General functions to generate, transform, display general and
particular linear Gaussian Bayesian networks [/nbn/] are provided.
Specific /nbn/ are chain and crossed /nbn/s. Focus is given in getting joint and conditional probability distributions of the set of nodes.
rbmn stands for R'eseau Bay'esien MultiNormal.
Some basic concepts:
chain /nbn/s are /nbn/s where all nodes are connected with two other nodes, except the two ending nodes of the chain having only one connection. (This is not the usual terminology in graphical models but I didn't find a more appropriate word: suggestions are welcome.)
crossed /nbn/s are /nbn/s having the node set defined as a
Cartesian product of two series of items, and a DAG based on this
structure. See the
crossed4nbn1nbn function and/or Tian (2013) for
An adjacency matrix is a matrix equivalent to the DAG
associated to a /nbn/. Its rows as well as its columns are associated
to the set of nodes. The
(i,j) cell is one when there is an arc going
j and zero otherwise.
Three equivalent ways can be used to represent the joint probability distribution of a set of nodes respectively associated to the structures /mn/, /nbn/ and /gema/:
/mn/ (for multivariate normal) is just the list of the
$mu) and the variance matrix (
/nbn/ (for normal Bayesian network) is a simple list, a component a node described with a list. The names are node names and each list associated to a node provides the conditional expectation and variance, the parent (if any) and the associated regression coefficients.
/gema/ (for generating matrices) is a list of a vector
mu) and a matrix (
li) such that the vector of the
nodes can be defined by
X = mu + li%*%E where
E is a
normal random vector with expectation zero and variance matrix
It is planned to add a fourth one under the name of /gbn/.
To relieve the memory effort, most names of the functions have been given a two (or more) components structure separated with a figure. This idea will be explained and exploited in a package to come named documair. The approximate meaning of the figures are:
0 (similar to 'o')
rbmn0chain.01 to indicate an object
example provided by rbmn.
1 (similar to an ~ and) ??? to link different objects or
train1car for train and car.
2 (as usual but only one-to-one)
\"transforming a /nbn/ into a /gema/ objects\".
3 (remind the 'belong to' sign)
form3repeat could be
interpreted as "repeat action from the series of 'form' functions".
4 (associated to 'from')
adja4nbn means "get the adjacency
matrix from a /nbn/ object".
7 (upper bar of '7' similar to the hyphen)
means "get the arc-numbers from a /nbn/".
8 (similar to 'a')
for \"generating or printing a /nbn/ object\".
A number of ancillary functions have not been exported to give a better
access to the main function of /rbmn/. Nevertheless they are available
../rbmn/R/ directory, and with all their comments
Rd files into
directory). Some of them are visible when defining the default
arguments of some functions.
Generalize the /mn/ object with a regression part like
the output of function
condi4joint when argument
pour is not of length zero and argument
x2 is not
null. With such a structure, every node of a /nbn/ could be
described with a /mn/ comprising a unique variable... Also the two
arguments of function
mn4joint1condi would be just two /mn/
objects... This is also the generalized /mn/ proposed in function
simulate8gmn under the argument of
loi... Of course
almost all functions dealing with /nbn/ objects will be to rewrite!
Introduce a new object
gbn for Gaussian Bayesian
network similar to the list provided by function
Systemize the existence of
Introduce their systematic use conditionned with a
Follow the main checking of every functions
Give (and use) class attributes to the main objects.
Introduce the main objects in this short presentation.
Make a true small example in this short presentation.
Make the function
Add the computation made with /bnlearn/ in the example of
Check the topological order within
nbn2nbn depending on
Make a super transformation function from an object associated to a Bayesian network to any other type, including itself.
ord option in
Check the topological order in
Think about removing all
rmatrix transformations to the
benefit of the to-come
Introduce a check of non-negativity of
Add examples to all functions without any.
MIAj - Inra - Jouy-en-Josas
Maintainer: Jean-Baptiste Denis Jean-Baptiste.Denis@Jouy.Inra.Fr
(A technical report presenting the concepts used in rbmn is under redaction; it can be obtained as it is if asked.)
Scutari M (2010). "Learning Bayesian Networks with the bnlearn R Package". Journal of Statistical Software, 35(3), 1-22. URL http://www.jstatsoft.org/v35/i03/.
Tian S, Scutari M & Denis J-B (2013, submitted to JSFdS). "Predicting with Crossed Linear Gaussian Bayesian Networks".
1 2 3 4 5