Prediction of continuous variable using "bnlearn" package in R

Question

I use bnlearn package in R to learn the structure of my Bayesian Network and its parameters. What I want to do is to "predict" the value of a node given the value of other nodes as evidence (obviously, with the exception of the node whose values we are predicting).

I have continuous variables.

library(bnlearn)                       # Load the package in R
data(gaussian.test)
training.set = gaussian.test[1:4000, ] # This is training set to learn the parameters
test.set = gaussian.test[4001:4010, ]  # This is test set to give as evidence
res = hc(training.set)                 # learn BN structure on training set data 
fitted = bn.fit(res, training.set)     # learning of parameters
pred = predict(fitted$C, test.set)     # predicts the value of node C given test set
table(pred, test.set[, "C"])           # compares the predicted value as original

Now, this code works well and gives a table in which you can see that predicted values for node C are exactly same as the original value of node C in test set.

I do not understand the reason for that, could someone please explain it?

I know, I am providing entire df of test set that already has the value of node C in it. But if I give the data of other columns, it gives an error. So, I tried an alternative of putting other values to 0.

test.set$C = 0                     # To not give the original value of node C as evidence
pred = predict(fitted$C, test.set) # predicts the value of node C given test set
table(pred, test.set[, "C"])       # compares the predicted value as original

Is this approach wrong? (Using "NA" is not allowed.)

Answer 1

Why are you using table to compare the output? Using cbind to put the actual and predicted values side by side shows that the predictions are not the same as the actual, and you can compute standard accuracy metrics to quantify the degree to which they diverge.

library(bnlearn)                       # Load the package in R
library(forecast)

data(gaussian.test)
training.set = gaussian.test[1:4000, ] # This is training set to learn the parameters
test.set = gaussian.test[4001:4010, ]  # This is test set to give as evidence
res = hc(training.set)                 # learn BN structure on training set data 
fitted = bn.fit(res, training.set)     # learning of parameters
pred = predict(fitted, "C", test.set)  # predicts the value of node C given test set
cbind(pred, test.set[, "C"])           # compare the actual and predicted
accuracy(f = pred, x = test.set[, "C"])

Comparing the actual and predicted:

> cbind(predicted = pred, actual = test.set[, "C"])           
       predicted    actual
 [1,]  3.5749952  3.952410
 [2,]  0.7434548  1.443177
 [3,]  5.1731669  5.924198
 [4,] 10.0840800 10.296560
 [5,] 12.3966908 12.268170
 [6,]  9.1834888  9.725431
 [7,]  6.8067145  5.625797
 [8,]  9.9246630  9.597326
 [9,]  5.9426798  6.503896
[10,] 16.0056136 16.037176

Measuring accuracy of prediction:

> accuracy(f = pred, x = test.set[, "C"])
                ME      RMSE       MAE      MPE     MAPE
Test set 0.1538594 0.5804431 0.4812143 6.172352 11.26223

Answer 2

For both the predicted sets you proposed (with both the Original values and zeros) I found the same output in R.

[1]  3.5749952  0.7434548  5.1731669 10.0840800 12.3966908  9.1834888  6.8067145
[8]  9.9246630  5.9426798 16.0056136

This shows that the values of C are irrelevant. Furthermore, test.set$c provides you with:

[1]  3.952410  1.443177  5.924198 10.296560 12.268170  9.725431  5.625797  9.597326
[9]  6.503896 16.037176

which is inherently different from the predicted output. This leads me to believe that your code is in fact correct.

Answer 3

The equivalent for the discrete case occurs (inability to set the target variable to zero). In this case do the following:

test.set\$TARGET<-as.factor(0)  
levels(test.set\$TARGET) <- c(level1,level2,level3...)