Package 'SBMSplitMerge' reference manual

Title:	Inference for a Generalised SBM with a Split Merge Sampler
Description:	Inference in a Bayesian framework for a generalised stochastic block model. The generalised stochastic block model (SBM) can capture group structure in network data without requiring conjugate priors on the edge-states. Two sampling methods are provided to perform inference on edge parameters and block structure: a split-merge Markov chain Monte Carlo algorithm and a Dirichlet process sampler. Green, Richardson (2001) <doi:10.1111/1467-9469.00242>; Neal (2000) <doi:10.1080/10618600.2000.10474879>; Ludkin (2019) <arXiv:1909.09421>.
Authors:	Matthew Ludkin [aut, cre, cph]
Maintainer:	Matthew Ludkin <[email protected]>
License:	MIT + file LICENSE
Version:	1.1.1
Built:	2025-03-13 03:46:57 UTC
Source:	https://github.com/cran/SBMSplitMerge

accept `propsbm` with the acceptance probability alpha

Description

accept propsbm with the acceptance probability alpha

Usage

accept(currsbm, propsbm, edges, sbmmod, logjac = 0, logu = 0, ...)
accept(currsbm, propsbm, edges, sbmmod, logjac = 0, logu = 0, ...)

Arguments

`currsbm`	current `sbm` state
`propsbm`	proposed `sbm` state
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`logjac`	log Jacobian of transformation of variables
`logu`	log density for auxiliary variables
`...`	additional arguments to pass to `dedges`

Value

updated sbm object

Adjusted Rand Index

Description

Calculate the Adjusted Rand Index between two clusterings

Usage

ARI(z, truez)
ARI(z, truez)

Arguments

`z`	input vector
`truez`	reference vector

Value

Adjusted Rand Index of z against truez

Examples

ARI(c(1,1,2,2,3,3), c(2,2,1,1,3,3)) ## 1 - doesn't care for labels
ARI(c(1,1,2,2,3,3), c(1,1,1,1,2,2)) ## 0.444
ARI(c(1,1,2,2,3,3), c(2,2,1,1,3,3)) ## 1 - doesn't care for labels
ARI(c(1,1,2,2,3,3), c(1,1,1,1,2,2)) ## 0.444

Block matrix

Description

converts block assignments of a blocks object to a matrix of block assignments

Usage

## S3 method for class 'blocks'
blockmat(blocks, kappa)
## S3 method for class 'blocks'
blockmat(blocks, kappa)

Arguments

`blocks`	a `blocks` object
`kappa`	number of blocks in matrix

Value

matrix with kappa rows and a 1 at (k,i) if node i is in block k under blocks

Block matrix

Description

converts a vector of block assignments to a matrix of block assignments

Usage

## S3 method for class 'numeric'
blockmat(x, kappa)

## S3 method for class 'factor'
blockmat(x, kappa)
## S3 method for class 'numeric'
blockmat(x, kappa)

## S3 method for class 'factor'
blockmat(x, kappa)

Arguments

`x`	a numeric-vector of node-to-block assignments
`kappa`	number of blocks

Value

matrix with kappa rows and a 1 at (k,i) if node i is in block k under x

Block matrix

Description

converts block assignments of an sbm object to a matrix of block assignments

Usage

## S3 method for class 'sbm'
blockmat(SBM, kappa)
## S3 method for class 'sbm'
blockmat(SBM, kappa)

Arguments

`SBM`	an `sbm` object
`kappa`	number of blocks in matrix

Value

matrix with kappa rows and a 1 at (k,i) if node i is in block k under SBM

Block Model

Description

create a blockmod object

Usage

blockmod(fixkappa, logd, dcond, r, ...)
blockmod(fixkappa, logd, dcond, r, ...)

Arguments

`fixkappa`	Logical - is kappa fixed or can it vary under the model?
`logd`	`function(blocks)` - log density for `blocks`
`dcond`	`function(blocks, i)` - conditional density for the block assignment `i` in `blocks`
`r`	`function(n), sorted=FALSE` - samples a blocks object from the model
`...`	parameters of the model for use in `r`, `logd`, `dcond`

Details

A block model is a probability model for a blocks object. This class creates a closure with three functions: - a random method for sampling block a structure from the model with n nodes; a - a log-density method for computing the log-density of a given block structure in a blocks object - a conditional density function that takes a blocks object and a node i

Value

a blockmod object

Blocks object

Description

create a blocks object

Usage

blocks(z, kappa)
blocks(z, kappa)

Arguments

`z`	vector of block labels for each node
`kappa`	maximum number of blocks

Details

stores the block allocations and total number of blocks for a stochastic block model

Value

a blocks object

Examples

## Assign six nodes to four blocks:
b <- blocks(c(1,1,2,3,4,4), 4)
print(b)
plot(b) ## shows id two nodes are members of the same block
## Assign six nodes to four blocks:
b <- blocks(c(1,1,2,3,4,4), 4)
print(b)
plot(b) ## shows id two nodes are members of the same block

plot a trace of the blocks from MCMC samples

Description

plot a trace of the blocks from MCMC samples

Usage

blocktrace(postz, burnin)
blocktrace(postz, burnin)

Arguments

`postz`	output from sampler
`burnin`	which iterations to plot? defaults to all.

Value

'ggplot2' object

Chinese Restaurant Process

Description

A blockmod for the Chinese restaurant process (CRP)

Usage

crp(gamma)
crp(gamma)

Arguments

gamma

concentration parameter

Details

The CRP posits that each node arrives in turn. The first node joins the first block. Each subsequent node starts a new block with probability 'gamma' or joins an existing block proportional to the block size.

Value

a block model representing a CRP(gamma) distribution

Examples

## simulate from a CRP(5) prior
m <- crp(5)
print(m)
m$r(10)
## simulate from a CRP(5) prior
m <- crp(5)
print(m)
m$r(10)

Dirichlet distribution

Description

Density of Dirichlet distribution

Usage

ddirichlet(x, gam, log = FALSE)
ddirichlet(x, gam, log = FALSE)

Arguments

`x`	random variable in the d-dimensional simplex
`gam`	a length K concentration parameter
`log`	return the log-probability instead?

Value

the density

Examples

g <- rep(2,5)
p <- rdirichlet(1, g) ## a length-5 probability vector
ddirichlet(p, g)
g <- rep(2,5)
p <- rdirichlet(1, g) ## a length-5 probability vector
ddirichlet(p, g)

Density of edges

Description

Compute the probability density for an edges object

Usage

dedges(x, edges, edgemod, na.rm = TRUE, ...)
dedges(x, edges, edgemod, na.rm = TRUE, ...)

Arguments

`x`	an R object for dispatch
`edges`	an `edges` object
`edgemod`	an `edgemod` object
`na.rm`	remove NAs when calculating?
`...`	additional arguments

Value

matrix same size as edges$E with density of each edge

likelihood of edges

Description

likelihood of edges

Usage

## S3 method for class 'numeric'
dedges(x, edges, edgemod, na.rm = na.rm, ...)
## S3 method for class 'numeric'
dedges(x, edges, edgemod, na.rm = na.rm, ...)

Arguments

`x`	a matrix of parameters (with same size as `edges$E`)
`edges`	an `edges` object
`edgemod`	an `edgemod` object
`na.rm`	remove NAs when calculating?
`...`	additional arguments passed to `edgemod$logd`

Value

likelihood of edges under the edgemod using parameters in matrix pmat

Density of edges

Description

Compute the probability density for an edges object under an sbm object

Usage

## S3 method for class 'sbm'
dedges(x, edges, edgemod, na.rm = TRUE, ...)
## S3 method for class 'sbm'
dedges(x, edges, edgemod, na.rm = TRUE, ...)

Arguments

`x`	an `sbm` object
`edges`	an `edges` object
`edgemod`	an `edgemod` object
`na.rm`	remove NAs when calculating?
`...`	additional arguments for `dedges.params`

Value

matrix same size as edges$E with density of each edge

Examples

## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
dedges(s, e, model$edge)
## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
dedges(s, e, model$edge)

Delete a block move

Description

proposes deleting an empty block (chosen at random among empty Blocks)

Usage

delblock(sbm, edges, sbmmod, rho = 1)
delblock(sbm, edges, sbmmod, rho = 1)

Arguments

`sbm`	the current state of the sampler
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`rho`	probability of choosing to add a block

Value

an updated sbm object

Dirichlet Multinomial Allocation

Description

A blockmod for Dirichlet Multinomial Allocation (DMA)

Usage

dma(gamma, delta)
dma(gamma, delta)

Arguments

`gamma`	parameter for Dirichlet component
`delta`	parameter for Poison component

Details

This model posits:

$kappa-1 ~ Pois(delta)$

$omega|kappa, gamma ~ Dirichlet(gamma)$

$Z_i|omega ~ Multinomial(omega) for i=1 .. n$

Value

a block model representing a dma(gamma, delta) distribution

Examples

## simulate from a DMA(2, 5) prior
## This models the `number of blocks-1` as Poisson(5)
## and block assignments as Dirichlet-Multinomial(2, 2, ...)
m <- dma(2, 5)
print(m)
m$r(10)
## simulate from a DMA(2, 5) prior
## This models the `number of blocks-1` as Poisson(5)
## and block assignments as Dirichlet-Multinomial(2, 2, ...)
m <- dma(2, 5)
print(m)
m$r(10)

Draw block membership

Description

Draw block membership in a Dirichlet process sampler

Usage

drawblock.dp(i, currsbm, edges, sbmmod)
drawblock.dp(i, currsbm, edges, sbmmod)

Arguments

`i`	node to update
`currsbm`	current `sbm` object
`edges`	an `edges` object
`sbmmod`	an `sbmmod` object

Details

sample a new block assignment for i under a Dirichlet process. Care needs to be taken with singleton blocks to update the parameter model in currsbm.

Value

updated sbm object

Gibbs-like reassignment of nodes to the current set of blocks

Description

Reassign node 'i' to the current set of blocks given the current number of blocks and the other block assignments

Usage

drawblock.gibbs(i, currsbm, edges, sbmmod)
drawblock.gibbs(i, currsbm, edges, sbmmod)

Arguments

`i`	the node to reassign
`currsbm`	an `sbm` object
`edges`	an `edges` object
`sbmmod`	an `sbmmod` object

Value

updated sbm object with new block assignment for i

Draw block memberships

Description

Draw block memberships in a Dirichlet process sampler

Usage

drawblocks.dp(currsbm, edges, sbmmod)
drawblocks.dp(currsbm, edges, sbmmod)

Arguments

`currsbm`	current `sbm` object
`edges`	an `edges` object
`sbmmod`	an `sbmmod` object

Details

iteratively updates the block assignment of each node using a Dirichlet process update move

Value

updated sbm object

Gibbs-like reassignment of nodes to the current set of blocks

Description

Sweep through the set of nodes and reassign to the current set of blocks given the current number of blocks

Usage

drawblocks.gibbs(currsbm, edges, sbmmod)
drawblocks.gibbs(currsbm, edges, sbmmod)

Arguments

`currsbm`	an `sbm` object
`edges`	an `edges` object
`sbmmod`	an `sbmmod` object

Value

updated sbm object with new block assignments

Metropolis updates by drawing parameters

Description

Simulate parameters for the given model with a Metropolis-Hastings step

Usage

drawparams(sbm, edges, sbmmod, sigma = 0.1)
drawparams(sbm, edges, sbmmod, sigma = 0.1)

Arguments

`sbm`	current `sbm` object
`edges`	an `edges`
`sbmmod`	an `sbmmod`
`sigma`	parameter for `drawparam`

Details

iterate through the parameters in currsbm and update.

Value

updated sbm object

Class for edge models

Description

A class with a random and density method for edges objects

Usage

edgemod(logd, r, ...)
edgemod(logd, r, ...)

Arguments

`logd`	function(e, p) to calculate likelihood of edge an edge e given parameter array p
`r`	function(p) - simulate an edge given a parameter p (optional)
`...`	additional arguments to append to `edgemod` internal list

Value

an edgemod object

Note

the parameter for logd is an array of c(dimension of theta, dim(E)) e.g. from parammat

Class for edge data

Description

A class to hold edge data

Usage

edges(e, sym, loops, ...)
edges(e, sym, loops, ...)

Arguments

`e`	a matrix or array representing the raw edge-state data
`sym`	is the network symmetric? (`e[ji] = e[ji]`)
`loops`	does the network contain self-loops? (edges from node i to i)
`...`	additional arguments to append to edges internal list

Value

an edges object

Examples

## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
plot(e)
plot(e, s)
print(e)
## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
plot(e)
plot(e, s)
print(e)

Bernoulli edge model

Description

Make an edgemod model with Bernoulli edge-states

Usage

edges_bern(...)
edges_bern(...)

Arguments

...

additional parameters to pass to rbinom

Value

an edgemod

Examples

eb <- edges_bern() ## makes `eb` an edgemod for Bernoulli edge-states
eb <- edges_bern() ## makes `eb` an edgemod for Bernoulli edge-states

Negative-Binomial edge model

Description

Make an edgemod model with Negative-Binomial edge-states

Usage

edges_nbin(...)
edges_nbin(...)

Arguments

...

additional parameters to pass to rnbinom

Value

an edgemod

Examples

enb <- edges_nbin() ## makes `enb` an edgemod for Negative-Binomial edge-states
enb <- edges_nbin() ## makes `enb` an edgemod for Negative-Binomial edge-states

Normal edge model

Description

Make an edgemod model with Normal edge-states

Usage

edges_norm(...)
edges_norm(...)

Arguments

...

additional parameters to pass to rnorm

Value

an edgemod

Examples

en <- edges_norm() ## makes `en` an edgemod for Normal edge-states
en <- edges_norm() ## makes `en` an edgemod for Normal edge-states

Poisson edge model

Description

Make an edgemod model with Poisson edge-states

Usage

edges_pois(...)
edges_pois(...)

Arguments

...

additional parameters to pass to rpois

Value

an edgemod

Examples

ep <- edges_pois() ## makes `ep` an edgemod for Poisson edge-states
ep <- edges_pois() ## makes `ep` an edgemod for Poisson edge-states

The Enron data set as extracted from `igraph` using the script in data-raw

Description

A data set of counts of emails between email addresses This is a non-symmetric network. Nodes represent email address. The edge-state ij between two email addresses i and j is the number of emails sent from i to j The Groups vector is the node label from the igraph attribute "notes"

Usage

Enron
Enron

Format

A list containing

Edges: an edges object with each edge-state representing the number of emails between two email addresses
Groups: A vector giving a group name to which the email address belong. The order matches the edges such that Edges[i,j] is the edge-state between the nodes i and nodes j who are members of Groups[i] and Groups[j] respectively

Source

https://cran.r-project.org/package=igraphdata

get a set of evaluation plots from MCMC samples

Description

get a set of evaluation plots from MCMC samples

Usage

eval_plots(output, burnin, theta_index)
eval_plots(output, burnin, theta_index)

Arguments

`output`	from sampler
`burnin`	burn-in period (a vector of iteration numbers to subset outputs)
`theta_index`	which set of thetas to plot?

Value

list of ggplot objects (with descriptive names)

is.sbm

Description

Logical check if an object is an sbm object

Usage

is.sbm(x)
is.sbm(x)

Arguments

`x`	an R object

Value

Logical indicating if x is an sbm object

The Macaque data set as extracted from `igraph` using the script in data-raw

Description

The Macaque data set as extracted from igraph using the script in data-raw

Usage

Macaque
Macaque

Format

An edges object of activation counts between brain regions in a Macaque

Marginal likelihood model for Bernoulli distributed edges

Description

calculate the marginal likelihood for a node for samplers using conjugate models

Usage

marglike_bern(znoi, ei, parammod)
marglike_bern(znoi, ei, parammod)

Arguments

`znoi`	a matrix of block assignments without node i
`ei`	edge-states incident to i
`parammod`	a `parammod` object representing the Bernoulli-Beta model

Value

log-probability of node i belonging to each block

Marginal likelihood model for Normal distributed edges

Description

calculate the marginal likelihood for a node for samplers using conjugate models

Usage

marglike_norm(znoi, ei, parammod)
marglike_norm(znoi, ei, parammod)

Arguments

`znoi`	a matrix of block assignments without node i
`ei`	edge-states incident to i
`parammod`	a `parammod` object

Value

log-probability of node i belonging to each block

Marginal likelihood model for Poisson distributed edges

Description

calculate the marginal likelihood for a node for samplers using conjugate models

Usage

marglike_pois(znoi, ei, parammod)
marglike_pois(znoi, ei, parammod)

Arguments

`znoi`	a matrix of block assignments without node i
`ei`	edge-states incident to i
`parammod`	a `parammod` object

Value

log-probability of node i belonging to each block

Merge blocks

Description

Merge-move using an average to merge parameters

Usage

mergeavg(sbm, edges, sbmmod, ...)
mergeavg(sbm, edges, sbmmod, ...)

Arguments

`sbm`	the current state of the sampler
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`...`	additional parameter to 'accept'

Details

the blocks are chosen at random, the nodes reassigned to the block with the smallest index, then the parameters are combined using the average on the transformed scale

Value

an updated sbm object

merge move block merging

Description

merge move block merging

Usage

mergeblocks(currblocks, propparams, edges, sbmmod, k, l)
mergeblocks(currblocks, propparams, edges, sbmmod, k, l)

Arguments

`currblocks`	current blocks
`propparams`	proposed parameters
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`k`	Blocks to merge
`l`	Blocks to merge

Value

list(proposed block structure, log-acceptance-prob)

merge parameters

Description

merge parameters

Usage

mergeparams(x, ...)
mergeparams(x, ...)

Arguments

`x`	an object to dispatch on
`...`	additional arguments for methods

Value

merged parameters from x

Merge step: parameters

Description

Merge step: parameters

Usage

## Default S3 method:
mergeparams(params, k, l, parammod)
## Default S3 method:
mergeparams(params, k, l, parammod)

Arguments

`params`	a `params object`
`k`	Blocks to merge
`l`	Blocks to merge
`parammod`	a `parammod` object

Value

list(proposed_params, log-acceptance-prob)

Merge step - parameter merging

Description

Merge step - parameter merging

Usage

## S3 method for class 'numeric'
mergeparams(thetak, thetal, x, parammod)
## S3 method for class 'numeric'
mergeparams(thetak, thetal, x, parammod)

Arguments

`thetak`, `thetal`	parameters to merge
`x`	auxiliary parameter
`parammod`	a `parammod` object

Value

list(proposed_params, log-acceptance-prob)

modal block assignments from MCMC samples

Description

modal block assignments from MCMC samples

Usage

modeblocks(postz)
modeblocks(postz)

Arguments

postz

output from sampler

Value

a blocks object with the modal block assignments under postz

Multinomial block assignment

Description

A blockmod for Multinomial allocation

Usage

multinom(gamma, kappa)
multinom(gamma, kappa)

Arguments

`gamma`	parameter for Dirichlet component $Dirichlet(gamma, ..., gamma)$
`kappa`	the number of blocks

Details

This model posits that: for i=1:n

$Z_i ~ Multinomial(omega)$

where

$omega ~ Dirichlet(gamma)$

Value

a block model representing a Multinomial(gamma) distribution

Examples

## A fixed number of blocks with multinomial assignment of nodes
m <- multinom(1, 4)
print(m)
m$r(10) ## simulate a blocks object with 10 nodes
## A fixed number of blocks with multinomial assignment of nodes
m <- multinom(1, 4)
print(m)
m$r(10) ## simulate a blocks object with 10 nodes

Likelihood of node assignment

Description

Calculate the likelihood of a nod belonging to each of block

Usage

nodelike(blocks, params, edges, i, sbmmod, ...)
nodelike(blocks, params, edges, i, sbmmod, ...)

Arguments

`blocks`	an `blocks` object
`params`	an `params` object
`edges`	an `edges` object
`i`	the node of interest
`sbmmod`	an `sbmmod` object
`...`	additional arguments for `nodelike.blocks`

Details

the number of blocks considered is either the number of blocks in sbm (kappa) or kappa+1 when sbmmod has a variable number of blocks. care is taken for data which is directed and with loops.

Value

likelihood of edges emanating from node i

plot a trace of the number of blocks from MCMC samples

Description

plot a trace of the number of blocks from MCMC samples

Usage

numblockstrace(postk, burnin)
numblockstrace(postk, burnin)

Arguments

`postk`	output from sampler
`burnin`	which iterations to plot? defaults to all.

Value

'ggplot2' object

Beta parameter model

Description

A parammod with beta-distributed parameters

Usage

param_beta(a0, a1, b0, b1)
param_beta(a0, a1, b0, b1)

Arguments

`a0`	`theta_0 ~ Beta(a0,a1)`
`a1`	`theta_0 ~ Beta(a0,a1)`
`b0`	`theta_k ~ Beta(b0,b1)`
`b1`	`theta_k ~ Beta(b0,b1)`

Details

This model represents a prior on theta with:

$theta_0 ~ Beta(a0,a1)$

$theta_k ~ Beta(b0,b1)$

for k = 1 ... kappa

Value

a parammod

Examples

## theta0 ~ Beta(1,9); thetak ~ Beta(9,1)
pb <- param_beta(1,9,9,1)
pb$r(5) ## a draw with 5 within-block parameters
## theta0 ~ Beta(1,9); thetak ~ Beta(9,1)
pb <- param_beta(1,9,9,1)
pb$r(5) ## a draw with 5 within-block parameters

Gamma parameter model

Description

A parammod with gamma-distributed parameters

Usage

param_gamma(a0, a1, b0, b1)
param_gamma(a0, a1, b0, b1)

Arguments

`a0`	`theta_0 ~ Gamma(a0,a1)`
`a1`	`theta_0 ~ Gamma(a0,a1)`
`b0`	`theta_k ~ Gamma(b0,b1)`
`b1`	`theta_k ~ Gamma(b0,b1)`

Details

This model represents a prior on theta with:

$theta_0 ~ Gamma(a0,a1)$

$theta_k ~ Gamma(b0,b1)$

for k = 1 ... kappa

Value

a parammod

Examples

## theta0 ~ Gamma(1,1); thetak ~ Gamma(5,5)
pg <- param_gamma(1,1,5,5)
pg$r(5) ## a draw with 5 within-block parameters
## theta0 ~ Gamma(1,1); thetak ~ Gamma(5,5)
pg <- param_gamma(1,1,5,5)
pg$r(5) ## a draw with 5 within-block parameters

Parameter model for Negative Binomial

Description

Negative Binomial parameter model: theta_0 = (mu0, sigma0) theta_k = (muk, sigmak)

Usage

param_nbin(a0, a1, b0, b1, c0, c1, d0, d1)
param_nbin(a0, a1, b0, b1, c0, c1, d0, d1)

Arguments

`a0`, `a1`	`mu0 ~ Gamma(a0,a1)`
`b0`, `b1`	`sig_0 ~ Beta(b0,b1)`
`c0`, `c1`	`muk ~ Gamma(c0, c1)`
`d0`, `d1`	`sig_k ~ Beta(d0,d1)`

Value

parammod representing Negative-Binomial distributed parameters

Examples

## theta0 = (r0, p0); r0~Gamma(1,1); p0 ~ Beta(1,1);
## thetak = (rk, pk); rk~Gamma(3,3); pk ~ Beta(5,5);
pn <- param_nbin(1,1,1,1,3,3,5,5)
pn$r(5) ## a draw with 5 within-block parameters
## theta0 = (r0, p0); r0~Gamma(1,1); p0 ~ Beta(1,1);
## thetak = (rk, pk); rk~Gamma(3,3); pk ~ Beta(5,5);
pn <- param_nbin(1,1,1,1,3,3,5,5)
pn$r(5) ## a draw with 5 within-block parameters

Parameter model for Normal Model

Description

Normal parameter model: theta_0 = (mu0, sigma0) theta_k = (muk, sigmak)

Usage

param_norm(a0, a1, b0, b1, c0, c1, d0, d1)
param_norm(a0, a1, b0, b1, c0, c1, d0, d1)

Arguments

`a0`, `a1`	`mu0 ~ Normal(a0,a1)`
`b0`, `b1`	`sig_0 ~ Gamma(b0,b1)`
`c0`, `c1`	`muk ~ Normal(c0, c1)`
`d0`, `d1`	`sig_k ~ Gamma(d0,d1)`

Value

parammod representing Normal distributed parameters

Examples

## theta0 = (mu0, sigma0); mu0~Normal(0,5); sigma0 ~ Gamma(1,1);
## thetak = (muk, sigmak); muk~Normal(0,3); sigmak ~ Gamma(5,2);
pn <- param_norm(0,5,1,1,0,3,5,2)
pn$r(5) ## a draw with 5 within-block parameters
## theta0 = (mu0, sigma0); mu0~Normal(0,5); sigma0 ~ Gamma(1,1);
## thetak = (muk, sigmak); muk~Normal(0,3); sigmak ~ Gamma(5,2);
pn <- param_norm(0,5,1,1,0,3,5,2)
pn$r(5) ## a draw with 5 within-block parameters

Parameter Matrix

Description

Make a matrix of parameters

Usage

parammat(x, ...)
parammat(x, ...)

Arguments

`x`	object for dispatch
`...`	additional arguments for method

Value

a parameter matrix object

Parameter Matrix

Description

Make a matrix of parameters from a blocks and params object

Usage

## S3 method for class 'blocks'
parammat(x, params, ...)
## S3 method for class 'blocks'
parammat(x, params, ...)

Arguments

`x`	a `blocks` object
`params`	a `params` object
`...`	(unused)

Value

an NxN matrix P, with P[i,j] = the parameter governing edge ij

Parameter Matrix

Description

Make a matrix of parameters from a matrix of block assignments

Usage

## S3 method for class 'matrix'
parammat(zleft, zright, params, ...)
## S3 method for class 'matrix'
parammat(zleft, zright, params, ...)

Arguments

`zleft`	block assignment matrix on the left
`zright`	block assignment matrix on the right
`params`	the parameters object
`...`	(unused)

Value

a matrix of parameters of size |zleft| x |zright|

Parameter Matrix

Description

Make a matrix of parameters from a params object

Usage

## S3 method for class 'params'
parammat(x, kappa, ...)
## S3 method for class 'params'
parammat(x, kappa, ...)

Arguments

`x`	a `params` object
`kappa`	- number of blocks to compute for matrix (optional)
`...`	(unused)

Value

a matrix of parameters

Parameter Matrix

Description

Make a matrix of parameters from an sbm object

Usage

## S3 method for class 'sbm'
parammat(x, ...)
## S3 method for class 'sbm'
parammat(x, ...)

Arguments

`x`	an `sbm` object
`...`	(unused)

Value

a matrix of parameters

Parameter Model

Description

create a parammod object

Usage

parammod(logd, r, t, invt, loggradt, ...)
parammod(logd, r, t, invt, loggradt, ...)

Arguments

`logd`	`function(params)` - log-density function for parameters
`r`	`function(kappa)` - random function to draw parameters
`t`	mapping parameter space to real line
`invt`	mapping real line to parameter space
`loggradt`	log of the gradient of mapping `t`
`...`	additional arguments to store in the `parammod` object

Details

A parameter model is a probability model for a params object. This class creates a closure with five functions: - a random method for sampling a params object - a log-density method for computing the log-density of a given params object - a transformation function t that maps a parameter value to the real line - the inverse of t - the log-gradient of t

Value

a parammod object

`params` S3 object

Description

make a params object from the between-block parameter theta0 and a vector of within block parameters thetak

Usage

params(theta0, thetak)
params(theta0, thetak)

Arguments

`theta0`	between block parameters - a vector of length 'dimension of theta'
`thetak`	within block parameters - a matrix with `ncol=kappa` and `nrow=dimension of theta`

Value

a params object

Examples

p <- params(0.1, c(0.2,0.4,0.5))
p
p <- params(0.1, c(0.2,0.4,0.5))
p

plot a trace of parameter values from MCMC samples

Description

plot a trace of parameter values from MCMC samples

Usage

paramtrace(theta, range, burnin)
paramtrace(theta, range, burnin)

Arguments

`theta`	output from sampler
`range`	which thetas to plot? defaults to all.
`burnin`	which iterations to plot? defaults to all.

Value

'ggplot2' object

Plot blocks

Description

plots a block object

Usage

## S3 method for class 'blocks'
plot(x, col, xaxt = "n", yaxt = "n", xlab = "Nodes", ylab = "Nodes", ...)

## S3 method for class 'blocks'
image(x, col, xaxt = "n", yaxt = "n", xlab = "Nodes", ylab = "Nodes", ...)
## S3 method for class 'blocks'
plot(x, col, xaxt = "n", yaxt = "n", xlab = "Nodes", ylab = "Nodes", ...)

## S3 method for class 'blocks'
image(x, col, xaxt = "n", yaxt = "n", xlab = "Nodes", ylab = "Nodes", ...)

Arguments

`x`	a blocks object to plot
`col`	colours for the plot
`xaxt`	override `image` parameters
`yaxt`	override `image` parameters
`xlab`	override `image` parameters
`ylab`	override `image` parameters
`...`	additional parameters for `image`

Details

plot the block assignments in a blocks object as a matrix, color-coded by block membership

Examples

## Assign six nodes to four blocks:
b <- blocks(c(1,1,2,3,4,4), 4)
plot(b)
## note that the lower left corner has one 2x2 red square
## indicating node 1 and 2 belong to the same block
## Assign six nodes to four blocks:
b <- blocks(c(1,1,2,3,4,4), 4)
plot(b)
## note that the lower left corner has one 2x2 red square
## indicating node 1 and 2 belong to the same block

Plot

Description

plots an edges objects

Usage

## S3 method for class 'edges'
plot(x, Blocks, sorted = TRUE, xlab = "Node", ylab = "Node", ...)

## S3 method for class 'edges'
image(x, Blocks, sorted = TRUE, xlab = "Node", ylab = "Node", ...)
## S3 method for class 'edges'
plot(x, Blocks, sorted = TRUE, xlab = "Node", ylab = "Node", ...)

## S3 method for class 'edges'
image(x, Blocks, sorted = TRUE, xlab = "Node", ylab = "Node", ...)

Arguments

`x`	an `edges` object
`Blocks`	a blocks object or `sbm` object
`sorted`	sort by block membership in `sbm` before plotting?
`xlab`	label for x-axis
`ylab`	label for y-axis
`...`	parameters for `image`

Value

ggplot2 plot of edges in a raster

Examples

## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
plot(e)
plot(e, s)
print(e)
## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
plot(e)
plot(e, s)
print(e)

Plot for `sbm` object

Description

plot an sbm object as an image

Usage

## S3 method for class 'sbm'
plot(x, col, ...)

## S3 method for class 'sbm'
image(x, col, ...)
## S3 method for class 'sbm'
plot(x, col, ...)

## S3 method for class 'sbm'
image(x, col, ...)

Arguments

`x`	an `sbm` object
`col`	colours for each block - if missing, `rainbow` is used
`...`	additional arguments for plot

helper function for trace plots

Description

helper function for trace plots

Usage

plotpostpairs(mat)
plotpostpairs(mat)

Arguments

mat

matrix to plot as an image using ggplot2

Value

'ggplot2' plot objecy

mean proportion of times two nodes were in the same block under MCMC samples

Description

mean proportion of times two nodes were in the same block under MCMC samples

Usage

postpairs(postz)
postpairs(postz)

Arguments

postz

output from sampler

Value

matrix P with P[i,j] = proportion of times i and j are in the same block under postz

Draw draw Categorical distribution

Description

Draw draw Categorical distribution

Usage

rcat(n, p, replace = TRUE)
rcat(n, p, replace = TRUE)

Arguments

`n`	number of draws
`p`	a length-d probability vector
`replace`	should the categories be replaced? If so n < p required

Value

a draw from Categorical(p)

Examples

rcat(1, 1) ## returns 1 with probability 1
rcat(1, rep(1/6,6)) ## a dice roll
rcat(1, 1) ## returns 1 with probability 1
rcat(1, rep(1/6,6)) ## a dice roll

Dirichlet distribution

Description

Draw from Dirichlet distribution

Usage

rdirichlet(n, gam)
rdirichlet(n, gam)

Arguments

`n`	number of variates to draw
`gam`	a vector of concentration parameters of length `K`

Value

matrix dimension n*k of samples

Examples

rdirichlet(1, rep(2,5)) ## a length-5 probability vector
rdirichlet(1, rep(2,5)) ## a length-5 probability vector

Simulate edges

Description

Simulate edges from an sbm object with a given edgemod

Usage

redges(SBM, edgemod, sym = TRUE, loops = FALSE, ...)
redges(SBM, edgemod, sym = TRUE, loops = FALSE, ...)

Arguments

`SBM`	an `sbm` object
`edgemod`	an `edgemod` object
`sym`	should the network be symmetric?
`loops`	should the network have self-loops?
`...`	additional arguments passed to `edgemod$r`

Details

None

Value

an edges object

Examples

## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
plot(e)
plot(e, s)
print(e)
## make an sbm model, sample data then plot and print:
model <- sbmmod(dma(2,5), param_beta(1,1,1,1), edges_bern())
s <- model$r(100)
e <- redges(s, model$edge)
plot(e)
plot(e, s)
print(e)

Random Walk

Description

performs a random walk on a parameter value with a given parameter model

Usage

rw(p, pm, sigma)
rw(p, pm, sigma)

Arguments

`p`	a parameter
`pm`	a `parammod` object
`sigma`	- scale of random walk

Value

ist(proposed parameter, locjacobian)

top level sampler function

Description

top level sampler function

Usage

sampler(
  edges,
  sbmmod,
  nSteps = 1000,
  algorithm = "rj",
  sigma = 0.5,
  statusfreq,
  currsbm,
  ...
)
sampler(
  edges,
  sbmmod,
  nSteps = 1000,
  algorithm = "rj",
  sigma = 0.5,
  statusfreq,
  currsbm,
  ...
)

Arguments

`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`nSteps`	number of steps to run sampler
`algorithm`	choice of algorithm options are: `"conjugate", "gibbs", "dp", "rj"`
`sigma`	random walk parameter for `theta`
`statusfreq`	print the elapsed number of iterations every `statusfreq` iterations
`currsbm`	initial state for `sbm` object (optional - one is drawn from `sbmmod` if not supplied)
`...`	additional parameters to pass to step

Value

postz traces for block assignments z

postt traces for theta

postk traces for number of blocks kappa

postn traces for number of occupied blocks

nsteps number of iterations of chain

algorithm choice

Examples

## see vignette("Weibull-edges")
## see vignette("Weibull-edges")

Conjugate model sampler

Description

Conjugate model sampler

Usage

sampler.conj(currsbm, edges, sbmmod, sigma = NULL, ...)
sampler.conj(currsbm, edges, sbmmod, sigma = NULL, ...)

Arguments

`currsbm`	the current state of the sampler
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`sigma`	unused
`...`	additional arguments for `sbmmod$marglike`

Value

next state of currsbm object

Note

If using the CRP as the block model, then this is the IRM sampler of Schmidt or Morup (Schmidt, M.N. and Morup, M., 2013. Nonparametric Bayesian modeling of complex networks: An introduction. IEEE Signal Processing Magazine, 30(3), pp.110-128.)

Examples

model <- sbmmod(crp(3), param_beta(1,1,1,1), edges_bern(), marglike=marglike_bern)
trueSBM <- model$r(100)
Edges <- redges(trueSBM, model$edge)
out <- sampler(Edges, model, 10, "conjugate")
model <- sbmmod(crp(3), param_beta(1,1,1,1), edges_bern(), marglike=marglike_bern)
trueSBM <- model$r(100)
Edges <- redges(trueSBM, model$edge)
out <- sampler(Edges, model, 10, "conjugate")

Dirichlet process sampler

Description

Dirichlet process sampler

Usage

sampler.dp(currsbm, edges, sbmmod, sigma)
sampler.dp(currsbm, edges, sbmmod, sigma)

Arguments

`currsbm`	the current state of the sampler
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`sigma`	random walk parameter for theta

Value

next state of currsbm object

Examples

model <- sbmmod(crp(4), param_norm(0,0,1,1,3,3,1,1), edges_norm())
trueSBM <- model$r(100)
Edges <- redges(trueSBM, model$edge)
dp_out <- sampler(Edges, model, 25, "dp", sigma=0.1)
model <- sbmmod(crp(4), param_norm(0,0,1,1,3,3,1,1), edges_norm())
trueSBM <- model$r(100)
Edges <- redges(trueSBM, model$edge)
dp_out <- sampler(Edges, model, 25, "dp", sigma=0.1)

Gibbs sampling for node assignments

Description

Gibbs sampling for node assignments

Usage

sampler.gibbs(currsbm, edges, sbmmod, sigma)
sampler.gibbs(currsbm, edges, sbmmod, sigma)

Arguments

`currsbm`	the current state of the sampler
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`sigma`	random walk parameter for theta

Value

next state of currsbm object

Note

This requires a block model with a fixed kappa

Examples

model <- sbmmod(multinom(1, 3), param_gamma(1,1,1,1), edges_pois())
trueSBM <- model$r(10)
Edges <- redges(trueSBM, model$edge)
gibbs_out <- sampler(Edges, model, algorithm="gibbs", 10, sigma=0.1)
eval_plots(gibbs_out)
model <- sbmmod(multinom(1, 3), param_gamma(1,1,1,1), edges_pois())
trueSBM <- model$r(10)
Edges <- redges(trueSBM, model$edge)
gibbs_out <- sampler(Edges, model, algorithm="gibbs", 10, sigma=0.1)
eval_plots(gibbs_out)

reversible jump Markov chain Monte Carlo split-merge sampler

Description

reversible jump Markov chain Monte Carlo split-merge sampler

Usage

sampler.rj(currsbm, edges, sbmmod, sigma, rho = 10)
sampler.rj(currsbm, edges, sbmmod, sigma, rho = 10)

Arguments

`currsbm`	the current state of the sampler
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`sigma`	random walk parameter for `theta`
`rho`	propensity to add a block

Value

next state of currsbm object

Examples

model <- sbmmod(dma(1,10), param_nbin(1,1,4,4,0.5,0.5,0.5,0.5), edges_nbin())
trueSBM <- model$r(100)
Edges <- redges(trueSBM, model$edge)
rj_out <- sampler(Edges, model, 10, "rj", sigma=0.1)
model <- sbmmod(dma(1,10), param_nbin(1,1,4,4,0.5,0.5,0.5,0.5), edges_nbin())
trueSBM <- model$r(100)
Edges <- redges(trueSBM, model$edge)
rj_out <- sampler(Edges, model, 10, "rj", sigma=0.1)

Class `sbm`

Description

Class sbm

Usage

sbm(blocks, params)
sbm(blocks, params)

Arguments

`blocks`	a `blocks` object
`params`	a `params` object

Value

an sbm object

Examples

sbm(blocks(c(1,1,2,2,3,3)), params(0.1, c(0.4,0.5,0.6)))
sbm(blocks(c(1,1,2,2,3,3)), params(0.1, c(0.4,0.5,0.6)))

Stochastic block model object

Description

A wrapper for a block and parameter model

Usage

sbmmod(blockmod, parammod, edgemod, ...)
sbmmod(blockmod, parammod, edgemod, ...)

Arguments

`blockmod`	a `blockmod` object
`parammod`	a `parammod` object
`edgemod`	an `edgemod` object
`...`	additional arguments to store in the `sbmmod` object

Details

Simple wrapper for the block and parameter model for an sbm object

Value

an sbmmod object with a method 'r(n)' sampling an sbm object with n nodes from the model and a method logd(sbm) computing the log-density of sbm under the model

Author(s)

Matthew Ludkin

split move using average to merge parameters

Description

split move using average to merge parameters

Usage

splitavg(sbm, edges, sbmmod, ...)
splitavg(sbm, edges, sbmmod, ...)

Arguments

`sbm`	the current state of the sampler
`edges`	an `edges` object
`sbmmod`	an `sbmmod` model
`...`	additional parameter to 'accept'

Value

an updated sbm object

split move: blocks

Description

split move: blocks

Usage

splitblocks(currblocks, propparams, edges, sbmmod, k)
splitblocks(currblocks, propparams, edges, sbmmod, k)

Arguments

`currblocks`	current blocks
`propparams`	proposed parameters
`edges`	an `edges` object
`sbmmod`	a model list
`k`	block to split

Value

list(proposed block structure, log-acceptance-prob)

split move: parameters

Description

split move: parameters

Usage

splitparams(x, ...)
splitparams(x, ...)

Arguments

`x`	object for dispatch
`...`	additional arguments for method

Value

list(proposed_params, log-acceptance-prob)

split move: `params`

Description

split move: params

Usage

## S3 method for class 'numeric'
splitparams(theta, u, x, parammod)
## S3 method for class 'numeric'
splitparams(theta, u, x, parammod)

Arguments

`theta`	a parameter to split
`u`	auxiliary variable
`x`	auxiliary variable
`parammod`	`parammod` object

Value

list(proposed_params, log-acceptance-prob)

split move: `params`

Description

split move: params

Usage

## S3 method for class 'params'
splitparams(params, k, parammod)
## S3 method for class 'params'
splitparams(params, k, parammod)

Arguments

`params`	a `params` object to split
`k`	block to split
`parammod`	`parammod` object

Value

list(proposed_params, log-acceptance-prob)

The Stack-Overflow data set as extracted from `igraph` using the script in data-raw Extracted on 27/8/2019 from Kaggle (login required) using: `library(rvest)` `read_html("https://www.kaggle.com/stackoverflow/stack-overflow-tag-network/downloads/stack_network_links.csv/1")`

Description

The Stack-Overflow data set as extracted from igraph using the script in data-raw Extracted on 27/8/2019 from Kaggle (login required) using: library(rvest) read_html("https://www.kaggle.com/stackoverflow/stack-overflow-tag-network/downloads/stack_network_links.csv/1")

Usage

StackOverflow
StackOverflow

Format

An edges object of activation counts between brain regions in a Macaque

Source

https://www.kaggle.com/stackoverflow/stack-overflow-tag-network/

Update the block assignment of a node

Description

change the block assignment in x of a node to a new block

Usage

updateblock(x, ...)
updateblock(x, ...)

Arguments

`x`	object for dispatch
`...`	additional arguments for method

Value

object like 'x' with updated block structure

Update the block assignment of a node

Description

change the block assignment in an blocks object to a new block

Usage

## S3 method for class 'blocks'
updateblock(blocks, i, newblock)
## S3 method for class 'blocks'
updateblock(blocks, i, newblock)

Arguments

`blocks`	a `blocks` object
`i`	the node to update
`newblock`	the new block for node i

Value

new blocks object

Update the block assignment of a node

Description

change the block assignment in an sbm object to a new block

Usage

## S3 method for class 'sbm'
updateblock(currsbm, i, newblock, model)
## S3 method for class 'sbm'
updateblock(currsbm, i, newblock, model)

Arguments

`currsbm`	an `sbm` object
`i`	the node to update
`newblock`	the new block for node i
`model`	an `sbmmod` object

Value

new sbm object

Note

If adding a new block, this draws from the prior

V-measure

Description

Calculate the V-measure of two clusterings

Usage

vmeasure(z, truez, beta = 1)
vmeasure(z, truez, beta = 1)

Arguments

`z`	input vector
`truez`	reference vector
`beta`	parameter `beta=1` gives equal weight to homogeneity and completeness

Details

An information based measure of similarity between two clusterings

Value

v-measure of z against truez

Examples

vmeasure(c(1,1,2,2,3,3), c(2,2,1,1,3,3)) ## 1 - doesn't care for labels
vmeasure(c(1,1,2,2,3,3), c(1,1,2,2,2,2)) ## 0.7333
vmeasure(c(1,1,2,2,3,3), c(1,1,2,2,3,4)) ## 0.904
vmeasure(c(1,1,2,2,3,3), c(2,2,1,1,3,3)) ## 1 - doesn't care for labels
vmeasure(c(1,1,2,2,3,3), c(1,1,2,2,2,2)) ## 0.7333
vmeasure(c(1,1,2,2,3,3), c(1,1,2,2,3,4)) ## 0.904

Package 'SBMSplitMerge'

Help Index

accept propsbm with the acceptance probability alpha

Description

Usage

Arguments

Value

Add a block move

Description

Usage

Arguments

Value

Adjusted Rand Index

Description

Usage

Arguments

Value

Examples

Block matrix

Description

Usage

Arguments

Value

See Also

Block matrix

Description

Usage

Arguments

Value

Block matrix

Description

Usage

Arguments

Value

Block matrix

Description

Usage

Arguments

Value

Block Model

Description

Usage

Arguments

Details

Value

See Also

Blocks object

Description

Usage

Arguments

Details

Value

Examples

plot a trace of the blocks from MCMC samples

Description

Usage

Arguments

Value

Chinese Restaurant Process

Description

Usage

Arguments

Details

Value

Examples

Dirichlet distribution

Description

Usage

Arguments

Value

Examples

Density of edges

Description

Usage

Arguments

Value

See Also

likelihood of edges

Description

Usage

accept `propsbm` with the acceptance probability alpha