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en:dydaktyka:problog:lab1 [2017/05/29 19:31] msl [Predicting Treating Effects] |
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| - | ====== Probabilistic Programming --- Medical Cases ====== | + | ====== Probabilistic Programming — Diagnosis and Prediction ====== |
| 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. | 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. | ||
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| - Write the corresponding Problog program: | - Write the corresponding Problog program: | ||
| - Hints: | - Hints: | ||
| - | * logical or in Problog: <code prolog> a_or_b :- a. a_or_b :- b. </code> | + | * logical or in Problog: <code prolog>a_or_b :- a. |
| - | * you can have lung cancer even if you are not smoker, so you should add include in model something similar to the line below. Analogically other diseases ;) <code prolog>0.01::smoker.</code> | + | a_or_b :- b. </code> |
| + | * you can have lung cancer even if you are not a smoker, so don't forget to mention this fact in the model. There are two ways to do that: | ||
| + | * classical (Bayesian network):<code prolog>0.1::cancer :- smoker. | ||
| + | 0.01::cancer :- \+ smoker.</code> | ||
| + | * pros: it's a classical approach with clean Bayesian semantics | ||
| + | * cons: including new variables into the model can grow number of rules exponentially; also it may be required to modify already existing rules | ||
| + | * Problog 'additive way':<code prolog>0.1::cancer :- smoker. | ||
| + | 0.01::cancer.</code> | ||
| + | * pros: including new variable doesn't involve change of the old rules; you just add new rule per variable | ||
| + | * cons: the probabilities will be different than in the Bayesian network; so you can't just copy the Bayesian network structure ;) | ||
| + | * x-ray can be positive even if you're healthy | ||
| ==== Probabilities ==== | ==== Probabilities ==== | ||
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| <WRAP center round important 80%> | <WRAP center round important 80%> | ||
| - | If you receive an "Inconsistent Evidence" error, include leak probabilities in the model. Leak probabilities are probabilities stating that some random variable can be assigned to a value without any particular reason, e.g. here we state that variable ''var'' can't be true because of an external reason. | + | If you receive an "Inconsistent Evidence" error, it means that your model is not compatible. Sometimes the simplest way to solve this problem is to include leak probabilities in the model. Leak probabilities are probabilities stating that some random variable can be assigned to a value without any particular reason, e.g. here we state that variable ''var'' can't be true because of an external reason. |
| <code prolog> | <code prolog> | ||
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| * 0.01% of the population has been in Asia | * 0.01% of the population has been in Asia | ||
| * dyspnea is mostly caused by asthma and causes other than TB, lung cancer, or bronchitis | * dyspnea is mostly caused by asthma and causes other than TB, lung cancer, or bronchitis | ||
| - | * smoking has greater impact on lung cancer than bronchitis | + | * smoking has greater impact on lung cancer than on bronchitis |
| === Assignments === | === Assignments === | ||
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| === Assignments === | === Assignments === | ||
| - | - write a corresponding Problog program | + | - write a corresponding Problog program: |
| - | - what is the chance of successful treatment when we use both calcium and bisphosphonates | + | * you may have to introduce additional variables for every kind of treatment to indicate if the treatment is inhibited, e.g. calcium effects in **something** that treats the osteoporosis |
| + | - what is the chance of successful treatment when we use both calcium and bisphosphonates? | ||
