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ess: Eficient Stepwise Selection in Decomposable Models

Description

The class of graphical models is a family of probabilitydistributions for which conditional dependencies can be read offfrom a graph. If the graph is decomposable, the maximumlikelihood estimates of the parameters in the model can be shownto be on exact form. This is what enables ESS to be fast andefficient for model selection in decomposable graphical models.

Author(s)

Maintainer: Mads Lindskoumads@math.aau.dk

See Also

Useful links:

• https://github.com/mlindsk/ess

• Report bugs athttps://github.com/mlindsk/ess/issues

Adjacency List

Description

Extracts the adjacency list of agengraph

Usage

adj_lst(x)## S3 method for class 'gengraph'adj_lst(x)

Arguments

Value

An adjacency list

Adjacency Matrix

Description

Extracts the adjacency matrix of agengraph object

Usage

adj_mat(x)## S3 method for class 'gengraph'adj_mat(x)

Arguments

Value

An adjacency matrix

Converts an adjacency matrix to an adjacency list

Description

Converts an adjacency matrix to an adjacency list

Usage

as_adj_lst(A)

Arguments

Converts an adjacency list to an adjacency matrix

Description

Converts an adjacency list to an adjacency matrix

Usage

as_adj_mat(adj)

Arguments

Value

An adjacency matrix

Examples

adj <- list(a = c("b", "d"), b = c("a", "c", "d"), c = c("b", "d"), d = c("a", "c", "b"))as_adj_mat(adj)

Gengraph as igraph

Description

Convert agengraph object to anigraph object

Usage

as_igraph(x)## S3 method for class 'gengraph'as_igraph(x)

Arguments

Value

Anigraph object

Finds the components of a graph

Description

Finds the components of a graph

Usage

components(adj)

Arguments

Value

A list where the elements are the components of the graph

Dermatology Database

Description

This data set contains 358 observations (we have removed 8 with missing values).It contains 12 clinical attributes and 21 histopathological attributes. The ageattribute has been discretized. The class variable "ES" has six levels; eachdescribing a skin disease.

Usage

derma

Format

An object of classtbl_df (inherits fromtbl,data.frame) with 358 rows and 35 columns.

References

Dermatology Data Set

Depth First Search

Description

Finds the elements in the component ofroot

Usage

dfs(adj, root)

Arguments

Value

All nodes connected toroot

Examples

x <- list(a = c("b", "d"), b = c("a", "d"), c = c("b", "a"),          d = c("e", "f"), e = c("d", "f"), f = c("d", "e"))dfs(x, "a")

Simulate observations from a decomposable graphical model

Description

Simulate observations from a decomposable graphical model

Usage

dgm_sim_from_graph(g, lvls, nsim = 1000, cell_rate = 0.5)

Arguments

Value

This function returns a matrix of dimension where each row correspondto a simulated observation from a DGM represented byg.

Examples

g = list(  A = c("B", "X", "Y"),  B = c("A", "Y"),  X = c("A", "Y"),  Y = c("A", "X", "B"))lvls <- list(  A = c("0", "1"),  B = c("0", "1"),  X = c("a", "b", "c"),  Y = c("0", "1", "2"))dgm_sim_from_graph(g, lvls, nsim = 10)#'

Joint Entropy

Description

Calculates the joint entropy over discrete variables indf

Usage

entropy(df, thres = 5, npc = new.env())

Arguments

Value

A number representing the entropy of the variables indf.

Examples

entropy(derma[1:100, 1:3])

Fit a decomposable graphical model on each component

Description

Structure learning in decomposable graphical models onseveral components

Usage

fit_components(  df,  comp,  type = "fwd",  q = 0.5,  trace = FALSE,  thres = 5,  wrap = TRUE)

Arguments

Value

An adjacency list object

See Also

fit_graph,adj_lst.gengraph,adj_mat.gengraph,walk.fwd,walk.bwd,gengraph

Fit a decomposable graphical model

Description

A generic method for structure learning in decomposablegraphical models

Usage

fit_graph(  df,  type = "fwd",  q = 0.5,  trace = FALSE,  sparse_qic = FALSE,  thres = 5,  wrap = TRUE)

Arguments

Details

The types are

• "fwd": forward selection

• "bwd": backward selection

• "tree": Chow-Liu tree (first order interactions only)

• "tfwd": A combination of "tree" and "fwd". This can speed up runtime considerably in high dimensions.

Usingadj_lst on an object returned byfit_graph gives theadjacency list corresponding to the graph. Similarly one can useadj_matto obtain an adjacency matrix. Applying therip function on anadjacency list returns the cliques and separators of the graph.

Value

Agengraph object representing a decomposable graph.

References

https://arxiv.org/abs/1301.2267, doi:10.1109/ictai.2004.100

See Also

adj_lst,adj_mat,as_igraph,gengraph

Examples

g <- fit_graph(derma)print(g)plot(g)# Adjacency matrix and adjacency listadjm <- adj_mat(g)adjl <- adj_lst(g)

A generic and extendable structure for decomposable graphical models

Description

A generic structure for decomposable graphical models

Usage

gengraph(df, type = "fwd", q = 0.5, sparse_qic = TRUE)

Arguments

Value

Agengraph object with child classtype used for model selection.

See Also

adj_lst.gengraph,adj_mat.gengraph,fit_graph,walk.fwd,walk.bwd

Examples

gengraph(derma, type = "fwd")gengraph(derma, type = "bwd")

A test for decomposability in undirected graphs

Description

This function returnsTRUE if the graph is decomposable andFALSE otherwise

Usage

is_decomposable(adj)

Arguments

Value

Logial describing whether or notadj is decomposable

Examples

# 4-cycle:adj <- list(a = c("b", "d"), b = c("a", "c"), c = c("b", "d"), d = c("a", "c"))is_decomposable(adj) # FALSE# Two triangles:adj2 <- list(a = c("b", "d"), b = c("a", "c", "d"), c = c("b", "d"), d = c("a", "c", "b"))is_decomposable(adj2) # TRUE

Make a complete graph

Description

A helper function to make an adjacency list corresponding to a complete graph

Usage

make_complete_graph(nodes)

Arguments

Value

An adjacency list of a complete graph

Examples

d  <- derma[, 5:8]cg <- make_complete_graph(colnames(d))

Make a null graph

Description

A helper function to make an adjacency list corresponding to a null graph (no edges)

Usage

make_null_graph(nodes)

Arguments

Value

An adjacency list the null graph with no edges

Examples

d  <- derma[, 5:8]ng <- make_null_graph(colnames(d))

Maximum Cardinality Search

Description

Maximum Cardinality Search

Usage

mcs(adj, check = TRUE)

Arguments

Details

If adj is not the adjacency list of a decomposable graph an error is raised

Value

A list with a perfect numbering of the nodes and a perfect sequence of sets

Examples

x <- list(a = c("b", "d"), b = c("a", "c", "d"), c = c("b", "d"), d = c("a", "c", "b"))mcs(x)

Plot

Description

A wrapper around igraphs plot method forgengraph objects

Usage

## S3 method for class 'gengraph'plot(x, vc = NULL, ...)

Arguments

Value

No return value, called for side effects

Examples

d <- derma[, 10:25]g <- fit_graph(d)vs <- colnames(d)vcol <- structure(vector("character", length(vs)), names = vs)vcol[1:4]  <- "lightsteelblue2"vcol[5:7]  <- "orange"vcol[8:16] <- "pink"plot(g, vcol)

Print

Description

A print method forgengraph objects

Usage

## S3 method for class 'gengraph'print(x, ...)

Arguments

Print

Description

A print method fortree objects

Usage

## S3 method for class 'tree'print(x, ...)

Arguments

Runnining Intersection Property

Description

Given a decomposable graph, this functions finds a perfect numbering on the vertices using maximum cardinality search, and hereafter returns a list with two elements: "C" - A RIP-ordering of the cliques and "S" - A RIP ordering of the separators.

Usage

rip(adj, check = TRUE)

Arguments

Value

A list with cliques and separators ofadj

See Also

mcs,is_decomposable

Examples

x <- list(a = c("b", "d"), b = c("a", "c", "d"), c = c("b", "d"), d = c("a", "c", "b"))y <- rip(x)# Cliques:y$C# Separators:y$S

Subgraph

Description

Construct a subgraph with a given set of nodes removed

Usage

subgraph(x, g)

Arguments

Value

An adjacency list or adjacency matrix.

Examples

adj <- list(a = c("b", "d"), b = c("a", "c", "d"), c = c("b", "d"), d = c("a", "c", "b"))d <- data.frame(a = "", b = "", c ="", d = "") # Toy data so we can plot the graphsubgraph(c("c", "b"), adj)subgraph(c("b", "d"), as_adj_mat(adj))

Stepwise model selection

Description

Stepwise model selection in decomposable graphical models

Usage

walk(x, df, q, thres)

Arguments

Details

Afwd (orbwd) object can be created using thegengraph constructor withtype = "fwd".

Value

Afwd orbwd object with one additional edge than the input object.

See Also

fit_graph,walk.fwd,gengraph

Examples

d <- derma[, 10:25]g <- gengraph(d, type = "fwd")s <- walk(g, d)print(s)plot(s)adj_lst(s)adj_mat(s)

Stepwise backward selection

Description

Stepwise backward selection in decomposable graphical models

Usage

## S3 method for class 'bwd'walk(x, df, q = 0.5, thres = 5)

Arguments

Details

Abwd object can be created using thegengraph constructor withtype = "bwd"

Value

Abwd object; a subclass ofgengraph) used for backward selection.

See Also

fit_graph,walk.fwd,gengraph

Examples

d <- derma[, 10:25]g <- gengraph(d, type = "bwd")s <- walk(g, d)print(s)plot(s)adj_lst(s)adj_mat(s)

Stepwise efficient forward selection in decomposable graphical models

Description

Stepwise efficient forward selection in decomposable graphical models

Usage

## S3 method for class 'fwd'walk(x, df, q = 0.5, thres = 5)

Arguments

Details

Afwd object can be created using thegengraph constructor withtype = "fwd"

Value

Afwd object; a subclass ofgengraph) used for forward selection.

References

https://arxiv.org/abs/1301.2267, doi:10.1109/ictai.2004.100

See Also

fit_graph,walk.bwd,gengraph

Examples

d <- derma[, 10:25]g <- gengraph(d, type = "fwd")s <- walk(g, d)print(s)plot(s)adj_lst(s)adj_mat(s)