Deep Mixtures of Factor Analysers

Abstract

An efficient way to learn deep density models that have many layers of latent variables is to learn one layer at a time using a model that has only one layer of latent variables. After learning each layer, samples from the posterior distributions for that layer are used as training data for learning the next layer. This approach is commonly used with Restricted Boltzmann Machines, which are undirected graphical models with a single hidden layer, but it can also be used with Mixtures of Factor Analysers (MFAs) which are directed graphical models. In this paper, we present a greedy layer-wise learning algorithm for Deep Mixtures of Factor Analysers (DMFAs). Even though a DMFA can be converted to an equivalent shallow MFA by multiplying together the factor loading matrices at different levels, learning and inference are much more efficient in a DMFA and the sharing of each lower-level factor loading matrix by many different higher level MFAs prevents overfitting. We demonstrate empirically that DMFAs learn better density models than both MFAs and two types of Restricted Boltzmann Machine on a wide variety of datasets.

ICML2012

Cited by in corpus (10)

• RNADE: The real-valued neural autoregressive density-estimator
• Learning Generative Models with Visual Attention
• Neural Autoregressive Distribution Estimation
• A RAD approach to deep mixture models
• A Probabilistic Framework for Deep Learning
• Variational Inference and Sparsity in High-Dimensional Deep Gaussian Mixture Models
• Deep mixture of linear mixed models for complex longitudinal data
• Best-scored Random Forest Density Estimation
• Back to Square One: Superhuman Performance in Chutes and Ladders Through Deep Neural Networks and Tree Search
• Learning pose variations within shape population by constrained mixtures of factor analyzers