Table 1:

Glossary of general terms in probabilistic graphical modeling.

General term	Short description
Pearson correlation	measure of linear relationship between two variables, can take values between −1 and 1
first/second order partial correlation	correlation between two variables corrected for presence of one/two other variables at a time, can take values between −1 and 1
full order partial correlation	correlation between two variables corrected for presence of all other variables under investigation, can take values between −1 and 1
probability distribution P(X = x)	gives the probability that a random variable X takes on the value x in an experiment
statistical independence	two random variables X and Y are statistically independent if the probability that X will take on the value x does not affect the probability that Y will take on the value y and vice versa
conditional independence	two random variables X and Y are conditionally independent given the random variable Z if the probability that X will take on the value x does not affect the probability that Y will take on the value y and vice versa given that Z equals z
probabilistic graphical model (PGM)	describes conditional dependency structure of a set of random variables and represents it in a graph
node/vertex	represents one variable in PGM
edge	represents conditional dependency between two vertices given all other vertices in PGM; absence of an edge encodes conditional independency between two vertices given all remaining vertices
neighbor of vertex vi	vertex which is adjacent, i.e. directly connected by an edge, to vertex vi
first order neighborhood of vertex vi	complete set of neighbors of vertex vi
precision matrix	encodes conditional dependencies of PGM, whereas 0 typically represents conditional independence between two vertices
Gaussian Graphical Model (GGM)	PGM with only Gaussian distributed variables
discrete Markov Random Field	PGM with only discrete variables
Mixed Graphical Model (MGM)	PGM with mixed variable types, typically Gaussian and categorical variables
parameter regularization	penalization of complex models to reduce risk of overfitting
overfitting	the estimated model too closely describes the underlying relationships in the training data and is not generalizable to independent data sets
probabilistic graphical model learning	determining the presence and strength of each individual edge in a PGM
probabilistic graphical model selection	selection of one specific PGM out of a set of estimated PGMs based on the optimization of a certain model selection criterion