# Bayes Network with mixture of continuous (or discrete) and categorical nodes • ### Question

• I've seen https://social.microsoft.com/Forums/en-US/48d3450e-73d9-4ac5-ad61-b0ad7371d519/multiple-continuous-parents-and-a-combination-of-continuous-and-discrete-parents-examples?forum=infer.net , and while it is related to my question my variant is somewhat different.

Say I have nodes A and B.  A is continuous (let's say Gaussian) and B is categorical, and A -> B.  How would I go about setting this up?

A more concrete example would be a house.  A would be number of rooms (Gaussian is probably a poor choice in this case, so let's say Poisson), and B would be the category of a room type (e.g. bedroom, kitchen, etc.).  We could expect that the size of a house makes the probability of certain types of rooms appearing more likely (i.e.. most houses will have bedroom, but we would expect that only very large houses have butlers quarters).

Currently, I'm just making a categorical distribution for room size, but that would seem to throw out valuable information.

Tuesday, December 2, 2014 11:45 PM

### All replies

• Ok, so I've made some progress, maybe someone can tell me if my solution makes sense or if I've gone down the wrong path.

As I see it there are a couple cases:

All Categorical Parents -> Categorical Child  == Conditional Probability Table

All Continuous Parents -> Categorical Child == Softmax (or Bayes Point Machine)

All Categorical Parents -> Continuous Child == Conditional Gaussian Table (I'm assuming that all continous variables are Gaussians)

All Continuous Parents -> Continuous  Child == Bayes Linear Regression

And the tricky ones:

Mixed Parents -> Categorical Child == Some sort of Conditional Softmax table?

Mixed Parents -> Continuous Child == Some sort of Conditional Linear Regression table?

Mixed Parents -> Categorical Child == Some sort of Conditional Softmax table?
Mixed Parents -> Categorical Child == Some sort of Conditional Softmax table?
Thursday, December 4, 2014 4:57 PM
• A conditional probability table is a special case of softmax, and a conditional Gaussian table is a special case of linear regression, so the whole thing can be summarized as:

Categorical Child == Softmax

Continuous Child == linear regression

Friday, December 5, 2014 12:33 PM