CSC2535 Lecture 12
Learning Multiplicative Interactions
Two different meanings of “multiplicative”
But first: One final product of experts
Why products of HMM’s should be better than ordinary HMM’s.
How to reconstruct from a PoHMM
Back to multiplicative interactions
Learning how style and content interact
Some ways to use the bilinear model
Higher order Boltzmann machines (Sejnowski, ~1986)
A higher-order Boltzmann machine with one visible group and two hidden groups
Using higher-order Boltzmann
machines to model image transformations
(Memisevic and Hinton, 2007)
Making the reconstruction easier
The main problem with 3-way interactions
Factoring three-way interactions
Factoring the three-way interactions
A principle of hierarchical systems
Why hierarchical generative models require lateral interactions
Restricted Boltzmann Machines with multiplicative interactions
Factoring the three-way interactions
An advantage of modeling correlations between pixels rather than pixels
Keeping perceptual inference tractable
Why the hiddens remain conditionally independent
Where does the asymmetry in the independence relations of visibles and hiddens come?
Summary of the learning procedure
Learning a factored Boltzmann Machine
Linear filters learned by the factors on MNIST digits
Three-way interactions between pixels
Factoring the three-way interactions between pixels
How to create the reconstructions for linear visible units
How to learn a topographic map