ExtraTrees / Classifier Layer

Extremely Randomized Trees (ExtraTrees) Classifier: This class implements a meta estimator that fits a number of randomized decision trees (a.k.a. extra-trees) on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting.

Mathematical form: $f (x) = \frac{1}{M} m = 1 \sum M h_{m} (x)$ where:

$h_{m} (x)$ are randomized trees
M is number of trees
Random splits replace optimal splits

Key characteristics:

Extreme randomization
Faster than Random Forest
Lower variance
Parallel processing
Automatic feature selection

Common applications:

Large-scale classification
Rapid model development
Feature importance
Ensemble building
Online prediction

Computational notes:

Training: O(M * N * log(N)) or better
Memory: O(M * N)
Prediction: O(M * log(N))
Parallel capable

Outputs:

Predicted Table: Input data with predictions
Validation Results: Cross-validation metrics
Test Metric: Test set performance
ROC Curve Data: ROC analysis information
Confusion Matrix: Classification breakdown
Feature Importances: Variable importance scores

Table

Predicted Table

Validation Results

Test Metric

ROC Curve Data

Confusion Matrix

Feature Importances

SelectFeatures

[column, ...]

Feature columns for ExtraTrees Classification:

Data requirements:

General format:
- Numeric features
- Encoded categoricals
- No missing values
- Clean data
Preprocessing notes:
- No scaling needed
- Handles raw features
- Robust to outliers
- Automatic feature selection
Feature quality:
- Remove constants
- Handle missing data
- Check correlations
- Consider feature counts

Note: If empty, uses all numeric columns except target

SelectTarget

column

Target column for ExtraTrees Classification:

Requirements:

Data format:
- Categorical labels
- At least two classes
- No missing values
- Clean encoding
Class properties:
- Handles imbalance via weights
- Supports multi-class
- No ordinal assumptions
- Preserves class order
Quality checks:
- Verify encodings
- Check distributions
- Monitor rare classes
- Validate categories

Params

oneof

DefaultParams

Default configuration for ExtraTrees Classifier:

Ensemble settings:
- N estimators: 100 trees
- Bootstrap: False
- Max samples: Auto
Tree parameters:
- Criterion: Gini
- Max depth: None (unlimited)
- Max features: Sqrt
- Min samples split: 2
- Min samples leaf: 1
Randomization:
- Random splits
- Random features
- No bootstrapping
Regularization:
- No explicit pruning
- Default class weights
- CCP alpha: 0.0

Best suited for:

Initial modeling
Fast training needs
Medium to large datasets
General classification

CustomParams

Fine-tuned configuration for ExtraTrees Classifier:

Parameter categories:

Ensemble control
Tree construction
Randomization levels
Regularization options

Note: Randomization parameters particularly important for ExtraTrees

NEstimators

u32

100

Number of trees in forest:

Guidelines:

Small (50-100): Quick models
Medium (100-300): Standard use
Large (>300): Complex problems

Trade-offs:

More trees: Better stability
Parallel training possible
Diminishing returns

Criterion

enum

Gini

Split quality measures for extremely randomized trees:

Note: Applied after random split generation

Gini ~

Gini impurity criterion:

Formula: $1 - \sum_{k = 1}^{K} p_{k}^{2}$

Properties:

Range: [0, 1-1/K]
Fast computation
Default choice
Works with random splits

Entropy ~

Information gain criterion:

Formula: $- \sum_{k = 1}^{K} p_{k} lo g (p_{k})$

Properties:

Range: [0, log(K)]
More granular
Slower computation
Information theoretic

Logloss ~

Logarithmic loss criterion:

Formula: $- \sum_{k = 1}^{K} y_{k} lo g (p_{k})$

Properties:

Probability focused
Sensitive to uncertainties
Good for probabilities
Penalizes mistakes heavily

MaxDepth

u32

The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.

Values:

0: Unlimited (grow until pure)
>0: Explicit depth limit

Controls complexity and memory

MinSamplesSplit

u32

The minimum number of samples required to split an internal node:

Constraint: Nodes with < samples won't split
Higher values: More conservative trees
Prevents excessive randomization

MinSamplesLeaf

u32

The minimum number of samples required to be at a leaf node:

Ensures prediction stability
Controls overfitting
Affects tree depth

MinWeightFractionLeaf

f64

The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node:

Range: [0.0, 0.5]
Used with sample weights
Alternative size control

MaxFeatures

enum

Auto

Feature subset size for random split generation:

Note: Critical for ExtraTrees randomization

Auto ~

Use all features:

Formula: $F_{ma x} = F$

Properties:

Maximum information
Slower training
Less randomization
Good for few features

Sqrt ~

Square root of features:

Formula: $F_{ma x} = F$

Properties:

Standard choice
Good default
Balanced speed
Common in practice

Log2 ~

Logarithmic scaling:

Formula: $F_{ma x} = lo g_{2} (F)$

Properties:

More aggressive reduction
Fastest training
Maximum randomization
Good for many features

Custom ~

User-specified count:

Properties:

Full control
Problem-specific
Manual optimization
Research purposes

MaxFeaturesF

u32

Custom feature count:

Active when max_features=Custom
Must be ≥ 1 and ≤ total features

MaxLeafNodes

u32

Maximum leaf count:

0: Unlimited leaves
>0: Best-first growth with limit

Alternative to max_depth

MinImpurityDecrease

f64

Minimum impurity decrease:

Controls split quality
Useful with random splits
Pre-pruning mechanism

Bootstrap

bool

false

Whether bootstrap samples are used when building trees.

False: the whole dataset is used to build each tree
True: Additional randomization

Affects OOB score availability

OobScore

bool

false

Whether to use out-of-bag samples to estimate the generalization score.

Requires bootstrap=True
Provides validation estimate

RandomState

u64

Random seed control:

Affects:

Split generation
Feature selection
Bootstrap sampling
Set for reproducibility

WarmStart

bool

false

When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. Useful for optimization.

ClassWeight

enum

None

Class weighting schemes for ExtraTrees:

Note: Affects all trees in ensemble

None ~

Equal class weights:

Properties:

No bias adjustment
Natural distributions
Default behavior
Fast computation

Balanced ~

Inverse frequency weights:

Formula: $w_{i} = \frac{N}{K \times N _{i}}$

Properties:

Handles imbalance
Adjusts importance
Fair to minorities
Class-sensitive

CcpAlpha

f64

Cost-complexity pruning:

Post-pruning parameter
Larger values: More pruning
Controls tree complexity

MaxSamples

f64

The fraction of samples to draw from X to train each base estimator:

Range: [0.0, 1.0]
0.0: Auto (use all)
Used with bootstrap=True

GridSearch

Hyperparameter optimization for ExtraTrees Classifier:

Search dimensions:

Ensemble parameters:
- Number of trees
- Sampling strategy
- Feature selection
Tree construction:
- Split criteria
- Tree depth
- Node constraints
Randomization:
- Bootstrap options
- Feature subsets
- Sample fractions

Computational impact:

Time: O(n_params * n_trees * N * log(N))
Memory: O(n_params * n_trees)
Parallel training possible

Best practices:

Start with randomization levels
Then tune tree parameters
Finally adjust ensemble size

NEstimators

[u32, ...]

100

Number of trees to evaluate:

Common ranges:

Quick: [50, 100]
Standard: [100, 200, 300]
Extensive: [200, 400, 600]

Note: More trees increase stability

Criterion

[enum, ...]

Gini

Split quality measures for extremely randomized trees:

Note: Applied after random split generation

Gini ~

Gini impurity criterion:

Formula: $1 - \sum_{k = 1}^{K} p_{k}^{2}$

Properties:

Range: [0, 1-1/K]
Fast computation
Default choice
Works with random splits

Entropy ~

Information gain criterion:

Formula: $- \sum_{k = 1}^{K} p_{k} lo g (p_{k})$

Properties:

Range: [0, log(K)]
More granular
Slower computation
Information theoretic

Logloss ~

Logarithmic loss criterion:

Formula: $- \sum_{k = 1}^{K} y_{k} lo g (p_{k})$

Properties:

Probability focused
Sensitive to uncertainties
Good for probabilities
Penalizes mistakes heavily

MaxDepth

[u32, ...]

Tree depth limits to try:

Ranges:

Shallow: [5, 10, 15]
Medium: [10, 20, 30]
Deep/None: [0, 20, 40]

MinSamplesSplit

[u32, ...]

Minimum split samples to try:

Common ranges:

Fine: [2, 5, 10]
Medium: [5, 10, 20]
Coarse: [10, 20, 50]

MinSamplesLeaf

[u32, ...]

Minimum leaf samples to evaluate:

Ranges:

Fine: [1, 2, 4]
Medium: [4, 8, 16]
Coarse: [10, 20, 30]

MinWeightFractionLeaf

[f64, ...]

Minimum weighted fraction to try:

Ranges:

Light: [0.0, 0.1]
Medium: [0.0, 0.1, 0.2]
Heavy: [0.1, 0.2, 0.3]

MaxFeatures

[enum, ...]

Auto

Feature subset size for random split generation:

Note: Critical for ExtraTrees randomization

Auto ~

Use all features:

Formula: $F_{ma x} = F$

Properties:

Maximum information
Slower training
Less randomization
Good for few features

Sqrt ~

Square root of features:

Formula: $F_{ma x} = F$

Properties:

Standard choice
Good default
Balanced speed
Common in practice

Log2 ~

Logarithmic scaling:

Formula: $F_{ma x} = lo g_{2} (F)$

Properties:

More aggressive reduction
Fastest training
Maximum randomization
Good for many features

Custom ~

User-specified count:

Properties:

Full control
Problem-specific
Manual optimization
Research purposes

MaxFeaturesF

[u32, ...]

Custom feature counts to try:

Only used with max_features=Custom Typical: [2, 4, 8, 16] or powers of 2

MaxLeafNodes

[u32, ...]

Maximum leaf node counts:

Ranges:

Limited: [10, 20, 50]
Medium: [50, 100, 200]
Unlimited: Include [0]

MinImpurityDecrease

[f64, ...]

Impurity decrease thresholds:

Ranges:

Fine: [0.0, 0.0001, 0.001]
Medium: [0.0, 0.001, 0.01]
Coarse: [0.01, 0.05, 0.1]

Bootstrap

[bool, ...]

false

Bootstrap strategies:

Options:

[false]: Standard ExtraTrees
[true]: Additional randomization
[false, true]: Compare both

OobScore

[bool, ...]

false

OOB scoring options:

Options:

[false]: No OOB
[true]: Use OOB if possible Note: Requires bootstrap=True

WarmStart

[bool, ...]

false

Warm start options:

Options:

[false]: Fresh forests
[true]: Incremental building
[false, true]: Compare both

ClassWeight

[enum, ...]

None

Class weighting schemes for ExtraTrees:

Note: Affects all trees in ensemble

None ~

Equal class weights:

Properties:

No bias adjustment
Natural distributions
Default behavior
Fast computation

Balanced ~

Inverse frequency weights:

Formula: $w_{i} = \frac{N}{K \times N _{i}}$

Properties:

Handles imbalance
Adjusts importance
Fair to minorities
Class-sensitive

RandomState

u64

Random seed for reproducibility:

Controls:

Split generation
Feature selection
Cross-validation

CcpAlpha

[f64, ...]

Cost-complexity pruning alphas:

Ranges:

Light: [0.0, 0.001, 0.01]
Medium: [0.0, 0.01, 0.05]
Heavy: [0.05, 0.1, 0.2]

MaxSamples

[f64, ...]

Sample size fractions:

Ranges:

Small: [0.5, 0.7]
Medium: [0.7, 0.8, 0.9]
Large: [0.9, 1.0] Note: Used with bootstrap=True

RefitScore

enum

Accuracy

Performance evaluation metrics for classification:

Purpose:

Model evaluation
Ensemble selection
Early stopping
Performance tracking

Selection criteria:

Problem objectives
Class distribution
Ensemble size
Computation resources

Default ~

Uses ensemble's built-in scoring:

Properties:

Weighted accuracy metric
Ensemble-aware scoring
Fast computation
Boosting-compatible

Best for:

Standard problems
Quick evaluation
Initial testing
Performance tracking

Accuracy ~

Standard classification accuracy:

Formula: $Accuracy = \frac{Correct Predictions}{Total Samples}$

Properties:

Range: [0, 1]
Ensemble consensus
Intuitive metric
Equal error weights

Best for:

Balanced datasets
Equal error costs
Simple evaluation
Quick benchmarking

BalancedAccuracy ~

Class-normalized accuracy score:

Formula: $\frac{1}{K} \sum_{i = 1}^{K} \frac{T P _{i}}{T P _{i} + F N _{i}}$

Properties:

Range: [0, 1]
Class-weighted
Imbalance-robust
Fair evaluation

Best for:

Imbalanced data
Varied class sizes
Minority focus
Fair assessment

LogLoss ~

Logarithmic loss (Cross-entropy):

Formula: $- \frac{1}{N} \sum_{i = 1}^{N} \sum_{j = 1}^{K} y_{ij} lo g (p_{ij})$

Properties:

Range: [0, ∞)
Probability-sensitive
Boosting-optimal
Confidence-aware

Best for:

Probability estimation
Boosting optimization
Risk assessment
Model calibration

RocAuc ~

Area Under ROC Curve:

Properties:

Range: [0, 1]
Ranking quality
Threshold-invariant
Ensemble-appropriate

Best for:

Binary problems
Ranking tasks
Score calibration
Model comparison

Note: Extended to multi-class via averaging

Split

oneof

DefaultSplit

Standard train-test split configuration optimized for general classification tasks.

Configuration:

Test size: 20% (0.2)
Random seed: 98
Shuffling: Enabled
Stratification: Based on target distribution

Advantages:

Preserves class distribution
Provides reliable validation
Suitable for most datasets

Best for:

Medium to large datasets
Independent observations
Initial model evaluation

Splitting uses the ShuffleSplit strategy or StratifiedShuffleSplit strategy depending on the field stratified. Note: If shuffle is false then stratified must be false.

CustomSplit

Configurable train-test split parameters for specialized requirements. Allows fine-tuning of data division strategy for specific use cases or constraints.

Use cases:

Time series data
Grouped observations
Specific train/test ratios
Custom validation schemes

RandomState

u64

Random seed for reproducible splits. Ensures:

Consistent train/test sets
Reproducible experiments
Comparable model evaluations

Same seed guarantees identical splits across runs.

Shuffle

bool

true

Data shuffling before splitting. Effects:

true: Randomizes order, better for i.i.d. data
false: Maintains order, important for time series

When to disable:

Time dependent data
Sequential patterns
Grouped observations

TrainSize

f64

0.8

Proportion of data for training. Considerations:

Larger (e.g., 0.8-0.9): Better model learning
Smaller (e.g., 0.5-0.7): Better validation

Common splits:

0.8: Standard (80/20 split)
0.7: More validation emphasis
0.9: More training emphasis

Stratified

bool

false

Maintain class distribution in splits. Important when:

Classes are imbalanced
Small classes present
Representative splits needed

Requirements:

Classification tasks only
Cannot use with shuffle=false
Sufficient samples per class

Cv

oneof

DefaultCv

Standard cross-validation configuration using stratified 3-fold splitting.

Configuration:

Folds: 3
Method: StratifiedKFold
Stratification: Preserves class proportions

Advantages:

Balanced evaluation
Reasonable computation time
Good for medium-sized datasets

Limitations:

May be insufficient for small datasets
Higher variance than larger fold counts
May miss some data patterns

CustomCv

Configurable stratified k-fold cross-validation for specific validation requirements.

Features:

Adjustable fold count with NFolds determining the number of splits.
Stratified sampling
Preserved class distributions

Use cases:

Small datasets (more folds)
Large datasets (fewer folds)
Detailed model evaluation
Robust performance estimation

NFolds

u32

Number of cross-validation folds. Guidelines:

3-5: Large datasets, faster training
5-10: Standard choice, good balance
10+: Small datasets, thorough evaluation

Trade-offs:

More folds: Better evaluation, slower training
Fewer folds: Faster training, higher variance

Must be at least 2.

KfoldCv

K-fold cross-validation without stratification. Divides data into k consecutive folds for iterative validation.

Process:

Splits data into k equal parts
Each fold serves as validation once
Remaining k-1 folds form training set

Use cases:

Regression problems
Large, balanced datasets
When stratification unnecessary
Continuous target variables

Limitations:

May not preserve class distributions
Less suitable for imbalanced data
Can create biased splits with ordered data

NSplits

u32

Number of folds for cross-validation. Selection guide: Recommended values:

5: Standard choice (default)
3: Large datasets/quick evaluation
10: Thorough evaluation/smaller datasets

Trade-offs:

Higher values: More thorough, computationally expensive
Lower values: Faster, potentially higher variance

Must be at least 2 for valid cross-validation.

RandomState

u64

Random seed for fold generation when shuffling. Important for:

Reproducible results
Consistent fold assignments
Benchmark comparisons
Debugging and validation

Set specific value for reproducibility across runs.

Shuffle

bool

true

Whether to shuffle data before splitting into folds. Effects:

true: Randomized fold composition (recommended)
false: Sequential splitting

Enable when:

Data may have ordering
Better fold independence needed

Disable for:

Time series data
Ordered observations

StratifiedKfoldCv

Stratified K-fold cross-validation maintaining class proportions across folds.

Key features:

Preserves class distribution in each fold
Handles imbalanced datasets
Ensures representative splits

Best for:

Classification problems
Imbalanced class distributions
When class proportions matter

Requirements:

Classification tasks only
Sufficient samples per class
Categorical target variable

NSplits

u32

Number of stratified folds. Guidelines: Typical values:

5: Standard for most cases
3: Quick evaluation/large datasets
10: Detailed evaluation/smaller datasets

Considerations:

Must allow sufficient samples per class per fold
Balance between stability and computation time
Consider smallest class size when choosing

RandomState

u64

Seed for reproducible stratified splits. Ensures:

Consistent fold assignments
Reproducible results
Comparable experiments
Systematic validation

Fixed seed guarantees identical stratified splits.

Shuffle

bool

false

Data shuffling before stratified splitting. Impact:

true: Randomizes while maintaining stratification
false: Maintains data order within strata

Use cases:

true: Independent observations
false: Grouped or sequential data

Class proportions maintained regardless of setting.

ShuffleSplitCv

Random permutation cross-validator with independent sampling.

Characteristics:

Random sampling for each split
Independent train/test sets
More flexible than K-fold
Can have overlapping test sets

Advantages:

Control over test size
Fresh splits each iteration
Good for large datasets

Limitations:

Some samples might never be tested
Others might be tested multiple times
No guarantee of complete coverage

NSplits

u32

Number of random splits to perform. Consider: Common values:

5: Standard evaluation
10: More thorough assessment
3: Quick estimates

Trade-offs:

More splits: Better estimation, longer runtime
Fewer splits: Faster, less stable estimates

Balance between computation and stability.

RandomState

u64

Random seed for reproducible shuffling. Controls:

Split randomization
Sample selection
Result reproducibility

Important for:

Debugging
Comparative studies
Result verification

TestSize

f64

0.2

Proportion of samples for test set. Guidelines: Common ratios:

0.2: Standard (80/20 split)
0.25: More validation emphasis
0.1: More training data

Considerations:

Dataset size
Model complexity
Validation requirements

It must be between 0.0 and 1.0.

StratifiedShuffleSplitCv

Stratified random permutation cross-validator combining shuffle-split with stratification.

Features:

Maintains class proportions
Random sampling within strata
Independent splits
Flexible test size

Ideal for:

Imbalanced datasets
Large-scale problems
When class distributions matter
Flexible validation schemes

NSplits

u32

Number of stratified random splits. Guidelines: Recommended values:

5: Standard evaluation
10: Detailed analysis
3: Quick assessment

Consider:

Sample size per class
Computational resources
Stability requirements

RandomState

u64

Seed for reproducible stratified sampling. Ensures:

Consistent class proportions
Reproducible splits
Comparable experiments

Critical for:

Benchmarking
Research studies
Quality assurance

TestSize

f64

0.2

Fraction of samples for stratified test set. Best practices: Common splits:

0.2: Balanced evaluation
0.3: More thorough testing
0.15: Preserve training size

Consider:

Minority class size
Overall dataset size
Validation objectives

It must be between 0.0 and 1.0.

TimeSeriesSplitCv

Time Series cross-validator. Provides train/test indices to split time series data samples that are observed at fixed time intervals, in train/test sets. It is a variation of k-fold which returns first k folds as train set and the k + 1th fold as test set. Note that unlike standard cross-validation methods, successive training sets are supersets of those that come before them. Also, it adds all surplus data to the first training partition, which is always used to train the model. Key features:

Maintains temporal dependence
Expanding window approach
Forward-chaining splits
No future data leakage

Use cases:

Sequential data
Financial forecasting
Temporal predictions
Time-dependent patterns

Note: Training sets are supersets of previous iterations.

NSplits

u32

Number of temporal splits. Considerations: Typical values:

5: Standard forward chaining
3: Limited historical data
10: Long time series

Impact:

Affects training window growth
Determines validation points
Influences computational load

MaxTrainSize

u64

Maximum size of training set. Should be strictly less than the number of samples. Applications:

0: Use all available past data
>0: Rolling window of fixed size

Use cases:

Limit historical relevance
Control computational cost
Handle concept drift
Memory constraints

TestSize

u64

Number of samples in each test set. When 0:

Auto-calculated as n_samples/(n_splits+1)
Ensures equal-sized test sets

Considerations:

Forecast horizon
Validation requirements
Available future data

Gap

u64

Number of samples to exclude from the end of each train set before the test set.Gap between train and test sets. Uses:

Avoid data leakage
Model forecast lag
Buffer periods

Common scenarios:

0: Continuous prediction
>0: Forward gap for realistic evaluation
Match business forecasting needs