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Sparse Matrices

Source: vignettes/Sparse matrices.Rmd
Sparse matrices.Rmd

1) Introduction

Starting with the 0.9.7 version released in March 2020, the naivebayes R package introduces specialized implementations of the Naïve Bayes model that support sparse matrices. These implementations include:

  • multinomial_naive_bayes(): Specifically designed for multinomial data, this function handles cases where the features are discrete and have multiple categories (e.g., word counts for text classification).
  • bernoulli_naive_bayes(): Ideal for binary data, this function handles cases where the features are binary (0 or 1).
  • poisson_naive_bayes() Tailored for count data, this function is suitable for situations where the features represent counts or frequencies.
  • gaussian_naive_bayes(): Suitable for continuous data, this function assumes that the features follow a Gaussian (normal) distribution.

Note: nonparametric_naive_bayes currently does not support sparse matrices.

These specialized functions are optimized to take advantage of sparsity, which can significantly enhance computational efficiency. To leverage this capability, users can provide the functions with a matrix of class dgCMatrix from the excellent Matrix1 package. Importantly, this new functionality has been introduced without any breaking changes and aligns with the no-dependency philosophy of the naivebayes project. Users can seamlessly incorporate sparse matrices into their Naïve Bayes modeling workflow, enhancing performance while maintaining compatibility with existing code.

2) Usage

In the provided example, we showcase the training of a Multinomial Naive Bayes model using a simulated sparse matrix. The code snippet demonstrates the steps involved in preparing the data, training the model, and making predictions.

# Simulate ~95% sparse matrix
cols <- 10 ; rows <- 100
M <- matrix(sample(0:5, rows * cols, TRUE, prob = c(0.95, rep(0.01, 5))), 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)))

# Check fraction of zeros
mean(M == 0)
## [1] 0.955
# Cast the matrix to "dgCMatrix" object
M_sparse <- Matrix::Matrix(M, sparse = TRUE)

### Train the Multinomial Naive Bayes and predict the training data
mnb <- naivebayes::multinomial_naive_bayes(x = M_sparse, y = y, laplace = 1)
head(predict(mnb, M_sparse))
## [1] classB classB classB classB classB classB
## Levels: classA classB

In the above code, we start by simulating a sparse matrix M with approximately 95% sparsity. The matrix has 100 rows and 10 columns, filled with random values between 0 and 5. We also generate a corresponding factor variable y representing the class labels.

Next, we check the fraction of zeros in the matrix to confirm its sparsity level. We then cast the matrix M into a “dgCMatrix” object M_sparse using the Matrix::Matrix() function, specifying the sparse = TRUE argument.

Afterward, we proceed to train the Multinomial Naive Bayes model mnb using the naivebayes::multinomial_naive_bayes() function. We provide the sparse matrix M_sparse as the input x, and the class labels y. The laplace = 1 argument is used to apply Laplace smoothing2 3 during model training.

Finally, we demonstrate making predictions on the training data using the predict() function, passing in the trained model mnb and the sparse matrix M_sparse.

It’s important to note that the classifier and the corresponding prediction function automatically recognize the sparse matrix and do not require additional parameters. However, it’s worth mentioning that dense matrices are not internally converted to the dgCMatrix class. If required, such conversions need to be explicitly performed by the user.