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
details.
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
from node i
to 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
expectation ($mu
) and the variance matrix ($gamma
).
/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
unity.
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
actions train1car
for train and car.
2 (as usual but only one-to-one) nbn2gema
means
\"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) arc7nb4nbn
means "get the arc-numbers from a /nbn/".
8 (similar to 'a') generate8nbn
or print8nbn
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
in the ../rbmn/R/
directory, and with all their comments
(equivalent to Rd
files into ../rbmn/inst/original/
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 nbn2rr
.
Systemize the existence of check8object
functions
Introduce their systematic use conditionned with a
rbmn0check
variable.
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 nbn4string7dag
.
Add the computation made with /bnlearn/ in the example of
estimate8nbn
.
Check the topological order within nbn2nbn
depending on
rbmn0check
value.
Make a super transformation function from an object associated to a Bayesian network to any other type, including itself.
Correct the ord
option in order4chain
.
Check the topological order in rm8nd4adja
.
Think about removing all rmatrix
transformations to the
benefit of the to-come gbn
object.
Introduce a check of non-negativity of ma
into
cor4var
.
Add examples to all functions without any.
Jean-Baptiste Denis
MIAj - Inra - Jouy-en-Josas
F-78532 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".
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