Bayes Network and Bayes Rule

As explained by Sebastin Thrun in the AI course:

Bayes Rule:

Example:

Whats the likelihood that a person has cancer (A) given that they have had a positive cancer diagnostic test (B)?

• Likelihood: Probability of +ve cancer test (B) given that the person has cancer (A)
• Prior: Probability of getting that type of cancer (A)
• Marginal likelihood: Sum of probability of
  (+ve test given that you have the cancer x probability of having that cancer)
  (+ve test given that you don’t have the cancer (false positive) x probability of not having that cancer)

Bayes Network:

 

Inferring P(B):

Wikipedia:

Baye’s Rule: http://en.wikipedia.org/wiki/Bayes_rule

Baye’s Network: http://en.wikipedia.org/wiki/Bayes_network

Infer.Net–Machine Learning framework for .Net

From MSR

Infer.NET is a framework for running Bayesian inference in graphical models.  You can use it to solve many different kinds of machine learning problems, from standard problems like classification or clusteringthrough to customised solutions to domain-specific problems. Infer.NET has been used in a wide variety of domains including information retrieval, bioinformatics, epidemiology, vision, and many others.

One of the interesting aspects of Infer.Net is that you define your problem as a model and Infer.Net creates source code based on that definition, which is then used to generate results.

Notes:

Machine for .Net Learning on CodePlex: http://machine.codeplex.com/ (Binary and multi-class classification and clustering algorithm implementations). Project has been developed by Seth Juarez.

At this point Infer.Net cannot be used in a commercial application. Whereas, Seth Juarez’s library can be used in a commercial application.