GaussL0penObsScore-class function

Class "GaussL0penObsScore"

This class represents a score for causal inference from observational Gaussian data; it is used in the causal inference function ges. class

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Details

The class implements an $ℓ0$-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 $λ$ is chosen as $log(n)/2$, which corresponds to the BIC score.

Extends

Class "Score", directly.

All reference classes extend and inherit methods from "envRefClass".

Fields

The class GaussL0penObsScore has the same fields as Score. They need not be accessed by the user.

Constructor

new("GaussL0penObsScore",
  data = matrix(1, 1, 1),
  lambda = 0.5*log(nrow(data)), 
  intercept = TRUE, 
  use.cpp = TRUE, 
  ...)

• data: Data matrix with $n$ rows and $p$ columns. Each row corresponds to one observational realization.
• lambda: Penalization constant (cf. details)
• intercept: Indicates whether an intercept is allowed in the linear structural equations, or, equivalently, if a mean different from zero is allowed for the observational distribution.
• use.cpp: Indicates whether the calculation of the score should be done by the C++ library of the package, which speeds up calculation. This parameter should only be set to FALSE in the case of problems.

Methods

• local.score(vertex, parents, ...): Calculates the local score of a vertex and its parents. Since this score has no obvious interpretation, it is rather for internal use.

• global.score.int(edges, ...): Calculates the global score of a DAG, represented as a list of in-edges: for each vertex in the DAG, this list contains a vector of parents.

• global.score(dag, ...): Calculates the global score of a DAG, represented as an object of a class derived from ParDAG.

• local.mle(vertex, parents, ...): Calculates the local MLE of a vertex and its parents. The result is a vector of parameters encoded as follows:

    * First element: variance of the Gaussian error term
    * Second element: intercept
    * Following elements: regression coefficients; one per parent vertex
  

• global.mle(dag, ...): Calculates the global MLE of a DAG, represented by an object of a class derived from ParDAG. The result is a list of vectors, one per vertex, each in the same format as the result vector of local.mle.

Author(s)

Alain Hauser (alain.hauser@bfh.ch )

Examples

##################################################
## Using Gaussian Data
##################################################
## Load predefined data
data(gmG)

## Define the score object
score <- new("GaussL0penObsScore", gmG$x) 

## Score of the true underlying DAG
score$global.score(as(gmG$g, "GaussParDAG"))

## Score of the DAG that has only one edge from 1 to 2
A <- matrix(0, ncol(gmG$x), ncol(gmG$x))
A[1, 2] <- 1
score$global.score(as(A, "GaussParDAG"))
## (Note: this is lower than the score of the true DAG.)

See Also

ges, GaussL0penIntScore, Score