Introduction to Bayesian Networks and bnlearn
Bayesian networks are a graphical representation of probabilistic relationships between variables. They are widely used in statistics, machine learning, and data analysis due to their ability to model complex relationships between variables.
In this article, we will explore how to graph a Bayesian network with instantiated nodes using the bnlearn library in R, and how to use graphviz to visualize the networks.
Installing Required Libraries
To start working with Bayesian networks and bnlearn, we need to install the required libraries. First, we’ll install the necessary packages:
install.packages("bnlearn")
install.packages("Rgraphviz")
Once installed, we can load the packages using the following commands:
library(bnlearn)
library(Rgraphviz)
Creating a Bayesian Network
To create a Bayesian network, we need to define the variables and their relationships. This is typically done using a directed acyclic graph (DAG) structure.
Data Preparation
Let’s prepare some sample data for our Bayesian network:
# Generate random data
data_clean <- data.frame(
a = runif(min = 0, max = 100, n = 1000),
b = runif(min = 0, max = 100, n = 1000),
c = runif(min = 0, max = 100, n = 1000),
d = runif(min = 0, max = 100, n = 1000),
e = runif(min = 0, max = 100, n = 1000)
)
# Discretize the data into bins
bins <- 3
data_discrete <- discretize(data_clean, breaks = bins)
# Create factors for each bin in the data
lv <- c("low", "med", "high")
for (i in names(data_discrete)) {
levels(data_discrete[, i]) <- lv
}
Structure Learning and Model Fitting
To structure learn our Bayesian network, we need to define a whitelist of edges that are known to exist between the variables.
# Define the whitelist of edges
whitelist <- matrix(c("a", "b", "b", "c", "c", "e", "a", "d", "d", "e"),
ncol = 2, byrow = TRUE, dimnames = list(NULL, c("from", "to")))
Next, we can structure learn our Bayesian network using the following command:
# Structure learn the DAG from the training set
bn.hc <- hc(data_discrete, whitelist = whitelist)
Plotting the Network
We can plot our Bayesian network using graphviz. First, let’s create an instance of the graph:
# Create factors for each bin in the data
lv <- c("low", "med", "high")
cpt.a <- matrix(c(1, 0, 0), ncol = 3, dimnames = list(NULL, lv))
cpt.c <- c(1, 0, 0,
0, 1, 0,
0, 0, 1)
dim(cpt.c) <- c(3, 3)
dimnames(cpt.c) <- list("c" = lv, "b" = lv)
cpt.b <- c(1, 0, 0,
0, 1, 0,
0, 0, 1)
dim(cpt.b) <- c(3, 3)
dimnames(cpt.b) <- list("b" = lv, "a" = lv)
cpt.d <- c(0, 0, 1,
0, 1, 0,
1, 0, 0)
dim(cpt.d) <- c(3, 3)
dimnames(cpt.d) <- list("d" = lv, "a" = lv)
# Assign the evidence to the nodes
fitted_evidence$a <- cpt.a
fitted_evidence$b <- cpt.b
fitted_evidence$c <- cpt.c
fitted_evidence$d <- cpt.d
# Plotting the DAG with instantiation and posterior for response
graphviz.chart(fitted_evidence, type = "barprob", layout = "dot")
Estimating Posterior Probabilities Using Copula Distribution
Instead of manually instantiating the nodes, we can estimate the updated parameters using copula distribution.
# Estimate the posterior probabilities using cpdist
set.seed(69184390) # for sampling
ev <- list(a = "low", b = "low", c = "low", d = "high")
updated_dat <- cpdist(fitted, nodes=bnlearn::nodes(fitted), evidence=ev, method="lw", n=1e6)
# Refit the network using updated parameters
updated_fit <- bn.fit(bn.hc, data = updated_dat)
Plotting the DAG with Instantiated Nodes
Finally, we can plot our Bayesian network with instantiated nodes and posterior probabilities.
par(mar=rep(0,4))
graphviz.chart(updated_fit, type = "barprob", layout = "dot")
Conclusion
In this article, we’ve explored how to graph a Bayesian network with instantiated nodes using the bnlearn library in R. We discussed structure learning and model fitting, as well as plotting the networks.
We also explored an alternative approach of estimating posterior probabilities using copula distribution, which can be useful for larger networks where manual instantiation becomes impractical.
Last modified on 2023-09-12