| Title: | Bayesian Networks |
|---|---|
| Description: | Probability propagation in Bayesian networks, also known as graphical independence networks. Documentation of the package is provided in vignettes included in the package and in the paper by Højsgaard (2012, <doi:10.18637/jss.v046.i10>). See 'citation("gRain")' for details. |
| Authors: | Søren Højsgaard [aut, cre] |
| Maintainer: | Søren Højsgaard <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.4.5 |
| Built: | 2024-10-18 12:36:27 UTC |
| Source: | CRAN |
Compile conditional probability tables / cliques potentials as a preprocessing step for creating a graphical independence network
compileCPT(x, ..., forceCheck = TRUE) compilePOT(x, ..., forceCheck = TRUE)compileCPT(x, ..., forceCheck = TRUE) compilePOT(x, ..., forceCheck = TRUE)
x |
To |
... |
Additional arguments; currently not used. |
forceCheck |
Controls if consistency checks of the probability tables should be made. |
* `compileCPT` is relevant for turning a collection of cptable's into an object from which a network can be built. For example, when specification of a cpt is made with cptable then the levels of the node is given but not the levels of the parents. `compileCPT` checks that the levels of variables in the cpt's are consistent and also that the specifications define a dag. * `compilePOT` is not of direct relevance for the user for the moment. However, the elements of the input should be arrays which define a chordal undirected graph and the arrays should, if multiplied, form a valid probability density.
A list with a class attribute.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
extract_cpt, extract_pot, extract_marg
example("example_chest_cpt") x <- compile_cpt(chest_cpt) class(x) grain(x)example("example_chest_cpt") x <- compile_cpt(chest_cpt) class(x) grain(x)
Extract list of conditional probability tables and list of clique potentials from data.
extract_cpt(data_, graph, smooth = 0) extract_pot(data_, graph, smooth = 0) extract_marg(data_, graph, smooth = 0) marg2pot(marg_rep) pot2marg(pot_rep)extract_cpt(data_, graph, smooth = 0) extract_pot(data_, graph, smooth = 0) extract_marg(data_, graph, smooth = 0) marg2pot(marg_rep) pot2marg(pot_rep)
data_ |
A named array or a dataframe. |
graph |
An |
smooth |
See 'details' below. |
marg_rep |
An object of class |
pot_rep |
An object of class |
If smooth is non-zero then smooth is added
to all cell counts before normalization takes place.
extract_cpt: A list of conditional probability tables.
extract_pot: A list of clique potentials.
extract_marg: A list of clique marginals.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
## Extract cpts / clique potentials from data and graph # specification and create network. There are different ways: data(lizard, package="gRbase") # DAG: height <- species -> diam daG <- dag(~species + height:species + diam:species, result="igraph") # UG : [height:species][diam:species] uG <- ug(~height:species + diam:species, result="igraph") pt <- extract_pot(lizard, ~height:species + diam:species) cp <- extract_cpt(lizard, ~species + height:species + diam:species) pt cp # Both specify the same probability distribution tabListMult(pt) |> as.data.frame.table() tabListMult(cp) |> as.data.frame.table() ## Not run: # Bayesian networks can be created as bn.uG <- grain(pt) bn.daG <- grain(cp) # The steps above are wrapped into a convenience method which # builds a network from at graph and data. bn.uG <- grain(uG, data=lizard) bn.daG <- grain(daG, data=lizard) ## End(Not run)## Extract cpts / clique potentials from data and graph # specification and create network. There are different ways: data(lizard, package="gRbase") # DAG: height <- species -> diam daG <- dag(~species + height:species + diam:species, result="igraph") # UG : [height:species][diam:species] uG <- ug(~height:species + diam:species, result="igraph") pt <- extract_pot(lizard, ~height:species + diam:species) cp <- extract_cpt(lizard, ~species + height:species + diam:species) pt cp # Both specify the same probability distribution tabListMult(pt) |> as.data.frame.table() tabListMult(cp) |> as.data.frame.table() ## Not run: # Bayesian networks can be created as bn.uG <- grain(pt) bn.daG <- grain(cp) # The steps above are wrapped into a convenience method which # builds a network from at graph and data. bn.uG <- grain(uG, data=lizard) bn.daG <- grain(daG, data=lizard) ## End(Not run)
Compile conditional probability tables / cliques potentials as a preprocessing step for creating a graphical independence network
compile_cpt(x, ..., forceCheck = TRUE) compile_pot(x, ..., forceCheck = TRUE) parse_cpt(xi)compile_cpt(x, ..., forceCheck = TRUE) compile_pot(x, ..., forceCheck = TRUE) parse_cpt(xi)
x |
To |
... |
Additional arguments; currently not used. |
forceCheck |
Controls if consistency checks of the probability tables should be made. |
xi |
cpt in some representation |
* `compileCPT` is relevant for turning a collection of cptable's into an object from which a network can be built. For example, when specification of a cpt is made with cptable then the levels of the node is given but not the levels of the parents. `compileCPT` checks that the levels of variables in the cpt's are consistent and also that the specifications define a dag. * `compilePOT` is not of direct relevance for the user for the moment. However, the elements of the input should be arrays which define a chordal undirected graph and the arrays should, if multiplied, form a valid probability density.
A list with a class attribute.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
extract_cpt, extract_pot, extract_marg
example("example_chest_cpt") x <- compile_cpt(chest_cpt) class(x) grain(x)example("example_chest_cpt") x <- compile_cpt(chest_cpt) class(x) grain(x)
Creates conditional probability tables of the form p(v|pa(v)).
cpt(names, levels, values, normalize = "first", smooth = 0) cptable(vpar, levels = NULL, values = NULL, normalize = TRUE, smooth = 0)cpt(names, levels, values, normalize = "first", smooth = 0) cptable(vpar, levels = NULL, values = NULL, normalize = TRUE, smooth = 0)
names |
Specifications of the names in P(v|pa1,...pak). See section 'details' for information about the form of the argument. |
levels |
|
values |
Probabilities; recycled if necessary. Regarding the order, please see section 'details' and the examples. |
normalize |
See 'details' below. |
smooth |
Should values be smoothed, see 'Details' below. |
vpar |
node an its parents |
cptable is simply a wrapper for cpt and the functions can hence
be used synonymously.
If smooth is non–zero, then this value is added to all cells before
normalization takes place.
Regarding the form of the argument names: To specify
one may write ~a|b:c, ~a:b:c,
~a|b+c, ~a+b+c or c("a","b","c"). Internally,
the last form is used. Notice that the + and :
operator are used as a separators only. The order of the variables IS
important so the operators DO NOT commute.
The first variable in levels varies fastest.
An array.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
andtable, ortable,
extract_cpt, compileCPT,
extract_cpt, compilePOT,
grain
## See the wet grass example at ## https://en.wikipedia.org/wiki/Bayesian_network yn <- c("yes", "no") ssp <- list(R=yn, S=yn, G=yn) # state space ## Different forms t1 <- cpt(c("S", "R"), levels=ssp, values=c(.01, .99, .4, .6)) t2 <- cpt(~S:R, levels=ssp, values=c(.01, .99, .4, .6)) t3 <- cpt(~S:R, levels=c(2, 2), values=c(.01, .99, .4, .6)) t4 <- cpt(~S:R, levels=yn, values=c(.01, .99, .4, .6)) t1; t2; t3; t4 varNames(t1) valueLabels(t1) ## Wet grass example ssp <- list(R=yn, S=yn, G=yn) # state space p.R <- cpt(~R, levels=ssp, values=c(.2, .8)) p.S_R <- cpt(~S:R, levels=ssp, values=c(.01, .99, .4, .6)) p.G_SR <- cpt(~G:S:R, levels=ssp, values=c(.99, .01, .8, .2, .9, .1, 0, 1)) wet.cpt <- compileCPT(p.R, p.S_R, p.G_SR) wet.cpt wet.cpt$S # etc # A Bayesian network is created with: wet.bn <- grain(wet.cpt)## See the wet grass example at ## https://en.wikipedia.org/wiki/Bayesian_network yn <- c("yes", "no") ssp <- list(R=yn, S=yn, G=yn) # state space ## Different forms t1 <- cpt(c("S", "R"), levels=ssp, values=c(.01, .99, .4, .6)) t2 <- cpt(~S:R, levels=ssp, values=c(.01, .99, .4, .6)) t3 <- cpt(~S:R, levels=c(2, 2), values=c(.01, .99, .4, .6)) t4 <- cpt(~S:R, levels=yn, values=c(.01, .99, .4, .6)) t1; t2; t3; t4 varNames(t1) valueLabels(t1) ## Wet grass example ssp <- list(R=yn, S=yn, G=yn) # state space p.R <- cpt(~R, levels=ssp, values=c(.2, .8)) p.S_R <- cpt(~S:R, levels=ssp, values=c(.01, .99, .4, .6)) p.G_SR <- cpt(~G:S:R, levels=ssp, values=c(.99, .01, .8, .2, .9, .1, 0, 1)) wet.cpt <- compileCPT(p.R, p.S_R, p.G_SR) wet.cpt wet.cpt$S # etc # A Bayesian network is created with: wet.bn <- grain(wet.cpt)
Conditional probability tables for the chest clinic example.
yn <- c("yes", "no") a <- cpt(~asia, values=c(1,99),levels=yn) t.a <- cpt(~tub|asia, values=c(5,95,1,99),levels=yn) s <- cpt(~smoke, values=c(5,5), levels=yn) l.s <- cpt(~lung|smoke, values=c(1,9,1,99), levels=yn) b.s <- cpt(~bronc|smoke, values=c(6,4,3,7), levels=yn) e.lt <- cpt(~either|lung:tub,values=c(1,0,1,0,1,0,0,1),levels=yn) x.e <- cpt(~xray|either, values=c(98,2,5,95), levels=yn) d.be <- cpt(~dysp|bronc:either, values=c(9,1,7,3,8,2,1,9), levels=yn) chest_cpt <- list(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) ## bn <- grain(compile_cpt(chest_cpt))yn <- c("yes", "no") a <- cpt(~asia, values=c(1,99),levels=yn) t.a <- cpt(~tub|asia, values=c(5,95,1,99),levels=yn) s <- cpt(~smoke, values=c(5,5), levels=yn) l.s <- cpt(~lung|smoke, values=c(1,9,1,99), levels=yn) b.s <- cpt(~bronc|smoke, values=c(6,4,3,7), levels=yn) e.lt <- cpt(~either|lung:tub,values=c(1,0,1,0,1,0,0,1),levels=yn) x.e <- cpt(~xray|either, values=c(98,2,5,95), levels=yn) d.be <- cpt(~dysp|bronc:either, values=c(9,1,7,3,8,2,1,9), levels=yn) chest_cpt <- list(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) ## bn <- grain(compile_cpt(chest_cpt))
Conditional probability tables for the wet grass example.
yn <- c("yes", "no") p.R <- cpt(~R, values=c(.2, .8), levels=yn) p.S_R <- cpt(~S:R, values=c(.01, .99, .4, .6), levels=yn) p.G_SR <- cpt(~G:S:R, values=c(.99, .01, .8, .2, .9, .1, 0, 1), levels=yn) grass_cpt <- list(p.R, p.S_R, p.G_SR) ## bn <- grain(compile_cpt(grass_cpt))yn <- c("yes", "no") p.R <- cpt(~R, values=c(.2, .8), levels=yn) p.S_R <- cpt(~S:R, values=c(.01, .99, .4, .6), levels=yn) p.G_SR <- cpt(~G:S:R, values=c(.99, .01, .8, .2, .9, .1, 0, 1), levels=yn) grass_cpt <- list(p.R, p.S_R, p.G_SR) ## bn <- grain(compile_cpt(grass_cpt))
Set, retrieve, and retract finding in Bayesian network. NOTICE: The functions described here are kept only for backward compatibility; please use the corresponding evidence-functions in the future.
setFinding(object, nodes = NULL, states = NULL, flist = NULL, propagate = TRUE)setFinding(object, nodes = NULL, states = NULL, flist = NULL, propagate = TRUE)
object |
A "grain" object |
nodes |
A vector of nodes |
states |
A vector of states (of the nodes given by 'nodes') |
flist |
An alternative way of specifying findings, see examples below. |
propagate |
Should the network be propagated? |
NOTICE: The functions described here are kept only for backward compatibility; please use the corresponding evidence-functions in the future:
setEvidence() is an improvement of setFinding() (and as such
setFinding is obsolete). Users are recommended to use
setEvidence() in the future.
setEvidence() allows to specification of "hard evidence" (specific
values for variables) and likelihood evidence (also known as virtual
evidence) for variables.
The syntax of setEvidence() may change in the future.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
setEvidence, getEvidence,
retractEvidence, pEvidence,
querygrain
## setFindings yn <- c("yes", "no") a <- cpt(~asia, values=c(1, 99),levels=yn) t.a <- cpt(~tub+asia, values=c(5, 95, 1, 99),levels=yn) s <- cpt(~smoke, values=c(5,5), levels=yn) l.s <- cpt(~lung+smoke, values=c(1, 9, 1, 99), levels=yn) b.s <- cpt(~bronc+smoke, values=c(6, 4, 3, 7), levels=yn) e.lt <- cpt(~either+lung+tub,values=c(1, 0, 1, 0, 1, 0, 0, 1),levels=yn) x.e <- cpt(~xray+either, values=c(98, 2, 5, 95), levels=yn) d.be <- cpt(~dysp+bronc+either, values=c(9, 1, 7, 3, 8, 2, 1, 9), levels=yn) chest.cpt <- compileCPT(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) chest.bn <- grain(chest.cpt) ## These two forms are equivalent bn1 <- setFinding(chest.bn, nodes=c("chest", "xray"), states=c("yes", "yes")) bn2 <- setFinding(chest.bn, flist=list(c("chest", "yes"), c("xray", "yes"))) getFinding(bn1) getFinding(bn2) pFinding(bn1) pFinding(bn2) bn1 <- retractFinding(bn1, nodes="asia") bn2 <- retractFinding(bn2, nodes="asia") getFinding(bn1) getFinding(bn2) pFinding(bn1) pFinding(bn2)## setFindings yn <- c("yes", "no") a <- cpt(~asia, values=c(1, 99),levels=yn) t.a <- cpt(~tub+asia, values=c(5, 95, 1, 99),levels=yn) s <- cpt(~smoke, values=c(5,5), levels=yn) l.s <- cpt(~lung+smoke, values=c(1, 9, 1, 99), levels=yn) b.s <- cpt(~bronc+smoke, values=c(6, 4, 3, 7), levels=yn) e.lt <- cpt(~either+lung+tub,values=c(1, 0, 1, 0, 1, 0, 0, 1),levels=yn) x.e <- cpt(~xray+either, values=c(98, 2, 5, 95), levels=yn) d.be <- cpt(~dysp+bronc+either, values=c(9, 1, 7, 3, 8, 2, 1, 9), levels=yn) chest.cpt <- compileCPT(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) chest.bn <- grain(chest.cpt) ## These two forms are equivalent bn1 <- setFinding(chest.bn, nodes=c("chest", "xray"), states=c("yes", "yes")) bn2 <- setFinding(chest.bn, flist=list(c("chest", "yes"), c("xray", "yes"))) getFinding(bn1) getFinding(bn2) pFinding(bn1) pFinding(bn2) bn1 <- retractFinding(bn1, nodes="asia") bn2 <- retractFinding(bn2, nodes="asia") getFinding(bn1) getFinding(bn2) pFinding(bn1) pFinding(bn2)
Generic functions etc for the gRain package
nodeNames(object) ## S3 method for class 'grain' nodeNames(object) nodeStates(object, nodes = nodeNames(object)) ## S3 method for class 'grain' nodeStates(object, nodes = nodeNames(object)) universe(object, ...) ## S3 method for class 'grain' universe(object, ...) isCompiled(object) isPropagated(object) ## S3 method for class 'cpt_spec' vpar(object, ...) ## S3 method for class 'cpt_grain' vpar(object, ...) ## S3 method for class 'grain' rip(object, ...)nodeNames(object) ## S3 method for class 'grain' nodeNames(object) nodeStates(object, nodes = nodeNames(object)) ## S3 method for class 'grain' nodeStates(object, nodes = nodeNames(object)) universe(object, ...) ## S3 method for class 'grain' universe(object, ...) isCompiled(object) isPropagated(object) ## S3 method for class 'cpt_spec' vpar(object, ...) ## S3 method for class 'cpt_grain' vpar(object, ...) ## S3 method for class 'grain' rip(object, ...)
object |
A relevant object. |
nodes |
Some nodes of the object. |
... |
Additional arguments; currently not used. |
Compiles a Bayesian network. This means creating a junction tree and establishing clique potentials.
## S3 method for class 'grain' compile( object, propagate = FALSE, tug = NULL, root = NULL, control = object$control, details = 0, ... )## S3 method for class 'grain' compile( object, propagate = FALSE, tug = NULL, root = NULL, control = object$control, details = 0, ... )
object |
A grain object. |
propagate |
If TRUE the network is also propagated meaning that the cliques of the junction tree are calibrated to each other. |
tug |
A triangulated undirected graph. |
root |
A set of variables which must be in the root of the junction tree |
control |
Controlling the compilation process. |
details |
For debugging info. Do not use. |
... |
Currently not used. |
A compiled Bayesian network; an object of class
grain.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
grain, propagate,
propagate.grain,
triangulate, rip,
junctionTree
Set, update and remove evidence.
evidence_add(object, evidence, propagate = TRUE, details = 0) evidence_get(object, short = TRUE) evidence_drop(object, nodes = NULL, propagate = TRUE) evidence_prob(object, evidence = NULL)evidence_add(object, evidence, propagate = TRUE, details = 0) evidence_get(object, short = TRUE) evidence_drop(object, nodes = NULL, propagate = TRUE) evidence_prob(object, evidence = NULL)
object |
A "grain" object |
evidence |
A list of name=value. See examples below. |
propagate |
Should the network be propagated? |
details |
Debugging information |
short |
If TRUE a dataframe with a summary is returned; otherwise a list with all details. |
nodes |
A vector of nodes. |
A list of tables with potentials.
setEvidence() is an improvement of setFinding()
(and as such setFinding is obsolete). Users are
recommended to use setEvidence() in the future.
setEvidence() allows to specification of "hard evidence" (specific
values for variables) and likelihood evidence (also known as virtual
evidence) for variables.
The syntax of setEvidence() may change in the future.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
setFinding, getFinding,
retractFinding, pFinding
example("grain") chest_bn <- grain(compileCPT(chest_cpt)) bn2 <- chest_bn |> evidence_add(list(asia="yes", xray="yes")) bn3 <- chest_bn |> evidence_add(list(asia=c(0.8, 0.1), xray="yes")) bn2 |> evidence_get() bn3 |> evidence_get() bn2 |> evidence_prob() bn3 |> evidence_prob() bn2 |> evidence_drop("xray") bn3 |> evidence_drop("xray") bn2 |> evidence_drop("xray") |> evidence_get() bn3 |> evidence_drop("xray") |> evidence_get() ## For backward compatibility these functions are available now but # may be deprecated later. bb2 <- setEvidence(chest_bn, c("asia", "xray"), c("yes", "yes")) bb3 <- setEvidence(chest_bn, c("asia", "xray"), list(c(0.8, 0.2), "yes")) bb4 <- setFinding(chest_bn, c("asia", "xray"), c("yes", "yes")) bb2 |> getEvidence() bb3 |> getEvidence() bb2 |> retractEvidence("xray") bb3 |> retractEvidence("xray") bb2 |> pEvidence() bb3 |> pEvidence() bb2 |> retractEvidence("xray") |> getEvidence() bb3 |> retractEvidence("xray") |> getEvidence()example("grain") chest_bn <- grain(compileCPT(chest_cpt)) bn2 <- chest_bn |> evidence_add(list(asia="yes", xray="yes")) bn3 <- chest_bn |> evidence_add(list(asia=c(0.8, 0.1), xray="yes")) bn2 |> evidence_get() bn3 |> evidence_get() bn2 |> evidence_prob() bn3 |> evidence_prob() bn2 |> evidence_drop("xray") bn3 |> evidence_drop("xray") bn2 |> evidence_drop("xray") |> evidence_get() bn3 |> evidence_drop("xray") |> evidence_get() ## For backward compatibility these functions are available now but # may be deprecated later. bb2 <- setEvidence(chest_bn, c("asia", "xray"), c("yes", "yes")) bb3 <- setEvidence(chest_bn, c("asia", "xray"), list(c(0.8, 0.2), "yes")) bb4 <- setFinding(chest_bn, c("asia", "xray"), c("yes", "yes")) bb2 |> getEvidence() bb3 |> getEvidence() bb2 |> retractEvidence("xray") bb3 |> retractEvidence("xray") bb2 |> pEvidence() bb3 |> pEvidence() bb2 |> retractEvidence("xray") |> getEvidence() bb3 |> retractEvidence("xray") |> getEvidence()
Makes predictions (either as the most likely state or as the conditional distributions) of variables conditional on finding (evidence) on other variables in an independence network.
## S3 method for class 'grain' predict( object, response, predictors = setdiff(names(newdata), response), newdata, type = "class", ... )## S3 method for class 'grain' predict( object, response, predictors = setdiff(names(newdata), response), newdata, type = "class", ... )
object |
A grain object |
response |
A vector of response variables to make predictions on |
predictors |
A vector of predictor variables to make predictions from. Defaults to all variables that are note responses. |
newdata |
A data frame |
type |
If "class", the most probable class is returned; if "distribution" the conditional distribution is returned. |
... |
Not used |
A list with components
pred |
A list with the predictions |
pFinding |
A vector with the probability of the finding (evidence) on which the prediction is based |
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
example("example_chest_cpt") data(chestSim500) chest.bn <- grain(compileCPT(chest_cpt)) nd <- chestSim500[1:4] predict(chest.bn, response="bronc", newdata=nd) predict(chest.bn, response="bronc", newdata=nd, type="distribution")example("example_chest_cpt") data(chestSim500) chest.bn <- grain(compileCPT(chest_cpt)) nd <- chestSim500[1:4] predict(chest.bn, response="bronc", newdata=nd) predict(chest.bn, response="bronc", newdata=nd, type="distribution")
Propagation refers to calibrating the cliques of the junction tree so that the clique potentials are consistent on their intersections; refer to the reference below for details.
## S3 method for class 'grain' propagate(object, details = object$details, engine = "cpp", ...) propagateLS(cq_pot_list, rip, initialize = TRUE, details = 0)## S3 method for class 'grain' propagate(object, details = object$details, engine = "cpp", ...) propagateLS(cq_pot_list, rip, initialize = TRUE, details = 0)
object |
A grain object |
details |
For debugging info |
engine |
Either "R" or "cpp"; "cpp" is the default and the fastest. |
... |
Currently not used |
cq_pot_list |
List of clique potentials |
rip |
A rip ordering |
initialize |
Always true. |
The propagate method invokes propagateLS
which is a pure R implementation of the Lauritzen-Spiegelhalter
algorithm. The c++ based version is several times faster than
the purely R based version.
A compiled and propagated grain object.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
example("grain") ## Uncompiled and unpropageted network: bn0 <- grain(chest_cpt, compile=FALSE) bn0 ## Compiled but unpropageted network: bn1 <- compile(bn0, propagate=FALSE) ## Compiled and propagated network bn2 <- propagate(bn1) bn2 ## Default is that networks are compiled but not propagated at creation time: bn3 <- grain(chest_cpt) bn3example("grain") ## Uncompiled and unpropageted network: bn0 <- grain(chest_cpt, compile=FALSE) bn0 ## Compiled but unpropageted network: bn1 <- compile(bn0, propagate=FALSE) ## Compiled and propagated network bn2 <- propagate(bn1) bn2 ## Default is that networks are compiled but not propagated at creation time: bn3 <- grain(chest_cpt) bn3
Create Bayesian network (grain objects (graphical independence network)).
grain(x, ...) ## S3 method for class 'cpt_spec' grain(x, control = list(), smooth = 0, compile = TRUE, details = 0, ...) ## S3 method for class 'CPTspec' grain(x, control = list(), smooth = 0, compile = TRUE, details = 0, ...) ## S3 method for class 'pot_spec' grain(x, control = list(), smooth = 0, compile = TRUE, details = 0, ...) ## S3 method for class 'igraph' grain( x, control = list(), smooth = 0, compile = TRUE, details = 0, data = NULL, ... ) ## S3 method for class 'dModel' grain( x, control = list(), smooth = 0, compile = TRUE, details = 0, data = NULL, ... )grain(x, ...) ## S3 method for class 'cpt_spec' grain(x, control = list(), smooth = 0, compile = TRUE, details = 0, ...) ## S3 method for class 'CPTspec' grain(x, control = list(), smooth = 0, compile = TRUE, details = 0, ...) ## S3 method for class 'pot_spec' grain(x, control = list(), smooth = 0, compile = TRUE, details = 0, ...) ## S3 method for class 'igraph' grain( x, control = list(), smooth = 0, compile = TRUE, details = 0, data = NULL, ... ) ## S3 method for class 'dModel' grain( x, control = list(), smooth = 0, compile = TRUE, details = 0, data = NULL, ... )
x |
An argument to build an independence network from. Typically a list of conditional probability tables, a DAG or an undirected graph. In the two latter cases, data must also be provided. |
... |
Additional arguments, currently not used. |
control |
A list defining controls, see 'details' below. |
smooth |
A (usually small) number to add to the counts of a table if the grain is built from a graph plus a dataset. |
compile |
Should network be compiled. |
details |
Debugging information. |
data |
An optional data set (currently must be an array/table) |
If 'smooth' is non-zero then entries of 'values' which a zero are replaced by the value of 'smooth' - BEFORE any normalization takes place.
An object of class "grain"
A change from earlier versions of this package is that grain objects are now compiled upon creation.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
cptable, compile.grain,
propagate.grain, setFinding,
setEvidence, getFinding,
pFinding, retractFinding,
extract_cpt, extract_pot,
compileCPT, compilePOT
## Create network from conditional probability tables CPTs: yn <- c("yes", "no") a <- cpt(~asia, values=c(1,99), levels=yn) t.a <- cpt(~tub + asia, values=c(5,95,1,99), levels=yn) s <- cpt(~smoke, values=c(5,5), levels=yn) l.s <- cpt(~lung + smoke, values=c(1,9,1,99), levels=yn) b.s <- cpt(~bronc + smoke, values=c(6,4,3,7), levels=yn) e.lt <- cpt(~either + lung + tub, values=c(1,0,1,0,1,0,0,1), levels=yn) x.e <- cpt(~xray + either, values=c(98,2,5,95), levels=yn) d.be <- cpt(~dysp + bronc + either, values=c(9,1,7,3,8,2,1,9), levels=yn) cpt_list <- list(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) chest_cpt <- compileCPT(cpt_list) ## Alternative: chest_cpt <- compileCPT(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) chest_bn <- grain(chest_cpt) ## Create network from data and graph specification. data(lizard, package="gRbase") ## From a DAG: height <- species -> diam daG <- dag(~species + height:species + diam:species) ## From an undirected graph UG : [height:species][diam:species] uG <- ug(~height:species + diam:species) liz_ug <- grain(uG, data=lizard) liz_dag <- grain(daG, data=lizard)## Create network from conditional probability tables CPTs: yn <- c("yes", "no") a <- cpt(~asia, values=c(1,99), levels=yn) t.a <- cpt(~tub + asia, values=c(5,95,1,99), levels=yn) s <- cpt(~smoke, values=c(5,5), levels=yn) l.s <- cpt(~lung + smoke, values=c(1,9,1,99), levels=yn) b.s <- cpt(~bronc + smoke, values=c(6,4,3,7), levels=yn) e.lt <- cpt(~either + lung + tub, values=c(1,0,1,0,1,0,0,1), levels=yn) x.e <- cpt(~xray + either, values=c(98,2,5,95), levels=yn) d.be <- cpt(~dysp + bronc + either, values=c(9,1,7,3,8,2,1,9), levels=yn) cpt_list <- list(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) chest_cpt <- compileCPT(cpt_list) ## Alternative: chest_cpt <- compileCPT(a, t.a, s, l.s, b.s, e.lt, x.e, d.be) chest_bn <- grain(chest_cpt) ## Create network from data and graph specification. data(lizard, package="gRbase") ## From a DAG: height <- species -> diam daG <- dag(~species + height:species + diam:species) ## From an undirected graph UG : [height:species][diam:species] uG <- ug(~height:species + diam:species) liz_ug <- grain(uG, data=lizard) liz_dag <- grain(daG, data=lizard)
Simulate data from an independence network.
## S3 method for class 'grain' simulate(object, nsim = 1, seed = NULL, ...)## S3 method for class 'grain' simulate(object, nsim = 1, seed = NULL, ...)
object |
An independence network. |
nsim |
Number of cases to simulate. |
seed |
An optional integer controlling the random number generation. |
... |
Not used. |
A data frame
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
tf <- system.file("huginex", "chest_clinic.net", package = "gRain") chest <- loadHuginNet(tf, details=1) simulate(chest,n=10) chest2 <- setFinding(chest, c("VisitToAsia", "Dyspnoea"), c("yes", "yes")) simulate(chest2, n=10)tf <- system.file("huginex", "chest_clinic.net", package = "gRain") chest <- loadHuginNet(tf, details=1) simulate(chest,n=10) chest2 <- setFinding(chest, c("VisitToAsia", "Dyspnoea"), c("yes", "yes")) simulate(chest2, n=10)
These functions can load a net file saved in the 'Hugin format' into R and save a network in R as a file in the 'Hugin format'.
loadHuginNet(file, description = NULL, details = 0) saveHuginNet(gin, file, details = 0)loadHuginNet(file, description = NULL, details = 0) saveHuginNet(gin, file, details = 0)
file |
Name of Hugin net file. Convenient to give the file the extension '.net' |
description |
A text describing the network, defaults to
|
details |
Debugging information. |
gin |
An independence network |
An object of class grain.
In Hugin, it is possible to specify the potential of a node as a
functional relation between other nodes. In a .net file, such a
specification will appear as 'function' rather than as
'node'. Such a specification is not recognized by loadHuginNet.
It is recommended to avoid the text node as part of the name of
a node.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
## Load HUGIN net file tf <- system.file("huginex", "chest_clinic.net", package = "gRain") chest <- loadHuginNet(tf, details=1) chest ## Save a copy td <- tempdir() saveHuginNet(chest, paste(td,"/chest.net",sep='')) ## Load the copy chest2 <- loadHuginNet(paste(td,"/chest.net",sep='')) tf <- system.file("huginex", "golf.net", package = "gRain") golf <- loadHuginNet(tf, details=1) saveHuginNet(golf, paste(td,"/golf.net",sep='')) golf2 <- loadHuginNet(paste(td,"/golf.net",sep=''))## Load HUGIN net file tf <- system.file("huginex", "chest_clinic.net", package = "gRain") chest <- loadHuginNet(tf, details=1) chest ## Save a copy td <- tempdir() saveHuginNet(chest, paste(td,"/chest.net",sep='')) ## Load the copy chest2 <- loadHuginNet(paste(td,"/chest.net",sep='')) tf <- system.file("huginex", "golf.net", package = "gRain") golf <- loadHuginNet(tf, details=1) saveHuginNet(golf, paste(td,"/golf.net",sep='')) golf2 <- loadHuginNet(paste(td,"/golf.net",sep=''))
Generate conditional probability tables based on the logical expressions AND and OR.
booltab(vpa, levels = c(TRUE, FALSE), op = `&`) andtab(vpa, levels = c(TRUE, FALSE)) ortab(vpa, levels = c(TRUE, FALSE)) andtable(vpa, levels = c(TRUE, FALSE)) ortable(vpa, levels = c(TRUE, FALSE))booltab(vpa, levels = c(TRUE, FALSE), op = `&`) andtab(vpa, levels = c(TRUE, FALSE)) ortab(vpa, levels = c(TRUE, FALSE)) andtable(vpa, levels = c(TRUE, FALSE)) ortable(vpa, levels = c(TRUE, FALSE))
vpa |
Node and two parents; as a formula or a character vector. |
levels |
The levels (or rather labels) of v, see 'examples' below. |
op |
A logical operator. |
Regarding the form of the argument vpa: To specify
one may write ~a|b+c or ~a+b+c or
~a|b:c or ~a:b:c or c("a","b","c").
Internally, the last form is used. Notice that the + and
: operator are used as separators only. The order of the
variables is important so + and : DO NOT commute.
An array.
andtable and ortable are aliases for
andtab and ortab and are kept for backward
compatibility.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
## Logical OR: ## A variable v is TRUE if either of its parents pa1 and pa2 are TRUE: ortab( c("v", "pa1", "pa2") ) |> ftable(row.vars="v") ## TRUE and FALSE can be recoded to e.g. yes and no: ortab( c("v", "pa1", "pa2"), levels=c("yes", "no") ) |> ftable(row.vars="v") ## Logical AND: ## Same story here: andtab(c("v", "pa1", "pa2") ) |> ftable(row.vars="v") andtab(c("v", "pa1", "pa2"), levels=c("yes", "no") ) |> ftable(row.vars="v") ## Combined approach booltab(c("v", "pa1", "pa2"), op=`&`) |> ftable(row.vars="v") ## AND booltab(c("v", "pa1", "pa2"), op=`|`) |> ftable(row.vars="v") ## OR booltab(~v + pa1 + pa2, op=`&`) |> ftable(row.vars="v") ## AND booltab(~v + pa1 + pa2, op=`|`) |> ftable(row.vars="v") ## OR## Logical OR: ## A variable v is TRUE if either of its parents pa1 and pa2 are TRUE: ortab( c("v", "pa1", "pa2") ) |> ftable(row.vars="v") ## TRUE and FALSE can be recoded to e.g. yes and no: ortab( c("v", "pa1", "pa2"), levels=c("yes", "no") ) |> ftable(row.vars="v") ## Logical AND: ## Same story here: andtab(c("v", "pa1", "pa2") ) |> ftable(row.vars="v") andtab(c("v", "pa1", "pa2"), levels=c("yes", "no") ) |> ftable(row.vars="v") ## Combined approach booltab(c("v", "pa1", "pa2"), op=`&`) |> ftable(row.vars="v") ## AND booltab(c("v", "pa1", "pa2"), op=`|`) |> ftable(row.vars="v") ## OR booltab(~v + pa1 + pa2, op=`&`) |> ftable(row.vars="v") ## AND booltab(~v + pa1 + pa2, op=`|`) |> ftable(row.vars="v") ## OR
Generate conditional probability table for Mendelian segregation.
mendel(allele, names = c("child", "father", "mother"))mendel(allele, names = c("child", "father", "mother"))
allele |
A character vector. |
names |
Names of columns in dataframe. |
No error checking at all on the input.
## Inheritance of the alleles "y" and "g" men <- mendel(c("y","g"), names=c("ch", "fa", "mo")) men## Inheritance of the alleles "y" and "g" men <- mendel(c("y","g"), names=c("ch", "fa", "mo")) men
Extract list of conditional probability tables and list of clique potentials from data.
extractCPT(data_, graph, smooth = 0) extractPOT(data_, graph, smooth = 0) extractMARG(data_, graph, smooth = 0)extractCPT(data_, graph, smooth = 0) extractPOT(data_, graph, smooth = 0) extractMARG(data_, graph, smooth = 0)
data_ |
A named array or a dataframe. |
graph |
An |
smooth |
See 'details' below. |
If smooth is non-zero then smooth is added
to all cell counts before normalization takes place.
extract_cpt: A list of conditional probability tables.
extract_pot: A list of clique potentials.
extract_marg: A list of clique marginals.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
## Extract cpts / clique potentials from data and graph # specification and create network. There are different ways: data(lizard, package="gRbase") # DAG: height <- species -> diam daG <- dag(~species + height:species + diam:species, result="igraph") # UG : [height:species][diam:species] uG <- ug(~height:species + diam:species, result="igraph") pt <- extract_pot(lizard, ~height:species + diam:species) cp <- extract_cpt(lizard, ~species + height:species + diam:species) pt cp # Both specify the same probability distribution tabListMult(pt) |> as.data.frame.table() tabListMult(cp) |> as.data.frame.table() ## Not run: # Bayesian networks can be created as bn.uG <- grain(pt) bn.daG <- grain(cp) # The steps above are wrapped into a convenience method which # builds a network from at graph and data. bn.uG <- grain(uG, data=lizard) bn.daG <- grain(daG, data=lizard) ## End(Not run)## Extract cpts / clique potentials from data and graph # specification and create network. There are different ways: data(lizard, package="gRbase") # DAG: height <- species -> diam daG <- dag(~species + height:species + diam:species, result="igraph") # UG : [height:species][diam:species] uG <- ug(~height:species + diam:species, result="igraph") pt <- extract_pot(lizard, ~height:species + diam:species) cp <- extract_cpt(lizard, ~species + height:species + diam:species) pt cp # Both specify the same probability distribution tabListMult(pt) |> as.data.frame.table() tabListMult(cp) |> as.data.frame.table() ## Not run: # Bayesian networks can be created as bn.uG <- grain(pt) bn.daG <- grain(cp) # The steps above are wrapped into a convenience method which # builds a network from at graph and data. bn.uG <- grain(uG, data=lizard) bn.daG <- grain(daG, data=lizard) ## End(Not run)
Set, update and remove evidence.
setEvidence( object, nodes = NULL, states = NULL, evidence = NULL, propagate = TRUE, details = 0 ) retractEvidence(object, nodes = NULL, propagate = TRUE) absorbEvidence(object, propagate = TRUE) getEvidence(object, short = TRUE) pEvidence(object, evidence = NULL)setEvidence( object, nodes = NULL, states = NULL, evidence = NULL, propagate = TRUE, details = 0 ) retractEvidence(object, nodes = NULL, propagate = TRUE) absorbEvidence(object, propagate = TRUE) getEvidence(object, short = TRUE) pEvidence(object, evidence = NULL)
object |
A "grain" object |
nodes |
A vector of nodes. |
states |
A vector of states (of the nodes given by 'nodes'). Now deprecated; use argument 'evidence' instead. |
evidence |
A list of name=value. See examples below. |
propagate |
Should the network be propagated? |
details |
Debugging information |
short |
If TRUE a dataframe with a summary is returned; otherwise a list with all details. |
A list of tables with potentials.
setEvidence() is an improvement of setFinding()
(and as such setFinding is obsolete). Users are
recommended to use setEvidence() in the future.
setEvidence() allows to specification of "hard evidence" (specific
values for variables) and likelihood evidence (also known as virtual
evidence) for variables.
The syntax of setEvidence() may change in the future.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
setFinding, getFinding,
retractFinding, pFinding
example("grain") chest_bn <- grain(compileCPT(chest_cpt)) bn2 <- chest_bn |> evidence_add(list(asia="yes", xray="yes")) bn3 <- chest_bn |> evidence_add(list(asia=c(0.8, 0.1), xray="yes")) bn2 |> evidence_get() bn3 |> evidence_get() bn2 |> evidence_prob() bn3 |> evidence_prob() bn2 |> evidence_drop("xray") bn3 |> evidence_drop("xray") bn2 |> evidence_drop("xray") |> evidence_get() bn3 |> evidence_drop("xray") |> evidence_get() ## For backward compatibility these functions are available now but # may be deprecated later. bb2 <- setEvidence(chest_bn, c("asia", "xray"), c("yes", "yes")) bb3 <- setEvidence(chest_bn, c("asia", "xray"), list(c(0.8, 0.2), "yes")) bb4 <- setFinding(chest_bn, c("asia", "xray"), c("yes", "yes")) bb2 |> getEvidence() bb3 |> getEvidence() bb2 |> retractEvidence("xray") bb3 |> retractEvidence("xray") bb2 |> pEvidence() bb3 |> pEvidence() bb2 |> retractEvidence("xray") |> getEvidence() bb3 |> retractEvidence("xray") |> getEvidence()example("grain") chest_bn <- grain(compileCPT(chest_cpt)) bn2 <- chest_bn |> evidence_add(list(asia="yes", xray="yes")) bn3 <- chest_bn |> evidence_add(list(asia=c(0.8, 0.1), xray="yes")) bn2 |> evidence_get() bn3 |> evidence_get() bn2 |> evidence_prob() bn3 |> evidence_prob() bn2 |> evidence_drop("xray") bn3 |> evidence_drop("xray") bn2 |> evidence_drop("xray") |> evidence_get() bn3 |> evidence_drop("xray") |> evidence_get() ## For backward compatibility these functions are available now but # may be deprecated later. bb2 <- setEvidence(chest_bn, c("asia", "xray"), c("yes", "yes")) bb3 <- setEvidence(chest_bn, c("asia", "xray"), list(c(0.8, 0.2), "yes")) bb4 <- setFinding(chest_bn, c("asia", "xray"), c("yes", "yes")) bb2 |> getEvidence() bb3 |> getEvidence() bb2 |> retractEvidence("xray") bb3 |> retractEvidence("xray") bb2 |> pEvidence() bb3 |> pEvidence() bb2 |> retractEvidence("xray") |> getEvidence() bb3 |> retractEvidence("xray") |> getEvidence()
Replace CPTs of Bayesian network.
replaceCPT(object, value)replaceCPT(object, value)
object |
A |
value |
A named list, see examples below. |
When a Bayesian network (BN) is constructed from a list of
conditional probability tables (CPTs) (e.g. using the function
grain()), various actions are taken:
It is checked that the list of CPTs define a directed acyclic graph (DAG).
The DAG is moralized and triangulated.
A list of clique potentials (one for each clique in the triangulated graph) is created from the list of CPTs.
The clique potentials are, by default, calibrated to each other so that the potentials contain marginal distributions.
The function described here bypass the first two steps which can provide an important gain in speed compared to constructing a new BN with a new set of CPTs with the same DAG.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
grain, propagate,
triangulate, rip,
junctionTree
## See the wet grass example at ## https://en.wikipedia.org/wiki/Bayesian_network yn <- c("yes", "no") p.R <- cptable(~R, values=c(.2, .8), levels=yn) p.S_R <- cptable(~S:R, values=c(.01, .99, .4, .6), levels=yn) p.G_SR <- cptable(~G:S:R, values=c(.99, .01, .8, .2, .9, .1, 0, 1), levels=yn) wet.bn <- compileCPT(p.R, p.S_R, p.G_SR) |> grain() getgrain(wet.bn, "cpt")[c("R","S")] # Update some CPTs wet.bn <- replace_cpt(wet.bn, list(R=c(.3, .7), S=c(.1, .9, .7, .3))) getgrain(wet.bn, "cpt")[c("R","S")]## See the wet grass example at ## https://en.wikipedia.org/wiki/Bayesian_network yn <- c("yes", "no") p.R <- cptable(~R, values=c(.2, .8), levels=yn) p.S_R <- cptable(~S:R, values=c(.01, .99, .4, .6), levels=yn) p.G_SR <- cptable(~G:S:R, values=c(.99, .01, .8, .2, .9, .1, 0, 1), levels=yn) wet.bn <- compileCPT(p.R, p.S_R, p.G_SR) |> grain() getgrain(wet.bn, "cpt")[c("R","S")] # Update some CPTs wet.bn <- replace_cpt(wet.bn, list(R=c(.3, .7), S=c(.1, .9, .7, .3))) getgrain(wet.bn, "cpt")[c("R","S")]
Query an independence network, i.e. obtain the conditional distribution of a set of variables - possibly (and typically) given finding (evidence) on other variables.
querygrain( object, nodes = nodeNames(object), type = "marginal", evidence = NULL, exclude = TRUE, normalize = TRUE, simplify = FALSE, result = "array", details = 0 )querygrain( object, nodes = nodeNames(object), type = "marginal", evidence = NULL, exclude = TRUE, normalize = TRUE, simplify = FALSE, result = "array", details = 0 )
object |
A |
nodes |
A vector of nodes; those nodes for which the (conditional) distribution is requested. |
type |
Valid choices are |
evidence |
An alternative way of specifying findings (evidence), see examples below. |
exclude |
If |
normalize |
Should the results be normalized to sum to one. |
simplify |
Should the result be simplified (to a dataframe) if possible. |
result |
If "data.frame" the result is returned as a data frame (or possibly as a list of dataframes). |
details |
Debugging information |
A list of tables with potentials.
setEvidence() is an improvement of setFinding()
(and as such setFinding is obsolete). Users are
recommended to use setEvidence() in the future.
setEvidence() allows to specification of "hard evidence" (specific
values for variables) and likelihood evidence (also known as virtual
evidence) for variables.
The syntax of setEvidence() may change in the future.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
setEvidence, getEvidence,
retractEvidence, pEvidence
testfile <- system.file("huginex", "chest_clinic.net", package = "gRain") chest <- loadHuginNet(testfile, details=0) qb <- querygrain(chest) qb lapply(qb, as.numeric) # Safe sapply(qb, as.numeric) # Riskytestfile <- system.file("huginex", "chest_clinic.net", package = "gRain") chest <- loadHuginNet(testfile, details=0) qb <- querygrain(chest) qb lapply(qb, as.numeric) # Safe sapply(qb, as.numeric) # Risky
Repeated patterns is a useful model specification short cut for Bayesian networks
repeat_pattern(plist, instances, unlist = TRUE, data = NULL)repeat_pattern(plist, instances, unlist = TRUE, data = NULL)
plist |
A list of conditional probability tables. The variable
names must have the form |
instances |
A vector of consecutive integers |
unlist |
If |
data |
A two column matrix. The first column is the index / name of a node; the second column is the index / name of the node's parent. |
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
yn <- c("yes", "no") n <- 3 ## Example: Markov chain x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) pat <- list(x_trans) rep.pat <- repeat_pattern(pat, instances=1:n) mc <- compile_cpt(c(list(x_init), rep.pat)) mc mc <- mc |> grain() ## Example: Hidden markov model: # The x[i]'s are unobserved, the y[i]'s can be observed. x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) y_emis <- cpt(~y[i]|x[i], values=c(10, 90, 20, 80), levels=yn) ## p(y[i]|x[i]) pat <- list(x_trans, y_emis) ## Pattern to be repeated rep.pat <- repeat_pattern(pat, instances=1:n) hmm <- compile_cpt(c(list(x_init), rep.pat)) hmm hmm <- hmm |> grain() ## Data-driven variable names dep <- data.frame(i=c(1, 2, 3, 4, 5, 6, 7, 8), p=c(0, 1, 2, 2, 3, 3, 4, 4)) x0 <- cpt(~x0, values=c(0.5, 0.5), levels=yn) xa <- cpt(~x[i] | x[data[i, "p"]], values=c(1, 9, 2, 8), levels=yn) xb <- repeat_pattern(list(xa), instances=1:nrow(dep), data=dep) tree <- compile_cpt(c(list(x0), xb)) tree tree <- tree |> grain() treeyn <- c("yes", "no") n <- 3 ## Example: Markov chain x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) pat <- list(x_trans) rep.pat <- repeat_pattern(pat, instances=1:n) mc <- compile_cpt(c(list(x_init), rep.pat)) mc mc <- mc |> grain() ## Example: Hidden markov model: # The x[i]'s are unobserved, the y[i]'s can be observed. x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) y_emis <- cpt(~y[i]|x[i], values=c(10, 90, 20, 80), levels=yn) ## p(y[i]|x[i]) pat <- list(x_trans, y_emis) ## Pattern to be repeated rep.pat <- repeat_pattern(pat, instances=1:n) hmm <- compile_cpt(c(list(x_init), rep.pat)) hmm hmm <- hmm |> grain() ## Data-driven variable names dep <- data.frame(i=c(1, 2, 3, 4, 5, 6, 7, 8), p=c(0, 1, 2, 2, 3, 3, 4, 4)) x0 <- cpt(~x0, values=c(0.5, 0.5), levels=yn) xa <- cpt(~x[i] | x[data[i, "p"]], values=c(1, 9, 2, 8), levels=yn) xb <- repeat_pattern(list(xa), instances=1:nrow(dep), data=dep) tree <- compile_cpt(c(list(x0), xb)) tree tree <- tree |> grain() tree
Repeated patterns is a useful model specification short cut for Bayesian networks
repeatPattern(plist, instances, unlist = TRUE, data = NULL)repeatPattern(plist, instances, unlist = TRUE, data = NULL)
plist |
A list of conditional probability tables. The variable
names must have the form |
instances |
A vector of consecutive integers |
unlist |
If |
data |
A two column matrix. The first column is the index / name of a node; the second column is the index / name of the node's parent. |
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
yn <- c("yes", "no") n <- 3 ## Example: Markov chain x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) pat <- list(x_trans) rep.pat <- repeat_pattern(pat, instances=1:n) mc <- compile_cpt(c(list(x_init), rep.pat)) mc mc <- mc |> grain() ## Example: Hidden markov model: # The x[i]'s are unobserved, the y[i]'s can be observed. x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) y_emis <- cpt(~y[i]|x[i], values=c(10, 90, 20, 80), levels=yn) ## p(y[i]|x[i]) pat <- list(x_trans, y_emis) ## Pattern to be repeated rep.pat <- repeat_pattern(pat, instances=1:n) hmm <- compile_cpt(c(list(x_init), rep.pat)) hmm hmm <- hmm |> grain() ## Data-driven variable names dep <- data.frame(i=c(1, 2, 3, 4, 5, 6, 7, 8), p=c(0, 1, 2, 2, 3, 3, 4, 4)) x0 <- cpt(~x0, values=c(0.5, 0.5), levels=yn) xa <- cpt(~x[i] | x[data[i, "p"]], values=c(1, 9, 2, 8), levels=yn) xb <- repeat_pattern(list(xa), instances=1:nrow(dep), data=dep) tree <- compile_cpt(c(list(x0), xb)) tree tree <- tree |> grain() treeyn <- c("yes", "no") n <- 3 ## Example: Markov chain x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) pat <- list(x_trans) rep.pat <- repeat_pattern(pat, instances=1:n) mc <- compile_cpt(c(list(x_init), rep.pat)) mc mc <- mc |> grain() ## Example: Hidden markov model: # The x[i]'s are unobserved, the y[i]'s can be observed. x_init <- cpt(~x0, values=c(1, 9), levels=yn) ## p(x0) x_trans <- cpt(~x[i]|x[i-1], values=c(1, 99, 2, 98), levels=yn) ## p(x[i]|x[i-1]) y_emis <- cpt(~y[i]|x[i], values=c(10, 90, 20, 80), levels=yn) ## p(y[i]|x[i]) pat <- list(x_trans, y_emis) ## Pattern to be repeated rep.pat <- repeat_pattern(pat, instances=1:n) hmm <- compile_cpt(c(list(x_init), rep.pat)) hmm hmm <- hmm |> grain() ## Data-driven variable names dep <- data.frame(i=c(1, 2, 3, 4, 5, 6, 7, 8), p=c(0, 1, 2, 2, 3, 3, 4, 4)) x0 <- cpt(~x0, values=c(0.5, 0.5), levels=yn) xa <- cpt(~x[i] | x[data[i, "p"]], values=c(1, 9, 2, 8), levels=yn) xb <- repeat_pattern(list(xa), instances=1:nrow(dep), data=dep) tree <- compile_cpt(c(list(x0), xb)) tree tree <- tree |> grain() tree
Replace CPTs of Bayesian network.
replace_cpt(object, value) ## S3 method for class 'cpt_grain' replace_cpt(object, value)replace_cpt(object, value) ## S3 method for class 'cpt_grain' replace_cpt(object, value)
object |
A |
value |
A named list, see examples below. |
When a Bayesian network (BN) is constructed from a list of
conditional probability tables (CPTs) (e.g. using the function
grain()), various actions are taken:
It is checked that the list of CPTs define a directed acyclic graph (DAG).
The DAG is moralized and triangulated.
A list of clique potentials (one for each clique in the triangulated graph) is created from the list of CPTs.
The clique potentials are, by default, calibrated to each other so that the potentials contain marginal distributions.
The function described here bypass the first two steps which can provide an important gain in speed compared to constructing a new BN with a new set of CPTs with the same DAG.
Søren Højsgaard, [email protected]
Søren Højsgaard (2012). Graphical Independence Networks with the gRain Package for R. Journal of Statistical Software, 46(10), 1-26. https://www.jstatsoft.org/v46/i10/.
grain, propagate,
triangulate, rip,
junctionTree
## See the wet grass example at ## https://en.wikipedia.org/wiki/Bayesian_network yn <- c("yes", "no") p.R <- cptable(~R, values=c(.2, .8), levels=yn) p.S_R <- cptable(~S:R, values=c(.01, .99, .4, .6), levels=yn) p.G_SR <- cptable(~G:S:R, values=c(.99, .01, .8, .2, .9, .1, 0, 1), levels=yn) wet.bn <- compileCPT(p.R, p.S_R, p.G_SR) |> grain() getgrain(wet.bn, "cpt")[c("R","S")] # Update some CPTs wet.bn <- replace_cpt(wet.bn, list(R=c(.3, .7), S=c(.1, .9, .7, .3))) getgrain(wet.bn, "cpt")[c("R","S")]## See the wet grass example at ## https://en.wikipedia.org/wiki/Bayesian_network yn <- c("yes", "no") p.R <- cptable(~R, values=c(.2, .8), levels=yn) p.S_R <- cptable(~S:R, values=c(.01, .99, .4, .6), levels=yn) p.G_SR <- cptable(~G:S:R, values=c(.99, .01, .8, .2, .9, .1, 0, 1), levels=yn) wet.bn <- compileCPT(p.R, p.S_R, p.G_SR) |> grain() getgrain(wet.bn, "cpt")[c("R","S")] # Update some CPTs wet.bn <- replace_cpt(wet.bn, list(R=c(.3, .7), S=c(.1, .9, .7, .3))) getgrain(wet.bn, "cpt")[c("R","S")]
Simplify output query to a Bayesian network to a dataframe provided that each node has the same levels.
simplify_query(b)simplify_query(b)
b |
Result from running querygrain. |