Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer) - A classic textbook that provides a foundational and comprehensive derivation of the Evidence Lower Bound within the context of variational inference.
Variational Inference: A Review for Statisticians, David M. Blei, Alp Kucukelbir, Jon D. McAuliffe, 2017Journal of the American Statistical Association, Vol. 112 (Taylor and Francis Ltd.)DOI: 10.1080/01621459.2017.1285773 - Offers a clear exposition of variational inference and the ELBO, presenting it from a statistical perspective.