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Having data sets regarding symptoms and diseases such that I use to observe the conditional distributions P(Disease X | Symptom A , Symptom H , Age >20 ) which I use for classification and diagnosis.

Now, a Domain expert comes and says - the data do not reflect reality, Disease X does not come really often with Symptom A. Or, Combination of Symptom H and A can also lead to Disease Y which never observed in the data.

What is the modern approach to combine the new knowledge that comes from domain experts to "tune" the classifiers / Augment the original data with the expert inputs? Without using just pure rule-base which won't help the model generalizes.

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The short answer to your question is Bayesian modelling.

Beta-distributed priors and Dirichlet priors - these are places to start with when you want to combine number statistics with export knowledge of expected distributions. Bayesian modelling is a whole subfield in itself, within statistics.

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  • $\begingroup$ Then the expert needs to choose the prior distribution family or the exact mean/variance of the distribution? $\endgroup$
    – Latent
    Commented Jul 21, 2020 at 17:36
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    $\begingroup$ The expert provides the prior parameter values. The Beta-distribution is for variables/outcomes with two possible values, the Dirichlet for more than 2 possible values. The choice of the type of distribution itself is given by your application domain. $\endgroup$
    – Match Maker EE
    Commented Jul 21, 2020 at 17:47
  • $\begingroup$ Expert won't give you the parameter values.. only confidence in rules, that is why i thought about augmentation that will change the distribution some how.. $\endgroup$
    – Latent
    Commented Jul 21, 2020 at 18:05
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    $\begingroup$ In the past, I use to work with researchers who elicited such probabilities from physicians through different gaming and estimation techniques. That's where such numbers can be obtained from. $\endgroup$
    – Match Maker EE
    Commented Jul 21, 2020 at 18:17
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    $\begingroup$ Take a look at LC van der Gaag et al (2002), Probabilities for a Probabilistic Network: A Case-study in Oesophageal Carcinoma: dspace.library.uu.nl/bitstream/handle/1874/2018/… $\endgroup$
    – Match Maker EE
    Commented Jul 22, 2020 at 7:55

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