lda_emp_bayes {sparsediscrim}

The Minimum Distance Empirical Bayesian Estimator (MDEB) classifier

Description

Given a set of training data, this function builds the MDEB classifier from Srivistava and Kubokawa (2007). The MDEB classifier is an adaptation of the linear discriminant analysis (LDA) classifier that is designed for small-sample, high-dimensional data. Rather than using the standard maximum likelihood estimator of the pooled covariance matrix, Srivastava and Kubokawa (2007) have proposed an Empirical Bayes estimator where the eigenvalues of the pooled sample covariance matrix are shrunken towards the identity matrix: the shrinkage constant has a closed form and is quick to calculate.

The MDEB classifier from Srivistava and Kubokawa (2007) is an adaptation of the linear discriminant analysis (LDA) classifier that is designed for small-sample, high-dimensional data. Rather than using the standard maximum likelihood estimator of the pooled covariance matrix, Srivastava and Kubokawa (2007) have proposed an Empirical Bayes estimator where the eigenvalues of the pooled sample covariance matrix are shrunken towards the identity matrix: the shrinkage constant has a closed form and is quick to calculate

Usage

lda_emp_bayes(x, ...)

## Default S3 method:
lda_emp_bayes(x, y, prior = NULL, ...)

## S3 method for class 'formula'
lda_emp_bayes(formula, data, prior = NULL, ...)

## S3 method for class 'lda_emp_bayes'
predict(object, newdata, type = c("class", "prob", "score"), ...)

Arguments

x

Matrix or data frame containing the training data. The rows are the sample observations, and the columns are the features. Only complete data are retained.

...

additional arguments (not currently used).

y

Vector of class labels for each training observation. Only complete data are retained.

prior

Vector with prior probabilities for each class. If NULL (default), then equal probabilities are used. See details.

formula

A formula of the form groups ~ x1 + x2 + ... That is, the response is the grouping factor and the right hand side specifies the (non-factor) discriminators.

data

data frame from which variables specified in formula are preferentially to be taken.

object

Fitted model object

newdata

Matrix or data frame of observations to predict. Each row corresponds to a new observation.

type

Prediction type: either "class", "prob", or "score".

Details

The matrix of training observations are given in x. The rows of x contain the sample observations, and the columns contain the features for each training observation.

The vector of class labels given in y are coerced to a factor. The length of y should match the number of rows in x.

An error is thrown if a given class has less than 2 observations because the variance for each feature within a class cannot be estimated with less than 2 observations.

The vector, prior, contains the a priori class membership for each class. If prior is NULL (default), the class membership probabilities are estimated as the sample proportion of observations belonging to each class. Otherwise, prior should be a vector with the same length as the number of classes in y. The prior probabilities should be nonnegative and sum to one.

Value

lda_emp_bayes object that contains the trained MDEB classifier

References

Srivastava, M. and Kubokawa, T. (2007). "Comparison of Discrimination Methods for High Dimensional Data," Journal of the Japanese Statistical Association, 37, 1, 123-134.

Examples

library(modeldata)
data(penguins)
pred_rows <- seq(1, 344, by = 20)
penguins <- penguins[, c("species", "body_mass_g", "flipper_length_mm")]
mdeb_out <- lda_emp_bayes(species ~ ., data = penguins[-pred_rows, ])
predicted <- predict(mdeb_out, penguins[pred_rows, -1], type = "class")

mdeb_out2 <- lda_emp_bayes(x = penguins[-pred_rows, -1], y = penguins$species[-pred_rows])
predicted2 <- predict(mdeb_out2, penguins[pred_rows, -1], type = "class")
all.equal(predicted, predicted2)