gaussian_naive_bayes {naivebayes}

Gaussian Naive Bayes Classifier

Description

gaussian_naive_bayes is used to fit the Gaussian Naive Bayes model in which all class conditional distributions are assumed to be Gaussian and be independent.

Usage

gaussian_naive_bayes(x, y, prior = NULL, ...)

Arguments

x

numeric matrix with metric predictors (matrix or dgCMatrix from Matrix package).

y

class vector (character/factor/logical).

prior

vector with prior probabilities of the classes. If unspecified, the class proportions for the training set are used. If present, the probabilities should be specified in the order of the factor levels.

...

not used.

Details

This is a specialized version of the Naive Bayes classifier, in which all features take on real values (numeric/integer) and class conditional probabilities are modelled with the Gaussian distribution.

The Gaussian Naive Bayes is available in both, naive_bayes and gaussian_naive_bayes.The latter provides more efficient performance though. Faster calculation times come from restricting the data to a matrix with numeric columns and taking advantage of linear algebra operations. Sparse matrices of class "dgCMatrix" (Matrix package) are supported in order to furthermore speed up calculation times.

The gaussian_naive_bayes and naive_bayes() are equivalent when the latter is used with usepoisson = FALSE and usekernel = FALSE; and a matrix/data.frame contains numeric columns.

The missing values (NAs) are omited during the estimation process. Also, the corresponding predict function excludes all NAs from the calculation of posterior probabilities (an informative warning is always given).

Value

gaussian_naive_bayes returns an object of class "gaussian_naive_bayes" which is a list with following components:

data

list with two components: x (matrix with predictors) and y (class variable).

levels

character vector with values of the class variable.

params

list with two matrices, first containing the class conditional means and the second containing the class conditional standard deviations.

prior

numeric vector with prior probabilities.

call

the call that produced this object.

Author(s)

Michal Majka, [e-mail]

See Also

naive_bayes, predict.gaussian_naive_bayes, plot.gaussian_naive_bayes, tables, get_cond_dist, %class%

Examples

# library(naivebayes)
set.seed(1)
cols <- 10 ; rows <- 100
M <- matrix(rnorm(rows * cols, 100, 15), nrow = rows, ncol = cols)
y <- factor(sample(paste0("class", LETTERS[1:2]), rows, TRUE, prob = c(0.3,0.7)))
colnames(M) <- paste0("V", seq_len(ncol(M)))


### Train the Gaussian Naive Bayes
gnb <- gaussian_naive_bayes(x = M, y = y)
summary(gnb)

# Classification
head(predict(gnb, newdata = M, type = "class")) # head(gnb %class% M)

# Posterior probabilities
head(predict(gnb, newdata = M, type = "prob")) # head(gnb %prob% M)

# Parameter estimates
coef(gnb)


### Sparse data: train the Gaussian Naive Bayes
library(Matrix)
M_sparse <- Matrix(M, sparse = TRUE)
class(M_sparse) # dgCMatrix

# Fit the model with sparse data
gnb_sparse <- gaussian_naive_bayes(M_sparse, y)

# Classification
head(predict(gnb_sparse, newdata = M_sparse, type = "class"))

# Posterior probabilities
head(predict(gnb_sparse, newdata = M_sparse, type = "prob"))

# Parameter estimates
coef(gnb_sparse)


### Equivalent calculation with general naive_bayes function.
### (no sparse data support by naive_bayes)

nb <- naive_bayes(M, y)
summary(nb)
head(predict(nb, type = "prob"))

# Obtain probability tables
tables(nb, which = "V1")
tables(gnb, which = "V1")

# Visualise class conditional Gaussian distributions
plot(nb, "V1", prob = "conditional")
plot(gnb, which = "V1", prob = "conditional")

# Check the equivalence of the class conditional distributions
all(get_cond_dist(nb) == get_cond_dist(gnb))