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Tractable representations, inference, and probabilistic learning models and their applications. It covers various models such as AoGs, PDGs, NBs, fully factorized sd-DNNF, PSDDs, trees, LTMs, DNNFs, OBDDs, CNets, SPNs, NADEs, thin junction trees, NNF, FBDDs, BDDs, ACs, VAEs, polytrees, d-NNFs, ADDs, SDDs, TACs, GANs, NFs, mixtures, XADDs, XSDDs, MNs, BNs, and FGs. The document also discusses why tractable inference is important and how probabilistic circuits provide a unified framework for tractable models. It also covers building circuits, learning them from data, and compiling other models. The document also discusses why probabilistic inference is important and how it can be used to answer probabilistic queries on a probabilistic model of the world. It also covers approximate inference and its guarantees.
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Guy Van den Broeck University of California, Los Angeles
based on a joint UAI-19 tutorial with Antonio Vergari University of California, Los Angeles Nicola Di Mauro University of Bari
September 23, 2019 - 35th International Conference on Logic Programming (ICLP 2019) Las Cruces, New Mexico, USA
AoGs PDGs NBs Fully factorized sd-DNNF PSDDs Trees LTMs DNNFs OBDDs CNets SPNs NADEs Thin Junction Trees NNF FBDDs BDDs ACs VAEs Polytrees d-NNFs ADDs SDDs TACs GANs NFs Mixtures XADDs XSDDs MNs BNs FGs
AoGs PDGs NBs Fully factorized sd-DNNF PSDDs Trees LTMs DNNFs OBDDs CNets SPNs NADEs Thin Junction Trees NNF FBDDs BDDs ACs VAEs Polytrees d-NNFs ADDs SDDs TACs GANs NFs Mixtures XADDs XSDDs MNs BNs FGs
AoGs PDGs NBs Fully factorized sd-DNNF PSDDs Trees LTMs DNNFs OBDDs CNets SPNs NADEs Thin Junction Trees NNF FBDDs BDDs ACs VAEs Polytrees d-NNFs ADDs SDDs TACs GANs NFs Mixtures XADDs XSDDs MNs BNs FGs
q 1 : What is the probability that today is a Monday and there is a traffic jam on Herzl Str.? q 2 : Which day is most likely to have a traffic jam on my route to work?
pinterest.com/pin/190417890473268205/
q 1 : What is the probability that today is a Monday and there is a traffic jam on Herzl Str.? q 2 : Which day is most likely to have a traffic jam on my route to work?
pinterest.com/pin/190417890473268205/
q 1 : What is the probability that today is a Monday and there is a traffic jam on Herzl Str.?
q 1 (m) = pm(Day = Mon, JamHerzl = 1)
pinterest.com/pin/190417890473268205/
q 1 : What is the probability that today is a Monday and there is a traffic jam on Herzl Str.?
q 1 (m) = pm(Day = Mon, JamHerzl = 1)
pinterest.com/pin/190417890473268205/
q 2 : Which day is most likely to have a traffic jam on my route to work?
q 2 (m) = argmaxd pm(Day = d ∧ ∨ i∈route JamStr i)
pinterest.com/pin/190417890473268205/
A class of queries Q is tractable on a family of probabilistic models M iff for any query q ∈ Q and model m ∈ M exactly computing q(m) runs in time O(poly(|q| · |m|)).
A class of queries Q is tractable on a family of probabilistic models M iff for any query q ∈ Q and model m ∈ M exactly computing q(m) runs in time O(poly(|q| · |m|)).
Note: if M and Q are compact in the number of random variables X, that is, |m|, |q| ∈ O(poly(|X|)), then query time is O(poly(|X|)).
[Dechter et al. 2002; Choi et al. 2010; Lowd et al. 2010; Sontag et al. 2011; Friedman et al. 2018]
