Reading Assignment 2: Partition Function & RBMs

From the Deep Learning Book - Chapter 18: Confronting the Partition Function, please read these sections:

• Sections 18 (intro), 18.1, 18.2 with focus on:
  • What are positive and negative phase of learning?
  • Which role does the partition function play in learning generative models?
  • How do we avoid to compute the partition function directly and why is it possible to do this?
  • How does Contrastive Divergence (CD) work and what (dis)advantages does this method have?
  • How does Persistent Contrastive Divergence (PCD) work and what (dis)advantages does this method have?
  • What is the relation between PCD and Stochastic Maximum Likelihood?
  • Optional, Section 18.3: What is the idea behind Pseudolikelihood?
• Sections 18.7 & 18.7.1 (optional, low priority):
  • What are possible ways of estimating the partition function?
  • What is the idea of Annealed Importance Sampling (AIS)?
  • Note: You will probably need to read the section on Importance Sampling (Chapter 17.2) to understand this.

For the actual application of these techniques, please read these sections from the Deep Learning Book - Chapter 20: Deep Generative Models:

• Sections 20 (intro), 20.1, 20.2 with focus on:
  • What are the Energy functions of a Boltzmann Machine (BM) and a Restricted Boltzmann Machine (RBM)?
  • How would the partition function of an RBM be computed?
  • What makes sampling in an RBM efficient?
  • What is the sampling procedure and how does it relate to MCMC?
  • How can BMs and RBMs be trained?
  • Where are the connections between training an RBM and the concepts of chapter 18 (partition function, CD/PCD, AIS)

Optional: DBMs and DBNs

If you are interested, you can also read Sections 20.3 on Deep Belief Networks, which incorporate both directed and undirected connections, and Section 20.4 on Deep Boltzmann Machines, a deep undirected model. Beyond that, Sections 20.4-20.8 discuss other Boltzmann Machine variants (such as Gaussian BMs for real-valued data). These topics will not be treated in this class.