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I have a Bayesian network of a given structure and nodes A, B, C, D, E and want to learn the parameters of the network, i.e. the conditional probabilities, from data with differing frequencies of observation at different timestamps.

For example, lets say I have measurements at timestamps T1, ...., T1000:

  • T1: A=true
  • T2: A=true, B=true, C=false
  • T3: A=false, B=true, C=false
  • T4: A=true, B=true, C=false, E=false
  • ...
  • T1000: A=true, B=false, C=false, D=true, E=false

The network has a fixed structure, lets say

A     D
|\   /
v  v
B  C
| /
v
E

Question: What is the best approach to estimate parameters for this network in this case?


Edit: one more remark

  • the frequency differs by orders of magnitude, E can be observed approximately once a month, whereas some nodes can have multiple measurements per minute
  • the network is assumed to be time-independent
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1 Answer 1

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From the graph you've drawn, I conclude that your Bayesian network does not account for any temporal dimension, i.e. the joint distribution $p(A,B,C,D,E)$ does not change over time. If that is the case, then you should treat observations at different timestamps as i.i.d. and learn the parameters in the usual way (i.e. using maximum likelihood or MAP).

From the data you have presented, it also seems that your data is incomplete. E.g.: At time T1, you only show the value of $A$. Are the values of $B$, $C$, $D$ and $E$ missing? If that's the case, then you'll need a fancier learning algorithm, like expectation maximization (EM).

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