Conditional CategoricalDistributions

Questions
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1

I want to take a CategoricalDistribution, impose a condition, and get a new CategoricalDistribution out. Here’s a notebook with an ugly solution that probably does not generalize well. Can someone come up with something better?

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2

We could make the code a little more general this way:

 conditionalDistribution[cd_CategoricalDistribution, outerlevel_] := 
 With[{queryElements = 
 PadRight[{outerlevel}, Length[Information[cd, "Categories"]], 
 Values]}, 
 CategoricalDistribution[Rest@Information[cd, "Categories"], 
 Normal@(Query @@ queryElements)[
 Information[cd, "ProbabilityTable"]]]
 ]

But that still seems suboptimal.

3

If all of the category values are all unique (as in your example), the following might suggest a more general approach:

cd = CategoricalDistribution[{{"A", "B", "C"}, {"\[Alpha]", "\[Beta]"},
   {"\[HappySmiley]", "\[SadSmiley]"}}, 
   {{{6, 84}, {8, 48}}, {{63, 91}, {88, 78}}, {{34, 72}, {74, 55}}}];

conditional[dist_, cValues_] := CategoricalDistribution[
  Select[Information[dist, "Probabilities"] // Normal, ContainsAll[#[[1]], cValues] &]];

cd1 = conditional[cd, {#}] & /@ Information[cd, "Categories"][[1]];
Information[#, "ProbabilityTable"] & /@ cd1

conditionalprobabilitytables.png
conditionalprobabilitytables.png528×241 3.71 KB

This also works for conditioning on multiple values (from different variables):

Information[conditional[cd, {"A", "\[Alpha]"}], "ProbabilityTable"]

2wayconditional.png

4

I came up with an idea that is more general and permits some fairly natural representations of the conditions. I plan on making this into a ResourceFunction. Comments welcome. Here’s a notebook containing the idea.

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