param_learn {gmgm}

Learn the parameters of a Gaussian mixture graphical model

Description

This function learns the parameters of a Gaussian mixture graphical model. Using the local decomposability of the log-likelihood, this task consists in learning each local conditional model independently with the EM algorithm (Koller and Friedman, 2009).

Usage

param_learn(
  gmgm,
  data,
  nodes = structure(gmgm)$nodes,
  col_seq = NULL,
  verbose = FALSE,
  ...
)

Arguments

gmgm

An initial object of class gmbn or gmdbn.

data

A data frame containing the data used for learning. Its columns must explicitly be named after the nodes of gmgm and must not contain missing values.

nodes

A character vector containing the nodes whose local conditional models are learned (by default all the nodes of gmgm). If gmgm is a gmdbn object, the same nodes are learned for each of its gmbn elements. This constraint can be overcome by passing a list of character vectors named after some of these elements (b_1, ...) and containing learned nodes specific to them.

col_seq

A character vector containing the column names of data that describe the observation sequence. If NULL (the default), all the observations belong to a single sequence. If gmgm is a temporal gmbn or gmdbn object, the observations of a same sequence must be ordered such that the tth one is related to time slice t (note that the sequences can have different lengths). If gmgm is a non-temporal gmbn object, this argument is ignored.

verbose

A logical value indicating whether learned nodes in progress are displayed.

...

Additional arguments passed to function em.

Value

A list with elements:

gmgm

The final gmbn or gmdbn object.

evol_loglik

A list with elements:

global

A numeric vector containing the global log-likelihood before and after learning.

local

For a gmbn object, a numeric matrix containing the local conditional log-likelihoods before and after learning. For a gmdbn object, a list of numeric matrices containing these values for each gmbn element.

References

Koller, D. and Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques. The MIT Press.

See Also

param_em, struct_em, struct_learn

Examples

data(data_body)
gmbn_1 <- gmbn(
  AGE = split_comp(add_var(NULL, data_body[, "AGE"]), n_sub = 3),
  FAT = split_comp(add_var(NULL,
                           data_body[, c("FAT", "GENDER", "HEIGHT", "WEIGHT")]),
                   n_sub = 2),
  GENDER = split_comp(add_var(NULL, data_body[, "GENDER"]), n_sub = 2),
  GLYCO = split_comp(add_var(NULL, data_body[, c("GLYCO", "AGE", "WAIST")]),
                     n_sub = 2),
  HEIGHT = split_comp(add_var(NULL, data_body[, c("HEIGHT", "GENDER")])),
  WAIST = split_comp(add_var(NULL,
                             data_body[, c("WAIST", "AGE", "FAT", "HEIGHT",
                                           "WEIGHT")]),
                     n_sub = 3),
  WEIGHT = split_comp(add_var(NULL, data_body[, c("WEIGHT", "HEIGHT")]),
                      n_sub = 2)
)
res_learn_1 <- param_learn(gmbn_1, data_body, verbose = TRUE)

library(dplyr)
data(data_air)
data <- data_air %>%
  group_by(DATE) %>%
  mutate(NO2.1 = lag(NO2), O3.1 = lag(O3), TEMP.1 = lag(TEMP),
         WIND.1 = lag(WIND)) %>%
  ungroup()
gmdbn_1 <- gmdbn(
  b_2 = gmbn(
    NO2 = split_comp(add_var(NULL, data[, c("NO2", "NO2.1", "WIND")]),
                     n_sub = 3),
    O3 = split_comp(add_var(NULL,
                            data[, c("O3", "NO2", "NO2.1", "O3.1", "TEMP",
                                     "TEMP.1")]),
                    n_sub = 3),
    TEMP = split_comp(add_var(NULL, data[, c("TEMP", "TEMP.1")]), n_sub = 3),
    WIND = split_comp(add_var(NULL, data[, c("WIND", "WIND.1")]), n_sub = 3)
  ),
  b_13 = gmbn(
    NO2 = split_comp(add_var(NULL, data[, c("NO2", "NO2.1", "WIND")]),
                     n_sub = 3),
    O3 = split_comp(add_var(NULL,
                            data[, c("O3", "O3.1", "TEMP", "TEMP.1", "WIND")]),
                    n_sub = 3),
    TEMP = split_comp(add_var(NULL, data[, c("TEMP", "TEMP.1")]), n_sub = 3),
    WIND = split_comp(add_var(NULL, data[, c("WIND", "WIND.1")]), n_sub = 3)
  )
)
res_learn_2 <- param_learn(gmdbn_1, data_air, col_seq = "DATE", verbose = TRUE)