Compile conditional probability tables / cliques potentials.

Description

Compile conditional probability tables / cliques potentials as a preprocessing step for creating a graphical independence network

Usage

compileCPT(x, ..., forceCheck = TRUE)

compilePOT(x, ..., forceCheck = TRUE)

Arguments

Details

* `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.

Value

A list with a class attribute.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

extract_cpt, extract_pot, extract_marg

Examples

example("example_chest_cpt")
x <- compile_cpt(chest_cpt)
class(x)
grain(x)

Extract conditional probabilities and clique potentials from data.

Description

Extract list of conditional probability tables and list of clique potentials from data.

Usage

extract_cpt(data_, graph, smooth = 0)

extract_pot(data_, graph, smooth = 0)

extract_marg(data_, graph, smooth = 0)

marg2pot(marg_rep)

pot2marg(pot_rep)

Arguments

Details

If smooth is non-zero then smooth is added to all cell counts before normalization takes place.

Value

• extract_cpt: A list of conditional probability tables.

• extract_pot: A list of clique potentials.

• extract_marg: A list of clique marginals.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

compileCPT, compilePOT, grain

Examples

## 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.

Description

Compile conditional probability tables / cliques potentials as a preprocessing step for creating a graphical independence network

Usage

compile_cpt(x, ..., forceCheck = TRUE)

compile_pot(x, ..., forceCheck = TRUE)

parse_cpt(xi)

Arguments

Details

* `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.

Value

A list with a class attribute.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

extract_cpt, extract_pot, extract_marg

Examples

example("example_chest_cpt")
x <- compile_cpt(chest_cpt)
class(x)
grain(x)

Create conditional probability tables (CPTs)

Description

Creates conditional probability tables of the form p(v|pa(v)).

Usage

cpt(names, levels, values, normalize = "first", smooth = 0)

cptable(vpar, levels = NULL, values = NULL, normalize = TRUE, smooth = 0)

Arguments

Details

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 P(a|b,c) 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.

Value

An array.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

andtable, ortable, extract_cpt, compileCPT, extract_cpt, compilePOT, grain

Examples

## 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)

Chest clinic example

Description

Conditional probability tables for the chest clinic example.

Examples

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))

Wet grass example

Description

Conditional probability tables for the wet grass example.

Examples

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.

Description

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.

Usage

setFinding(object, nodes = NULL, states = NULL, flist = NULL, propagate = TRUE)

Arguments

Note

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.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

setEvidence, getEvidence, retractEvidence, pEvidence, querygrain

Examples

## 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)

gRain generics

Description

Generic functions etc for the gRain package

Usage

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, ...)

Arguments

Create Bayesian network

Description

Create Bayesian network (grain objects (graphical independence network)).

Usage

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,
  ...
)

Arguments

Details

If 'smooth' is non-zero then entries of 'values' which a zero are replaced by the value of 'smooth' - BEFORE any normalization takes place.

Value

An object of class "grain"

Note

A change from earlier versions of this package is that grain objects are now compiled upon creation.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

cptable, compile.grain, propagate.grain, setFinding, setEvidence, getFinding, pFinding, retractFinding, extract_cpt, extract_pot, compileCPT, compilePOT

Examples

## 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 from Bayesian network

Description

Simulate data from an independence network.

Usage

## S3 method for class 'grain'
simulate(object, nsim = 1, seed = NULL, ...)

Arguments

Value

A data frame

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

Examples

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)

Compile Bayesian network.

Description

Compiles a Bayesian network. This means creating a junction tree and establishing clique potentials.

Usage

## S3 method for class 'grain'
compile(
  object,
  propagate = FALSE,
  tug = NULL,
  root = NULL,
  control = object$control,
  details = 0,
  ...
)

Arguments

Value

A compiled Bayesian network; an object of class grain.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain, propagate, propagate.grain, triangulate, rip, junctionTree

Set, update and remove evidence.

Description

Set, update and remove evidence.

Usage

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)

Arguments

Value

A list of tables with potentials.

Note

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.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

setFinding, getFinding, retractFinding, pFinding

Examples

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()

Make predictions from Bayesian network

Description

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.

Usage

## S3 method for class 'grain'
predict(
  object,
  response,
  predictors = setdiff(names(newdata), response),
  newdata,
  type = "class",
  ...
)

Arguments

Value

A list with components

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain

Examples

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")

Propagate in a Bayesian network

Description

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.

Usage

## S3 method for class 'grain'
propagate(object, details = object$details, engine = "cpp", ...)

propagateLS(cq_pot_list, rip, initialize = TRUE, details = 0)

Arguments

Details

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.

Value

A compiled and propagated grain object.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain, compile

Examples

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) 
bn3 

Internal functions for the gRain package

Description

These functions should not be called directly by the user

Load and save Hugin net files

Description

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'.

Usage

loadHuginNet(file, description = NULL, details = 0)

saveHuginNet(gin, file, details = 0)

Arguments

Value

An object of class grain.

Note

• 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.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain

Examples

## 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=''))

Conditional probability tables based on logical dependencies

Description

Generate conditional probability tables based on the logical expressions AND and OR.

Usage

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))

Arguments

Details

Regarding the form of the argument vpa: To specify P(a|b,c) 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.

Value

An array.

Note

andtable and ortable are aliases for andtab and ortab and are kept for backward compatibility.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

cptable

Examples

## 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

Mendelian segregation

Description

Generate conditional probability table for Mendelian segregation.

Usage

mendel(allele, names = c("child", "father", "mother"))

Arguments

Note

No error checking at all on the input.

Examples

## Inheritance of the alleles "y" and "g"

men <- mendel(c("y","g"), names=c("ch", "fa", "mo"))
men

Extract conditional probabilities and clique potentials from data.

Description

Extract list of conditional probability tables and list of clique potentials from data.

Usage

extractCPT(data_, graph, smooth = 0)

extractPOT(data_, graph, smooth = 0)

extractMARG(data_, graph, smooth = 0)

Arguments

Details

If smooth is non-zero then smooth is added to all cell counts before normalization takes place.

Value

• extract_cpt: A list of conditional probability tables.

• extract_pot: A list of clique potentials.

• extract_marg: A list of clique marginals.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

compileCPT, compilePOT, grain

Examples

## 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.

Description

Set, update and remove evidence.

Usage

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)

Arguments

Value

A list of tables with potentials.

Note

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.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

setFinding, getFinding, retractFinding, pFinding

Examples

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 in Bayesian network

Description

Replace CPTs of Bayesian network.

Usage

replaceCPT(object, value)

Arguments

Details

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:

1. It is checked that the list of CPTs define a directed acyclic graph (DAG).

2. The DAG is moralized and triangulated.

3. A list of clique potentials (one for each clique in the triangulated graph) is created from the list of CPTs.

4. 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.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain, propagate, triangulate, rip, junctionTree

Examples

## 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 a Bayesian network

Description

Query an independence network, i.e. obtain the conditional distribution of a set of variables - possibly (and typically) given finding (evidence) on other variables.

Usage

querygrain(
  object,
  nodes = nodeNames(object),
  type = "marginal",
  evidence = NULL,
  exclude = TRUE,
  normalize = TRUE,
  simplify = FALSE,
  result = "array",
  details = 0
)

Arguments

Value

A list of tables with potentials.

Note

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.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

setEvidence, getEvidence, retractEvidence, pEvidence

Examples

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) # Risky

Create repeated patterns in Bayesian networks

Description

Repeated patterns is a useful model specification short cut for Bayesian networks

Usage

repeatPattern(plist, instances, unlist = TRUE, data = NULL)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain, compile_cpt

Examples

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()
tree 

Create repeated patterns in Bayesian networks

Description

Repeated patterns is a useful model specification short cut for Bayesian networks

Usage

repeat_pattern(plist, instances, unlist = TRUE, data = NULL)

Arguments

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain, compile_cpt

Examples

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()
tree 

Replace CPTs in Bayesian network

Description

Replace CPTs of Bayesian network.

Usage

replace_cpt(object, value)

## S3 method for class 'cpt_grain'
replace_cpt(object, value)

Arguments

Details

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:

1. It is checked that the list of CPTs define a directed acyclic graph (DAG).

2. The DAG is moralized and triangulated.

3. A list of clique potentials (one for each clique in the triangulated graph) is created from the list of CPTs.

4. 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.

Author(s)

Søren Højsgaard, sorenh@math.aau.dk

References

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/.

See Also

grain, propagate, triangulate, rip, junctionTree

Examples

## 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

Description

Simplify output query to a Bayesian network to a dataframe provided that each node has the same levels.

Usage

simplify_query(b)

Arguments