What is the Indian Buffet Process 🌱

Motivation

• Dirichlet Process can give us clusters for data points, but it cannot cluster data into overlapping clusters.
• In many applications, data points exhibit properties of multiple latent features:
  • Images contain multiple objects, movies contain aspects of multiple genres, etc.
• Can we model a system where:
  • we allow each data point to exhibit multiple latent features, to varying degrees
  • we make the number of features unbounded a posteriori (like with the Dirichlet Process)

The Process

• $m_k$ is the number of previous customers who have sampled the dish.

Beta Bernoulli Model

• The Beta-Bernoulli model where we take the limit as the number of latent features goes to infinity describes the Indian Buffet Process

Infinite Gamma-Poisson Process