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Recommend a covariance backend from a network topology

Source: R/03_02_covariance_backends.R
covariance_structure_from_graph_model.Rd

Maps a graph_model name (see generate_random_network_skeleton()) to the covariance-factorisation structure most likely to help. This encodes the decision-tree workflow: the dense Cholesky is always a safe default; the structured backends are refinements when the covariance (not merely the precision) inherits exploitable structure.

Usage

covariance_structure_from_graph_model(graph_model)

Arguments

graph_model

One of "erdos_renyi", "hub", "star", "scale_free", "stochastic_block_model", "small_world", "band", "ar". Matching is case-insensitive.

Value

A single string: one of "dense", "block", "band", "sparse", "diag_lowrank".

Details

A sparse gene-network precision matrix \(\boldsymbol{\Omega}_j=\boldsymbol{\Sigma}_j^{-1}\) does not imply a sparse covariance \(\boldsymbol{\Sigma}_j\); the inverse of a sparse precision is generally dense. The mapping below therefore expresses modelling intent, and the returned structure only accelerates the likelihood when \(\boldsymbol{\Sigma}(\boldsymbol{p})\) itself (or a cheap representation of it) has that structure. Disconnected gene modules give an exactly block-diagonal covariance; shared regulatory programs give a diagonal-plus-low-rank covariance; a small set of bridge / housekeeping hubs gives an arrow pattern handled by the Schur complement.

See also

new_decovart_covariance()

Examples

covariance_structure_from_graph_model("stochastic_block_model")
#> [1] "block"
covariance_structure_from_graph_model("erdos_renyi")
#> [1] "sparse"