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Probabilistic Programming --- Medical Cases

This class will cover use cases of the Bayesian methods in the medical domain. First part of the class is based on article: “Local computations with probabilities on graphical structures and their application to expert systems” by Lauritzen, Steffen L. and David J. Spiegelhalter. Second part is inspired by “An intercausal cancellation model for bayesian-network engineering. International Journal of Approximate Reasoning” by S.P. Woudenberg, L. C. van der Gaag, and C. M. Rademaker.

Medical Diagnosis

In this section we will follow a simplified use case of the medical diagnosis, as defined in the following quote from the article.

Structure

First task of the “knowledge engineer” is to find a structure of Bayesion network which fits the story. There exist automatic tools to learn the structure from examples, but in this case the structure should be clear enough to create the network by hand.

Assignments

  1. Draw (on paper?) a Bayesian network describing the story from the previous section.
  2. Write the corresponding ProbLog program:
    1. there is no need for the first order logic here
    2. use arbitrary probabilities

Probabilities

The problem with Bayesian model you've just created is that it doesn't provide with any useful info. Mostly because of the arbitrary prior probabilities, you've used. Reality is rather harsh, often you don't have access to any realistic priors (one of the arguments of critics of Bayesian methods). In this section we will try to make up for that and find make the network useful.

Learning

The simplest way to have realistic priors is to not have any priors at all :) In other words — we assume, we know nothing about probabilities. In ProbLog you can state this fact by using t(_) predicate, e.g.

t(_)::smoker.

Says you do not know nothing about probability of patient being smoker.

en/dydaktyka/problog/lab1.1496060740.txt.gz · Last modified: 2019/06/27 16:00 (external edit)
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