Gaussian Conditional Sampler

Implements conditional sampling assuming features follow a multivariate Gaussian distribution. Computes conditional distributions analytically using standard formulas for multivariate normal distributions.

Details

For a joint Gaussian distribution \(X \sim N(\mu, \Sigma)\), partitioned as \(X = (X_A, X_B)\), the conditional distribution is:

$$X_B | X_A = x_A \sim N(\mu_{B|A}, \Sigma_{B|A})$$

where: $$\mu_{B|A} = \mu_B + \Sigma_{BA} \Sigma_{AA}^{-1} (x_A - \mu_A)$$ $$\Sigma_{B|A} = \Sigma_{BB} - \Sigma_{BA} \Sigma_{AA}^{-1} \Sigma_{AB}$$

This is equivalent to the regression formulation used by fippy: $$\beta = \Sigma_{BA} \Sigma_{AA}^{-1}$$ $$\mu_{B|A} = \mu_B + \beta (x_A - \mu_A)$$ $$\Sigma_{B|A} = \Sigma_{BB} - \beta \Sigma_{AB}$$

Assumptions:

• Features are approximately multivariate normal

• Only continuous features are supported

Advantages:

• Very fast (closed-form solution)

• Deterministic (given seed)

• No hyperparameters

• Memory efficient

Limitations:

• Strong distributional assumption

• May produce out-of-range values for bounded features

• Cannot handle categorical features

References

Anderson T (2003). An Introduction to Multivariate Statistical Analysis, 3rd edition. Wiley-Interscience, Hoboken, NJ. ISBN 9780471360919.

Super classes

xplainfi::FeatureSampler -> xplainfi::ConditionalSampler -> ConditionalGaussianSampler

Public fields

feature_types

(character()) Feature types supported by the sampler.

mu

(numeric()) Mean vector estimated from training data.

sigma

(matrix()) Covariance matrix estimated from training data.

Methods

Public methods

• ConditionalGaussianSampler$new()

• ConditionalGaussianSampler$clone()

Inherited methods

• xplainfi::FeatureSampler$print()
• xplainfi::ConditionalSampler$sample()
• xplainfi::ConditionalSampler$sample_newdata()

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Method new()

Creates a new ConditionalGaussianSampler.

Usage

ConditionalGaussianSampler$new(task, conditioning_set = NULL)

Arguments

task

(mlr3::Task) Task to sample from. Must have only numeric/integer features.

conditioning_set

(character | NULL) Default conditioning set to use in $sample().

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Method clone()

The objects of this class are cloneable with this method.

Usage

ConditionalGaussianSampler$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

library(mlr3)
task = tgen("friedman1")$generate(n = 100)
sampler = ConditionalGaussianSampler$new(task)

# Sample x2, x3 conditioned on x1
test_data = task$data(rows = 1:5)
sampled = sampler$sample_newdata(
  feature = c("important2", "important3"),
  newdata = test_data,
  conditioning_set = "important1"
)