discrim_regularized() defines a model that estimates a multivariate distribution for the predictors separately for the data in each class. The structure of the model can be LDA, QDA, or some amalgam of the two. Bayes' theorem is used to compute the probability of each class, given the predictor values. This function can fit classification models.

There are different ways to fit this model, and the method of estimation is chosen by setting the model engine. The engine-specific pages for this model are listed below.

• klaR¹²

¹ The default engine. ² Requires a parsnip extension package.

More information on how parsnip is used for modeling is at https://www.tidymodels.org/.

## Usage

discrim_regularized(
mode = "classification",
frac_common_cov = NULL,
frac_identity = NULL,
engine = "klaR"
)

## Arguments

mode

A single character string for the prediction outcome mode. Possible values for this model are "unknown", "regression", or "classification".

frac_common_cov, frac_identity

Numeric values between zero and one.

engine

A single character string specifying what computational engine to use for fitting.

## Details

There are many ways of regularizing models. For example, one form of regularization is to penalize model parameters. Similarly, the classic James–Stein regularization approach shrinks the model structure to a less complex form.

The model fits a very specific type of regularized model by Friedman (1989) that uses two types of regularization. One modulates how class-specific the covariance matrix should be. This allows the model to balance between LDA and QDA. The second regularization component shrinks the covariance matrix towards the identity matrix.

For the penalization approach, discrim_linear() with a mda engine can be used. Other regularization methods can be used with discrim_linear() and discrim_quad() can used via the sparsediscrim engine for those functions.

This function only defines what type of model is being fit. Once an engine is specified, the method to fit the model is also defined. See set_engine() for more on setting the engine, including how to set engine arguments.

The model is not trained or fit until the fit() function is used with the data.

## References

Friedman, J (1989). Regularized Discriminant Analysis. Journal of the American Statistical Association, 84, 165-175.

fit(), set_engine(), update(), klaR engine details