**CIAR Summer School Tutorial
Lecture 2a
Products of Experts**

**How to combine simple
density models**

**A picture of the two
combination methods**

**Products of Experts and
energies**

**How sharp are products of
experts?**

**Generating from a product of
experts**

**Relationship to causal
generative models**

**Ways to deal with the
intractable sum**

**The Markov chain for
unigauss experts**

**A neural network for the
naļve model**

**A neural network for a
mixture of naļve models**

**A neural network for a
product of naļve models**

**The distribution defined by
one hidden unit**

**The logistic function
computes a product of probabilities.**

**Restricted Boltzmann
Machines and products of experts**

**A picture of the Boltzmann
machine learning algorithm for an RBM**