**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…**