directed_factor_model {fastRG}

Create a directed factor model graph

Description

A directed factor model graph is a directed generalized Poisson random dot product graph. The edges in this graph are assumpted to be independent and Poisson distributed. The graph is parameterized by its expected adjacency matrix, with is ⁠E[A] = X S Y'⁠. We do not recommend that causal users use this function, see instead directed_dcsbm() and related functions, which will formulate common variants of the stochastic blockmodels as undirected factor models with lots of helpful input validation.

Usage

directed_factor_model(
  X,
  S,
  Y,
  ...,
  expected_in_degree = NULL,
  expected_out_degree = NULL,
  expected_density = NULL,
  poisson_edges = TRUE,
  allow_self_loops = TRUE
)

Arguments

X

A matrix() or Matrix() representing real-valued latent node positions encoding community structure of incoming edges. Entries must be positive.

S

A matrix() or Matrix() mixing matrix. Entries must be positive.

Y

A matrix() or Matrix() representing real-valued latent node positions encoding community structure of outgoing edges. Entries must be positive.

...

Ignored. For internal developer use only.

expected_in_degree

If specified, the desired expected in degree of the graph. Specifying expected_in_degree simply rescales S to achieve this. Defaults to NULL. Specify only one of expected_in_degree, expected_out_degree, and expected_density.

expected_out_degree

If specified, the desired expected out degree of the graph. Specifying expected_out_degree simply rescales S to achieve this. Defaults to NULL. Specify only one of expected_in_degree, expected_out_degree, and expected_density.

expected_density

If specified, the desired expected density of the graph. Specifying expected_density simply rescales S to achieve this. Defaults to NULL. Specify only one of expected_in_degree, expected_out_degree, and expected_density.

poisson_edges

Logical indicating whether or not multiple edges are allowed to form between a pair of nodes. Defaults to TRUE. When FALSE, sampling proceeds as usual, and duplicate edges are removed afterwards. Further, when FALSE, we assume that S specifies a desired between-factor connection probability, and back-transform this S to the appropriate Poisson intensity parameter to approximate Bernoulli factor connection probabilities. See Section 2.3 of Rohe et al. (2017) for some additional details.

allow_self_loops

Logical indicating whether or not nodes should be allowed to form edges with themselves. Defaults to TRUE. When FALSE, sampling proceeds allowing self-loops, and these are then removed after the fact.

Value

A directed_factor_model S3 class based on a list with the following elements:

• X: The incoming latent positions as a Matrix() object.

• S: The mixing matrix as a Matrix() object.

• Y: The outgoing latent positions as a Matrix() object.

• n: The number of nodes with incoming edges in the network.

• k1: The dimension of the latent node position vectors encoding incoming latent communities (i.e. in X).

• d: The number of nodes with outgoing edges in the network. Does not need to match n – rectangular adjacency matrices are supported.

• k2: The dimension of the latent node position vectors encoding outgoing latent communities (i.e. in Y).

• poisson_edges: Whether or not the graph is taken to be have Poisson or Bernoulli edges, as indicated by a logical vector of length 1.

• allow_self_loops: Whether or not self loops are allowed.

Examples

n <- 10000

k1 <- 5
k2 <- 3

d <- 5000

X <- matrix(rpois(n = n * k1, 1), nrow = n)
S <- matrix(runif(n = k1 * k2, 0, .1), nrow = k1, ncol = k2)
Y <- matrix(rexp(n = k2 * d, 1), nrow = d)

fm <- directed_factor_model(X, S, Y)
fm

fm2 <- directed_factor_model(X, S, Y, expected_in_degree = 50)
fm2