M.
      foaf_name: Eid, Mahmoud M.
      foaf_surname: Eid
  bibo_doi: 10.3390/stats9020023
  bibo_issue: '2'
  bibo_volume: 9
  dct_date: 2026^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/2571-905X
  dct_language: eng
  dct_publisher: MDPI AG@
  dct_title: 'The Path from PCA to Autoencoders to Variational Autoencoders: Building
    Intuition for Deep Generative Modeling@'
...