IMA Tutorial (part III):
Generative and probabilistic models of data

Probabilistic generative models

Models for Power Laws

An Introduction to the Power Law

Early Observations: Pareto on Income

Early Observations: Yule/Zipf

Early Observations: Lotka on Citations

Ranks versus Values

Equivalence of rank versus value formulation

Early modeling work

A model of Simon

Constructing a book: snapshot at time t

The Generative Model

Constructing a book: snapshot at time t

What’s going on?

What’s going on?

What’s going on?

What’s going on?

Models for power laws in the web graph

Why create such a model?

Random graph models

Desiderata for a graph model

Page creation on the web

Generally, would require…

A specific model

Example

Example

Degree sequences in this model

Model extensions

A model of Mandelbrot

Discussion of Mandelbrot’s model

Heuristically Optimized Trade-offs

Monkeys on Typewriters

Other Distributions

Quick characterization of lognormal distributions

One final direction…