Temporal Bayesian Information Criterion (Score criterion)

A Reference Class for Gaussian Observational Data Scoring with Tiered Background Knowledge. This class represents a score for causal discovery using tiered background knowledge from observational Gaussian data; it is used in the causal discovery function tges().

Arguments

data: A numeric matrix with \(n\) rows and \(p\) columns. Each row corresponds to one observational realization.
nodes: A character vector of variable names corresponding to the columns of the data.
lambda: Penalization constant (see details).
intercept: Logical; indicates whether an intercept is allowed in the linear structural equations (i.e., whether a nonzero mean is allowed).
format: Character; either "raw" or "scatter". If "raw", the score is calculated from the raw data matrix. If "scatter", the score is calculated from pre-calculated scatter matrices.
knowledge: A Knowledge object.
debug: Logical; indicates whether to perform validation of the vertex and parents in every local score calculation. Setting this to TRUE will slow down the algorithm, but may be useful for debugging.

Details

The class implements a score which scores all edges contradicting the ordering (edge going from a later tier to an earlier) to minus \(\infty\). If the edges does not contradict, the score is equal to that of the standard BIC. The class implements an \(\ell_0\)-penalized Gaussian maximum likelihood estimator. The penalization is a constant (specified by the argument lambda in the constructor) times the number of parameters of the DAG model. By default, the constant \(\lambda\) is chosen as \(\log(n)/2\), which corresponds to the BIC score.

Extends

Class GaussL0penObsScore from pcalg, directly.

All reference classes extend and inherit methods from envRefClass.

Constructor


new(
 "TemporalBIC",
 data = matrix(1, 1, 1),
 order =  rep(1,ncol(data)),
 lambda = 0.5 * log(nrow(data)),
 intercept = TRUE,
 ...
)

Author

Tobias Ellegaard Larsen

Examples

# Simulate Gaussian data
set.seed(1405)
n <- 500
child_x <- rnorm(n)
child_y <- 0.5 * child_x + rnorm(n)
child_z <- 2 * child_x + child_y + rnorm(n)

adult_x <- child_x + rnorm(n)
adult_z <- child_z + rnorm(n)
adult_w <- 2 * adult_z + rnorm(n)
adult_y <- 2 * child_x + adult_w + rnorm(n)

simdata <- data.frame(
  child_x,
  child_y,
  child_z,
  adult_x,
  adult_z,
  adult_w,
  adult_y
)

# Define order in prefix way
kn <- knowledge(
  simdata,
  tier(
    child ~ tidyselect::starts_with("child"),
    adult ~ tidyselect::starts_with("adult")
  )
)

# Define TBIC score
t_score <- new("TemporalBIC", knowledge = kn, data = simdata)
# Run tges
tges_pre <- tges_run(t_score)

# Plot MPDAG
# plot(tges_pre)