mMRFfit: Estimating mixed Markov fields

In jmbh/mMRF: Estimating mixed Markov random fields

Description

Estimates a mixed Markov random field using L1-constrained neighborhood regression.

Usage

mMRFfit(data, type, lev, lambda.sel="CV", folds = 10, gam = .25, d=1, rule.reg = "AND", rule.cat = "OR", pbar = "TRUE")

Arguments

data	n x p data matrix
type	p-vector containing the types of variable ("g" Gaussian, "e" Exponential, "p" Poisson, "c" Categorical)
lev	p-vector containing the number of levels for each variable p (lev=1 for all continuous variables)
lambda.sel	Procedure to select the lambda-parameter for L1-penalized regressions. The two options are cross validation "CV" (default) and "EBIC"; While cross validation is used in the paper (see below), the Extended Bayesian Information Criterion (EBIC, see Barber et al., 2015) is a useful alternative in cases where the cross validation-requirement that all categories are present in each fold is not met, because some categories are only present in few cases.
folds	The number of folds to be used for cross-validation in case lambda.sel="CV". Defaults to folds=10.
gam	Gamma hyperparameter when lambda.sel="EBIC". Defaults to gam=.25 (Barber et al., 2015)
d	Degrees of augmented interactions. The degree of augmented interactions reflects our belief about the maximal degree in the true graph. (see Loh & Wainwright, 2013)
rule.cat	Rule for combining parameters of interactions including categorical variables. The default, the "OR"-rule sets an edge to present when at least one parameter is non-zero. This corresponds to a conditional independence graph (Markov random field). Optionally, one can provide a matrix with the dimension of the parameter matrix to specify a costumized rule when to set an edge to present. Ones in this matrix indicate, that the parameter has to be present to render the corresponding edge present and a zero indicates that the parameter does not have to be zero in order to render the corresponding edge present. A matrix of ones would indicate that for each interaction, all parameters have to be nonzero to render the corresponding edge present. A matrix of zeros is equivalent to the "OR"-rule. For details see [REFERENCE TO JSTAT PAPER]. The "OR"-rule determines conditional dependence if at least one parameter is non-zero. The "AND"-rule determines conditional dependence if all parameters are non-zero.
rule.reg	Rule for combining the two parameters obtained for each edge due to the neighborhood-regression approach. The "OR"-rule determines conditional dependence if at least one of the two parameters is non-zero, the "AND"-rule determines conditional dependence if both parameters are non-zero.

Value

Returns a list containing:

adj	Adjacency matrix
wadj	Weighted adjacency matrix; Please note that the parameters of interactions including categorical variables are not interpretable; for the actual interaction parameters inspect wpar.matrix
wpar.matrix	Weighted model parameter matrix; This matrix is has the dimension of an overcomplete covariance matrix. By deleting empty columns/rows one obtains the minimal representation. It is given to enable the user to to inspect the exact interaction parameters involving categorical variables, which are (arbitrarily) aggregated in wadj by "rule.cat" (see above)
lambda	p x 2 matrix containing the L1 lambda parameter (selected with CV or EBIC) and the tau threshold (see Loh & Wainwright, 2013)

Author(s)

Jonas Haslbeck

References

Barber, R. F., & Drton, M. (2015). High-dimensional Ising model selection with Bayesian information criteria. Electronic Journal of Statistics, 9, 567-607.

Loh, P. L., & Wainwright, M. J. (2013). Structure estimation for discrete graphical models: Generalized covariance matrices and their inverses. The Annals of Statistics, 41(6), 3022-3049.

Yang, E., Baker, Y., Ravikumar, P., Allen, G., & Liu, Z. (2014). Mixed graphical models via exponential families. In Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics (pp. 1042-1050).

Examples

head(data_mixed) #example data

type <- c("c", "g", "p", "g") #data contains a categorical, a gaussian, a poisson and a gaussian variable in that order
lev <- c(3, 1, 1, 1) # the categorical variable has three categories

mMRFfit(data=data_mixed,  
        type=type,
        lev=lev,
        lambda.sel="CV",
        d=1, 
        rule.cat="OR",
        rule.reg="AND")
        

jmbh/mMRF documentation built on May 19, 2019, 1:51 p.m.