probabilistic_circuit (1108B)
1 # Probabilistic circuit 2 3 [circuit] which represents [probability_distribution] 4 5 - leaves: distribution on a subset of variables called its scope 6 - [product] of distributions, with [decomposability] 7 - sum with coefficients to [mix] distributions 8 9 optional conditions: 10 - [smooth] 11 - [determinism]: disjoint support on the inputs (= non-zero proba mass?) 12 - [structured] 13 14 we want to do [maximum_a_posteriori] on such circuits 15 - [marginal_maximum_a_posteriori], MMAP 16 - max_Q sum_H p(Q, H) 17 - the problem is that summing on a subset of the variables loses [circuit_determinism] 18 19 - a sum node is Q-deterministic if support is disjoint even when projecting out Q 20 - and a circuit is Q-det if all sum nodes are Q-det or their scope does not 21 involve variables of Q 22 23 - md-vtrees: a way to guarantee marginal determinism, just by labeling v-tree 24 nodes with a subset S of variables on which you have to be S-deterministic 25 26 connections to other kinds of [polynomials] than [probability_distributions]: see [broadrick2024polynomial] 27 28 See also: [arithmetic_circuit], [circuit_algebraic] 29 30 Up: [circuit], [probabilities]