Web Science/Part2: Emerging Web Properties/Generative Models for the Web/Sampling from a probability distribution

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Web Science/Part2: Emerging Web Properties

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Web Science/Part2: Emerging Web Properties/Generative Models for the Web/Sampling from a probability distribution

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Sampling from a probability distribution

Learning goals

Video

Script

Quiz

Further reading

Discussion

Learning goals

1. Understand how to sample values from an arbitrary probability distribution
2. Have seen yet another application of the cumulative distribution function
3. Understand that sampling from a distribution is just a coordinate transformation of the uniform distribution

Video

Script

The slides can be found at File:Sampling-from-a-probability-distribution.pdf

Quiz

what does our sampling process make sure?

	the sampled values will most likely follow the given probability distribution
	the sampled values will certainly follow the given probability distribution
	the sampled values are not biased but are uniformly distributed
	the value of the Kolmogorov Smirnov test for the sampled values and the original distribution should be smaller the more values are sampled
	the value of the Kolmogorov Smirnov test for the sampled values and the original distribution should be bigger the more values are sampled

Further reading

1. tba

Discussion

Navigation

1. How big is the World Wide Web
   1. Problems with the question about the size of the Web
   2. 3 ways to study the Web
   3. A simplistic descriptive model
   4. An unrealistic, simplistic generative model
   5. Summary, further reading, homework
2. Simple statistical descriptive Models for the Web
   1. Counting Words And Documents
   2. Typical length of a document
   3. How to formulate a research hypothesis
   4. Number of words needed to understand most of Wikipedia
   5. Linguists way of checking simplicity of text
3. Advanced statistical descriptive models for the Web
   1. The Zipf law for text
   2. Visually straight lines on log log plots
   3. Fitting a curve on a log log plot
   4. Zipf law powerlaw or pareto law.webm
4. Modelling Similarity of Text
   1. Similarity Measures and their Applications
   2. Jaccard Similarity for Sets
   3. Cosine Similarity For Vectorspaces
   4. Probabilistic Similarity Measures Kullback Leibler Divergence
   5. Comparing Results of Similarity Merasures
5. Generative Models for the Web
   1. Introduction to generative modelling.webm
   2. Sampling from a probability distribution
   3. Evaluating a generative model
   4. Pittfalls when increasing the number of model parameters
6. Modeling the Web as a graph
   1. Reviewing terms from graph theory
   2. The standard web graph model
   3. Descriptive statistics of the web graph
   4. Topology of the web graph
   5. Modelling-graphs-with-linear-algebra

Introduction to generative modelling.webm

Evaluating a generative model