---
title: "Feature Samplers"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Feature Samplers}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
	collapse = TRUE,
	comment = "#>",
	fig.width = 7,
	fig.height = 5
)
```

Feature samplers are a core component of perturbation-based feature importance methods (PFI, CFI, RFI) and any other methods based on some form of marginalization (SAGE).
They determine how features are replaced or perturbed when evaluating feature importance. 
This vignette introduces the different types of feature samplers available in xplainfi and demonstrates their use.

## Setup

We create two tasks: one with mixed features (the penguins data), and one with all-numeric features.

```{r load-libraries}
library(xplainfi)
library(mlr3)
library(mlr3learners)
library(data.table)

# Create a task for demonstration
task_mixed = tsk("penguins")
task_numeric = sim_dgp_correlated(n = 200)
```

## Base Class: FeatureSampler

All feature samplers inherit from the `FeatureSampler` base class, which provides a common interface for sampling features.

### Key Properties

**Feature Type Support**: Each sampler declares which feature types it supports:

```{r feature-types}
# Check supported feature types for different samplers
task_mixed$feature_types
permutation = MarginalPermutationSampler$new(task_mixed)
permutation$feature_types
```

**Two Sampling Methods**:

1. `$sample(feature, row_ids)` - Sample from the stored task
2. `$sample_newdata(feature, newdata)` - Sample using external data

Let's demonstrate both with the permutation sampler:

```{r sample-methods}
# Sample from stored task (using row_ids)
sampled_task = permutation$sample(
	feature = "bill_length",
	row_ids = 40:45
)
sampled_task

# Sample from "external" data
test_data = task_mixed$data(rows = 40:45)
sampled_external = permutation$sample_newdata(
	feature = "bill_length",
	newdata = test_data
)
sampled_external
```

Notice that:

- The sampled feature values change (they are permuted)
- Other features and the target remain unchanged
- The data structure is preserved

## Permutation Sampler

The `MarginalPermutationSampler` performs simple random permutation of features, breaking their relationship with the target and other features. This is the classic approach used in Permutation Feature Importance (PFI).

**How it works:**

- Each feature is randomly shuffled (permuted) independently
- The association between feature values and target values is broken
- The association between feature values **across rows** is broken
- The marginal distribution of each feature is preserved


```{r permutation-example}
# Create permutation sampler
permutation = MarginalPermutationSampler$new(task_mixed)

# Sample a continuous feature
original = task_mixed$data(rows = 1:10)
sampled = permutation$sample("bill_length", row_ids = 1:10)

# Compare original and sampled values
data.table(
	original_bill = original$bill_length,
	sampled_bill = sampled$bill_length,
	sex = original$sex # Unchanged
)
```

Note that the permutation is only performed _within_ the requested `row_ids`.

**Use in PFI**: The permutation sampler is used by default in Permutation Feature Importance

## Marginal Reference Sampler

The `MarginalReferenceSampler` is another type of marginal sampler that samples complete rows from reference data.
Unlike `MarginalPermutationSampler` which shuffles feature values independently, this sampler preserves within-row dependencies by sampling intact observations.

**Key differences from MarginalPermutationSampler:**

- **MarginalPermutationSampler**: Shuffles each feature independently -- breaks dependencies between sampled features
- **MarginalReferenceSampler**: Samples complete reference rows -- preserves dependencies of the sampled features

This is the approach used in [SAGE (Shapley Additive Global importancE)](https://github.com/iancovert/sage) for marginal feature importance. In this SAGE implementation, the [`MarginalImputer`](https://github.com/iancovert/sage/blob/master/sage/imputers.py#L44-L78), uses this approach.
The "imputer" name comes from the "imputation" of model predictions using out-of-coalition features by sampling from their marginal distribution.
In `xplainfi`, we separate the "feature sampling" and "model prediction" steps (for now), which is why we keep the sampling infrastructure independent.

**How it works:**

```{r marginal-ref-example}
# Create marginal reference sampler with n_samples reference pool
marginal_ref = MarginalReferenceSampler$new(task_mixed, n_samples = 30L)

# Sample a feature - each row gets values from a randomly sampled reference row
original = task_mixed$data(rows = 1:5)
sampled = marginal_ref$sample("bill_length", row_ids = 1:5)

# Compare
data.table(
	original_bill = original$bill_length,
	sampled_bill = sampled$bill_length,
	sex = original$sex # Unchanged
)
```

**Parameters:**

- `n_samples`: Controls the size of the reference data pool
  - If `NULL`: uses all task data
  - If specified: subsamples that many rows from task

**Preserving within-row correlations:**

To demonstrate the difference, consider features that are correlated as in `task_numeric`.
Here, `x1` and `x2` are correlated, and if we sample them jointly, only `MarginalReferenceSampler` retains their original correlation (approximately).

```{r correlation-preservation}
# Sample with MarginalPermutationSampler (breaks correlations)
perm = MarginalPermutationSampler$new(task_numeric)
sampled_perm = perm$sample(c("x1", "x2"), row_ids = 1:10)

# Sample with MarginalReferenceSampler (preserves within-row correlations)
ref = MarginalReferenceSampler$new(task_numeric, n_samples = 50L)
sampled_ref = ref$sample(c("x1", "x2"), row_ids = 1:10)

# Check correlations
cor_original = cor(task_numeric$data()$x1, task_numeric$data()$x2)
cor_perm = cor(sampled_perm$x1, sampled_perm$x2)
cor_ref = cor(sampled_ref$x1, sampled_ref$x2)

data.table(
	method = c("Original", "Permutation", "Reference"),
	correlation = c(cor_original, cor_perm, cor_ref)
)
```

The reference sampler better preserves the correlation structure because it samples complete rows, while permutation completely breaks the dependency.

## Conditional Samplers

Conditional samplers account for dependencies between features by sampling from $P(X_j | X_{-j})$ rather than the marginal $P(X_j)$.
This is relevant when features are correlated.

All conditional samplers inherit from `ConditionalSampler` and support:

- Specifying which features to condition on via `conditioning_set`
- Both `$sample()` and `$sample_newdata()` methods
- Mixed feature types (depending on the specific sampler)

### Gaussian Conditional Sampler

The `ConditionalGaussianSampler` assumes features follow a multivariate Gaussian distribution and uses closed-form conditional distributions.

**Advantages**:

- Very fast (no model fitting during sampling)
- Deterministic given a seed
- No hyperparameters

**Limitations**:

- Assumes multivariate normality
- Only supports continuous features
- May produce out-of-range values

```{r gaussian-sampler}
# Create Gaussian conditional sampler
gaussian = ConditionalGaussianSampler$new(task_numeric)

# Sample x1 conditioned on other features
sampled = gaussian$sample(
	feature = "x1",
	row_ids = 1:10,
	conditioning_set = c("x2", "x3", "x4")
)

# Compare original and conditionally sampled values
original = task_numeric$data(rows = 1:10)
data.table(
	original = original$x1,
	sampled = sampled$x1,
	x2 = original$x2 # Conditioning feature (unchanged)
)
```

Notice that the sampled values respect the conditional distribution - they're different from the original but plausible given the conditioning features.

### ARF Sampler

The `ConditionalARFSampler` uses Adversarial Random Forests to model complex conditional distributions.
It's the most flexible conditional sampler.

**Advantages**:

- Handles mixed feature types (continuous, categorical, ordered)
- No distributional assumptions
- Captures non-linear relationships

**Limitations**:

- Requires fitting ARF model (slower initialization and sampling for large data)
- More hyperparameters to tune
- Stochastic sampling

```{r arf-sampler}
# Create ARF sampler (works with full task including categorical features)
arf = ConditionalARFSampler$new(task_mixed, num_trees = 20, verbose = FALSE)

# Sample island conditioned on body measurements
sampled = arf$sample(
	feature = "island",
	row_ids = 1:10,
	conditioning_set = c("bill_length", "body_mass")
)

# Compare original and sampled island
original = task_mixed$data(rows = 1:10)
data.table(
	original_island = original$island,
	sampled_island = sampled$island,
	bill_length = original$bill_length, # Conditioning feature
	body_mass = original$body_mass # Conditioning feature
)
```

**Use in CFI**: ConditionalARFSampler is the default for Conditional Feature Importance since it can be used with any task, unlike other samplers.

### Ctree Conditional Sampler

The `ConditionalCtreeSampler` uses conditional inference trees to partition the feature space and sample from local neighborhoods.

**Advantages**:

- Handles mixed feature types
- Interpretable tree structure
- Automatic feature selection (only splits on informative features)

**Limitations**:

- Requires tree building (slower than kNN)
- May produce duplicates if terminal nodes are small

```{r ctree-sampler}
# Create ctree sampler
ctree = ConditionalCtreeSampler$new(task_mixed)

# Sample with default parameters
sampled = ctree$sample(
	feature = "bill_length",
	row_ids = 1:10,
	conditioning_set = "island"
)

original = task_mixed$data(rows = 1:10)
data.table(
	island = original$island, # Conditioning feature
	original = original$bill_length,
	sampled = sampled$bill_length
)
```

The ctree sampler partitions observations based on the conditioning features and samples from within the same partition (terminal node).

### kNN Conditional Sampler

The `ConditionalKNNSampler` finds k nearest neighbors based on conditioning features and samples from them.

**Advantages**:

- Very simple and intuitive
- Fast (no model fitting)
- Single hyperparameter (k)
- Automatic distance metric selection
- Supports mixed feature types (numeric, categorical, ordered, logical)

**Limitations**:

- Sensitive to choice of k
- May produce duplicates if k is small

**Distance metric**:

The sampler automatically selects the appropriate distance metric based on conditioning features:

- **Euclidean distance** when all conditioning features are numeric/integer (standardized)
- **Gower distance** when any conditioning features are categorical (factor, ordered, logical)

#### Example 1: All-numeric conditioning (Euclidean distance)

```{r knn-sampler-numeric}
# Create kNN sampler with k=5 neighbors
knn_numeric = ConditionalKNNSampler$new(task_numeric, k = 5)

# Sample x1 based on nearest neighbors in (x2, x3) space
sampled_numeric = knn_numeric$sample(
	feature = "x1",
	row_ids = 1:5,
	conditioning_set = c("x2", "x3")
)

original_numeric = task_numeric$data(rows = 1:5)
data.table(
	x2 = original_numeric$x2,
	x3 = original_numeric$x3,
	original_x1 = original_numeric$x1,
	sampled_x1 = sampled_numeric$x1
)
```

#### Example 2: Mixed-type conditioning (Gower distance)

```{r knn-sampler-mixed}
# Use task with categorical features
knn_mixed = ConditionalKNNSampler$new(task_mixed, k = 5)

# Sample bill_length conditioning on island (categorical) and body_mass (numeric)
sampled_mixed = knn_mixed$sample(
	feature = "bill_length",
	row_ids = 1:5,
	conditioning_set = c("island", "body_mass")
)

original_mixed = task_mixed$data(rows = 1:5)
data.table(
	island = original_mixed$island,
	body_mass = original_mixed$body_mass,
	original_bill = original_mixed$bill_length,
	sampled_bill = sampled_mixed$bill_length
)
```

The kNN sampler finds the k most similar observations (based on conditioning features) and samples from their feature values. The distance metric is chosen automatically based on feature types.

## Knockoff Samplers

Now that we've seen conditional samplers, we can understand an important limitation of knockoff samplers: unlike the conditional samplers above, knockoffs **don't support arbitrary conditioning sets**.

Knockoff samplers create synthetic features (knockoffs) that satisfy specific statistical properties. They must fulfill the **knockoff swap property**: swapping a feature with its knockoff should not change the joint distribution.

Knockoffs are a separate category because:

1. They require special construction to satisfy theoretical guarantees, and implementations are limited
2. They don't support conditional sampling with arbitrary conditioning sets
3. They're used primarily for feature selection with FDR control, not general importance

### Gaussian Knockoffs

For multivariate Gaussian data, we can construct exact knockoffs:

```{r knockoff-sampler}
# Create Gaussian knockoff sampler (using task_numeric from earlier)
knockoff = KnockoffGaussianSampler$new(task_numeric)

# Generate knockoffs
original = task_numeric$data(rows = 1:5)
knockoffs = knockoff$sample(
	feature = task_numeric$feature_names,
	row_ids = 1:5
)

# Original vs knockoff values
data.table(
	x1_original = original$x1,
	x1_knockoff = knockoffs$x1,
	x2_original = original$x2,
	x2_knockoff = knockoffs$x2
)
```

Key properties of knockoffs:

- Different values but similar statistical properties
- Pairwise exchangeability with originals
- Preserve correlation structure
- Cannot specify which features to condition on (determined by the knockoff construction)

**Conditional Independence Testing**: Knockoffs are particularly relevant for conditional independence testing as implemented in the [cpi package](https://cran.r-project.org/package=cpi). You can combine knockoff samplers with CFI and perform inference:

```{r cfi-knockoff, eval = FALSE}
# CFI with knockoff sampler for conditional independence testing
cfi_knockoff = CFI$new(
	task = task_numeric,
	learner = lrn("regr.ranger"),
	measure = msr("regr.mse"),
	sampler = knockoff
)

# Compute importance with CPI-based inference
cfi_knockoff$compute()
cfi_knockoff$importance(ci_method = "cpi")
```

See `vignette("inference")` for more details on statistical inference with feature importance.


**Key takeaways**:

- **Permutation sampling** produces any value from the marginal distribution
- **Conditional samplers** produce values consistent with conditioning features
- Choice of sampler affects feature importance estimates, especially when features are correlated

## Summary

| Sampler | Feature Types | Assumptions | Speed | Use Case |
|---------|--------------|-------------|-------|----------|
| `MarginalPermutationSampler` | All | None | Very fast | PFI, uncorrelated features |
| `KnockoffGaussianSampler` | Continuous | Multivariate normal | Fast | Model-X knockoffs |
| `ConditionalGaussianSampler` | Continuous | Multivariate normal | Very fast | CFI with continuous features |
| `ConditionalARFSampler` | All | None | Moderate | CFI, complex dependencies |
| `ConditionalCtreeSampler` | All | None | Moderate | CFI, interpretable sampling |
| `ConditionalKNNSampler` | All | None (auto-selects distance) | Fast | CFI, simple local structure |

**General guidelines**:

1. Use **permutation sampling** when features are independent or for baseline PFI
2. Use **Gaussian conditional** for fast conditional sampling with continuous features
3. Use **ARF** for the most flexible conditional sampling with mixed types
4. Use **kNN** for simple, fast conditional sampling
5. Use **ctree** when you want interpretable conditional sampling
6. Use **knockoffs** when you need theoretical guarantees for feature selection and inference
