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# Hierarchical IFA Belief Networks

*Proceedings of the Seventh International Workshop on Artificial Intelligence and Statistics*, PMLR R2:1-9, 1999.

#### Abstract

We introduce a new real-valued belief network, which is a multilayer generalization of independent factor analysis (IFA). At each level, this network extracts real-valued latent variables that are non-linear functions of the input data with a highly adaptive functional form, resulting in a hierarchical distributed representation of these data. The network is based on a probabilistic generative model, constructed by cascading single-layer IFA models. Whereas exact maximum-likelihood learning for this model is intractable, we present and demonstrate an algorithm that maximizes a lower bound on the likelihood. This algorithm is developed by formulating a variational approach to hierarchical IFA networks.