Sparse Bayesian PCA Signal Extraction

step_pca_sparse_bayes() creates a specification of a recipe step that will convert numeric data into one or more principal components that can have some zero coefficients.

Usage

step_pca_sparse_bayes(
  recipe,
  ...,
  role = "predictor",
  trained = FALSE,
  num_comp = 5,
  prior_slab_dispersion = 1,
  prior_mixture_threshold = 0.1,
  options = list(),
  res = NULL,
  prefix = "PC",
  keep_original_cols = FALSE,
  skip = FALSE,
  id = rand_id("pca_sparse_bayes")
)

Arguments

recipe: A recipe object. The step will be added to the sequence of operations for this recipe.
...: One or more selector functions to choose which variables will be used to compute the components. See selections() for more details. For the tidy method, these are not currently used.
role: For model terms created by this step, what analysis role should they be assigned? By default, the function assumes that the new principal component columns created by the original variables will be used as predictors in a model.
trained: A logical to indicate if the quantities for preprocessing have been estimated.
num_comp: The number of components to retain as new predictors. If num_comp is greater than the number of columns or the number of possible components, a smaller value will be used. If num_comp = 0 is set then no transformation is done and selected variables will stay unchanged, regardless of the value of keep_original_cols.
prior_slab_dispersion: This value is proportional to the dispersion (or scale) parameter for the slab portion of the prior. Smaller values result in an increase in zero coefficients.
prior_mixture_threshold: The parameter that defines the trade-off between the spike and slab components of the prior. Increasing this parameter increases the number of zero coefficients.
options: A list of options to the default method for VBsparsePCA::VBsparsePCA().
res: The rotation matrix once this preprocessing step has been trained by prep().
prefix: A character string that will be the prefix to the resulting new variables. See notes below.
keep_original_cols: A logical to keep the original variables in the output. Defaults to FALSE.
skip: A logical. Should the step be skipped when the recipe is baked by recipes::bake()? While all operations are baked when recipes::prep() is run, some operations may not be able to be conducted on new data (e.g. processing the outcome variable(s)). Care should be taken when using skip = TRUE as it may affect the computations for subsequent operations
id: A character string that is unique to this step to identify it.

Value

An updated version of recipe with the new step added to the sequence of existing steps (if any). For the tidy method, a tibble with columns terms (the selectors or variables selected), value (the loading), and component.

Details

The VBsparsePCA package is required for this step. If it is not installed, the user will be prompted to do so when the step is defined.

A spike-and-slab prior is a mixture of two priors. One (the "spike") has all of its mass at zero and represents a variable that has no contribution to the PCA coefficients. The other prior is a broader distribution that reflects the coefficient distribution of variables that do affect the PCA analysis. This is the "slab". The narrower the slab, the more likely that a coefficient will be zero (or are regularized to be closer to zero). The mixture of these two priors is governed by a mixing parameter, which itself has a prior distribution and a hyper-parameter prior.

PCA coefficients and their resulting scores are unique only up to the sign. This step will attempt to make the sign of the components more consistent from run-to-run. However, the sparsity constraint may interfere with this goal.

The argument num_comp controls the number of components that will be retained (the original variables that are used to derive the components are removed from the data). The new components will have names that begin with prefix and a sequence of numbers. The variable names are padded with zeros. For example, if num_comp < 10, their names will be PC1 - PC9. If num_comp = 101, the names would be PC1 - PC101.

Tidying

When you tidy() this step, a tibble is retruned with columns terms, value, component, and id:

terms: character, the selectors or variables selected
value: numeric, variable loading
component: character, principle component
id: character, id of this step

Tuning Parameters

This step has 3 tuning parameters:

num_comp: # Components (type: integer, default: 5)
prior_slab_dispersion: Dispersion of Slab Prior (type: double, default: 1)
prior_mixture_threshold: Threshold for Mixture Prior (type: double, default: 0.1)

Case weights

The underlying operation does not allow for case weights.

References

Ning, B. (2021). Spike and slab Bayesian sparse principal component analysis. arXiv:2102.00305.

Examples

library(recipes)
library(ggplot2)

data(ad_data, package = "modeldata")

ad_rec <-
  recipe(Class ~ ., data = ad_data) %>%
  step_zv(all_predictors()) %>%
  step_YeoJohnson(all_numeric_predictors()) %>%
  step_normalize(all_numeric_predictors()) %>%
  step_pca_sparse_bayes(
    all_numeric_predictors(),
    prior_mixture_threshold = 0.95,
    prior_slab_dispersion = 0.05,
    num_comp = 3,
    id = "sparse bayesian pca"
  ) %>%
  prep()

tidy(ad_rec, id = "sparse bayesian pca") %>%
  mutate(value = ifelse(value == 0, NA, value)) %>%
  ggplot(aes(x = component, y = terms, fill = value)) +
  geom_tile() +
  scale_fill_gradient2() +
  theme(axis.text.y = element_blank())