Calculate the expected edges in Poisson RDPG graph

Description

These calculations are conditional on the latent factors X and Y.

Usage

expected_edges(factor_model, ...)

expected_degree(factor_model, ...)

expected_in_degree(factor_model, ...)

expected_out_degree(factor_model, ...)

expected_density(factor_model, ...)

expected_degrees(factor_model, ...)

Arguments

Details

Note that the runtime of the fastRG algorithm is proportional to the expected number of edges in the graph. Expected edge count will be an underestimate of expected number of edges for Bernoulli graphs. See the Rohe et al for details.

Value

Expected edge counts, or graph densities.

References

Rohe, Karl, Jun Tao, Xintian Han, and Norbert Binkiewicz. 2017. "A Note on Quickly Sampling a Sparse Matrix with Low Rank Expectation." Journal of Machine Learning Research; 19(77):1-13, 2018. https://www.jmlr.org/papers/v19/17-128.html

Examples

##### an undirected blockmodel example

n <- 1000
pop <- n / 2
a <- .1
b <- .05

B <- matrix(c(a,b,b,a), nrow = 2)

b_model <- fastRG::sbm(n = n, k = 2, B = B, poisson_edges = FALSE)

b_model

A <- sample_sparse(b_model)

# compare
mean(rowSums(triu(A)))

pop * a + pop * b  # analytical average degree

##### more generic examples

n <- 10000
k <- 5

X <- matrix(rpois(n = n * k, 1), nrow = n)
S <- matrix(runif(n = k * k, 0, .1), nrow = k)

ufm <- undirected_factor_model(X, S)

expected_edges(ufm)
expected_degree(ufm)
eigs_sym(ufm)

n <- 10000
d <- 1000

k1 <- 5
k2 <- 3

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

dfm <- directed_factor_model(X = X, S = S, Y = Y)

expected_edges(dfm)
expected_in_degree(dfm)
expected_out_degree(dfm)

svds(dfm)