undirected_factor_model(). See below for details (#19). This also caused population singular values for undirected factors models to be off by a factor of 2 (#31).Specifying both k and B in dcsbm() and sbm() now results in an error. You should only specify one of these arguments.
It is now possible to specify the precise number of nodes in each block of a dcsbm() (and subclasses sbm() and planted_partition()) via the block_sizes argument. This makes it easier to construct blockmodels with exactly repeated eigenvalues. Additionally, the default behavior is now to use this argument and to balance block sizes as evenly as possible. Previously, the default behavior was to sample blocks memberships with equal probability.
vignette("consistency") demonstrating how to check consistency of spectral estimators using fastRG for sampling and population spectra computations (#33, #43)The fastRG sampling algorithm, as implemented in sample_edgelist.matrix(), is fundamentally a sampler for asymmetric, directed networks with conditional expectation $\mathbb E[A \mid X, S, Y] = X S Y^\top \in \mathbb R^{n_1 \times n_2}$. That is, you can think of the sampler as a very efficient procedure for iterating through $i = 1, ..., n_1$ and $j = 1, ..., n_2$ and sampling from a Poisson with rate $(X S Y^\top)_{ij}$.
However, we would also like to use this same sampler to sample from undirected networks. In an undirected networks, the conditional expectation $\mathbb E[A \mid X, S] = X S X^\top \in \mathbb R^{n \times n}$ is a square matrix with $(X S X^\top){ij} = (X S X^\top){ji}$. To sample from this matrix, it's typical to sample the upper triangle of $A$ from a Poisson with rate $(X S X^\top)_{ij}$ for all $1 \le i \le j \le n$, and then fill the lower triangle of $A$ to make $A$ symmetric.
Since the fastRG algorithm samples $A_{ij}$ for all $i, j$, not just the upper triangle of $A$, we use a trick to sample from undirected networks. First, we force the conditional expectation to be symmetric by symmetrizing $S$. Then, we still sample for all $i, j$. That is, to set $A_{ij}$ we sample once from a Poisson with rate $(X S X^\top){ij}$ and once from a Poisson with rate $(X S X^\top){ji}$ (these rates are equal by symmetry!). Then we set $A_{ij} = A_{ji}$ to the sum of these Poisson random variables. The issue is that this doubles the expected value of $A_{ij} = A_{ji}$ and so we sample twice as many edges as we should. Up until this release of fastRG, we've unfortunately been doing this double sampling in undirected networks (#19).
In this release, we fix this over-sampling. The key is that we divide $S$ by two at sampling time. We do not modify $S$ at all in the undirected_factor_model()! You can always use $X S X^\top$ to compute the expected value of $A$. This new change only affects sampling.
That is, instead of passing the $S$ from an undirected_factor_model() to the sampler sample_edgelist.matrix(), we pass $S / 2$ (see sample_edgelist.undirected_factor_model()). This fixes double sampling on the off-diagonal of $A$. The downside is that we're now undersampling by half the diagonal of $A$. I'm assuming that for most use cases this doesn't matter. We could correct for this undersampling of the diagonal of $A$, so please open an issue if self-loops are important to your project.
As a consequence of this change, $A$ and $\mathbb E[A | X, S]$ show now be on the same scale, rather than off by a factor of 2. Importantly, the spectrums should match up now, so you can now use fastRG to check how closely you're recovering the spectrum of the your model. See vignette("consistency") for a quick demonstration showing consistency of spectral estimates.
sort_nodes = TRUE (#35). Blocks are now only sorted when sort_nodes = TRUE, although they were previously always sorted. In directed stochastic blocks, flipped incoming and outgoing blocks, such that X now contains info about outgoing blocks and Y now contains info about incoming blocks, as you would expected if A[i, j] encodes an edge from node i to node jplot_expectation(), plot_sparse_matrix() and expectation() utilities (#34)expected_degrees() (#34)poisson_edges and allow_self_loops arguments to model object constructors (i.e. sbm()) rather than sample_*() methods. Additionally, when poisson_edges = FALSE, the mixing matrix S is taken (after degree-scaling and possible symmetrization for undirected models) to represent desired inter-factor connection probabilities, and thus should be between zero and one. This Bernoulli-parameterized S is then transformed into the equivalent (or approximately equivalent) Poisson S. See Section 2.3 of Rohe et al. (2017) for additional details about this conversion and approximation of Bernoulli graphs by Poisson graphs (#29).force_identifiability = TRUE, and in overlapping SBMs with force_pure = TRUE, which are now the default.theta_out is automatically generated for directed DC-SBMs (#22)svds() and eigs_sym() methods, which allow users to take spectral decompositions of expected adjacency matrices conditional X, S and Y.NEWS.md file to track changes to the package.