smoothing: Perform smoothing inference in a Gaussian mixture dynamic Bayesian network

Description

This function performs smoothing inference in a Gaussian mixture dynamic Bayesian network. For a sequence of \(T\) time slices, this task consists in estimating the state of the system at each time slice \(t\) (for \(1 \le t \le T\)) given all the data (the evidence) collected up to \(T\). Smoothing inference is performed by sequential importance resampling, which is a particle-based approximate method (Koller and Friedman, 2009).

Usage

smoothing(
  gmdbn,
  evid,
  nodes = names(gmdbn$b_1),
  col_seq = NULL,
  n_part = 1000,
  max_part_sim = 1e+06,
  min_ess = 1,
  verbose = FALSE
)

Value

A data frame (tibble) with a structure similar to evid

containing the estimated values of the inferred nodes and their observation sequences (if col_seq is not NULL).

Arguments

gmdbn: An object of class gmdbn.
evid: A data frame containing the evidence. Its columns must explicitly be named after nodes of gmdbn and can contain missing values (columns with no value can be removed).
nodes: A character vector containing the inferred nodes (by default all the nodes of gmdbn).
col_seq: A character vector containing the column names of evid that describe the observation sequence. If NULL (the default), all the observations belong to a single sequence. The observations of a same sequence must be ordered such that the \(t\)th one is related to time slice \(t\) (note that the sequences can have different lengths).
n_part: A positive integer corresponding to the number of particles generated for each observation sequence.
max_part_sim: An integer greater than or equal to n_part corresponding to the maximum number of particles that can be processed simultaneously. This argument is used to prevent memory overflow, dividing evid into smaller subsets that are handled sequentially.
min_ess: A numeric value in [0, 1] corresponding to the minimum ESS (expressed as a proportion of n_part) under which the renewal step of sequential importance resampling is performed. If 1 (the default), this step is performed at each time slice.
verbose: A logical value indicating whether subsets of evid and time slices in progress are displayed.

References

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

Examples

Run this code

# \donttest{
set.seed(0)
data(gmdbn_air, data_air)
evid <- data_air
evid$NO2[sample.int(7680, 1536)] <- NA
evid$O3[sample.int(7680, 1536)] <- NA
evid$TEMP[sample.int(7680, 1536)] <- NA
evid$WIND[sample.int(7680, 1536)] <- NA
smooth <- smoothing(gmdbn_air, evid, col_seq = "DATE", verbose = TRUE)# }