DecisionTree / Regressor Layer
Decision Tree Regression: Rule-based hierarchical modeling.
Mathematical formulation: where:
- Rₘ are regions (leaf nodes)
- cₘ are constant predictions
- I() is indicator function
Key characteristics:
-
Model structure:
- Hierarchical decisions
- Binary splits
- Recursive partitioning
- Piecewise constant predictions
-
Learning process:
- Greedy split selection
- Top-down growth
- Impurity reduction
- Local optimization
Advantages:
- Handles non-linear patterns
- No feature scaling needed
- Captures interactions
- Highly interpretable
Common applications:
- Structured regression
- Feature importance
- Rule extraction
- Decision support
Outputs:
- Predicted Table: Results with predictions
- Validation Results: Cross-validation metrics
- Test Metric: Hold-out performance
- Feature Importances: Split importance scores
SelectFeatures
[column, ...]Feature selection for Decision Tree:
Requirements:
-
Data types:
- Numeric features preferred
- Categorical (encoded)
- No missing values
- Finite numbers
-
Tree considerations:
- No scaling needed
- Handles non-linear
- Captures interactions
- Feature redundancy ok
-
Best practices:
- Remove irrelevant features
- Handle missing data
- Encode categories
- Consider domain knowledge
-
Performance impact:
- Tree depth
- Split quality
- Memory usage
- Training speed
Note: If empty, uses all numeric columns except target
SelectTarget
columnTarget variable for Decision Tree:
Requirements:
-
Data type:
- Numeric continuous
- No missing values
- Finite values
- Real-valued
-
Distribution properties:
- No scaling needed
- Any distribution ok
- Outliers handled
- Non-linear patterns ok
-
Model implications:
- Criterion choice
- Leaf size impact
- Prediction granularity
- Error distribution
-
Special cases:
- Count data: Use Poisson
- Heavy tails: Use MAE
- Clean data: Use MSE
- Outliers: Consider MAE
Note: Must be a single numeric column
Params
oneofDefault Decision Tree configuration:
-
Tree structure:
- Unlimited depth
- MSE criterion
- Best splitter
- All features
-
Node constraints:
- Min samples split: 2
- Min samples leaf: 1
- No leaf fraction limit
-
Optimization:
- No pre-pruning
- No cost-complexity
- Pure leaf targeting
Best suited for:
- Initial modeling
- Small datasets
- Exploratory analysis
- Baseline performance
Customizable Decision Tree parameters:
Control aspects:
-
Split quality:
- Criterion choice
- Feature selection
- Split strategy
-
Tree growth:
- Depth control
- Node constraints
- Leaf requirements
-
Pruning options:
- Pre-pruning rules
- Cost-complexity
- Impurity thresholds
Optimization goals:
- Model complexity
- Prediction accuracy
- Generalization power
Criterion
enumSplit quality measurement:
Available criteria:
-
Mean Squared Error:
- Variance reduction
- L2 loss minimization
- Standard choice
-
Friedman MSE:
- MSE with improvements
- Better split selection
- Potential gains
-
Absolute Error:
- L1 loss minimization
- Median-based splits
- Robust to outliers
-
Poisson:
- Deviance reduction
- Count data
- Non-negative targets
Mean squared error criterion:
Formula: Gain:
Properties:
- Minimizes variance
- Sensitive to outliers
- Mean-based splits
Best for:
- Normal distributions
- Continuous targets
- General regression
Friedman's MSE criterion:
Formula:
Properties:
- Enhanced MSE
- Split potential
- Local improvements
- Better splits
Best for:
- Complex patterns
- Gradient boosting
- Refined splitting
Mean absolute error criterion:
Formula: Gain:
Properties:
- Median-based splits
- Outlier resistant
- Robust predictions
Best for:
- Skewed distributions
- Outlier presence
- Robust modeling
Poisson deviance criterion:
Formula:
Properties:
- Count data modeling
- Non-negative targets
- Rate prediction
Best for:
- Count outcomes
- Event rates
- Frequency data
Splitter
enumSplit selection strategy:
-
Best splits:
- Exhaustive search
- Optimal local decisions
- Maximum gain selection
-
Random splits:
- Random feature subset
- Faster computation
- More diverse trees
Trade-offs:
- Computation vs optimality
- Deterministic vs random
- Speed vs precision
Best split selection:
Process:
- Evaluates all possible splits
- Chooses maximum gain
- Deterministic choices
Best for:
- Small to medium datasets
- Optimal local decisions
- Reproducible results
Random split selection:
Process:
- Random feature sampling
- Best split within subset
- Stochastic decisions
Best for:
- Large datasets
- Faster training
- Ensemble methods
MaxDepth
u32Maximum tree depth:
Control options:
- 0: Unlimited growth
- >0: Fixed depth limit
Impact:
- Model complexity
- Training time
- Memory usage
Guidelines:
- Small: 3-5 (simple)
- Medium: 5-10 (balanced)
- Large: >10 (complex)
Minimum samples for splitting:
Effects:
- Prevents overfitting
- Controls granularity
- Ensures stability
Typical values:
- 2: Maximum splits
- 5-10: Balanced
- >10: Conservative
Minimum samples in leaves:
Purpose:
- Ensures prediction stability
- Prevents single-point leaves
- Controls overfitting
Common settings:
- 1: Maximum detail
- 5-10: Stable predictions
- >10: Smooth regions
Minimum weighted leaf fraction:
Usage:
- 0.0: No constraint
- >0.0: Forces larger leaves
- Handles imbalanced data
Range: [0.0, 0.5]
MaxFeatures
enumFeature subset size for splits:
Options:
- All features: n_features
- Square root: √n_features
- Log base 2: log₂(n_features)
- Custom count: user-defined
Impact:
- Split quality
- Training speed
- Tree diversity
- Memory usage
Use all features:
Properties:
- Maximum information
- Slower computation
- Optimal splits
Best for:
- Small feature sets
- Important decisions
- Single trees
Square root of features:
Formula:
Benefits:
- Balanced selection
- Reduced computation
- Common default
Best for:
- Random forests
- General usage
- Medium feature sets
Log base 2 of features:
Formula:
Benefits:
- Smaller subsets
- Faster splitting
- High dimensions
Best for:
- Many features
- Quick training
- Feature sampling
User-defined feature count:
Properties:
- Flexible control
- Manual optimization
- Problem-specific
Best for:
- Expert tuning
- Known requirements
- Special cases
MaxFeaturesF
u32Custom feature count:
Usage:
- Active when max_features=Custom
- Must be ≤ total features
Selection guide:
- Small: More randomization
- Large: Better splits
- Trade-off: Speed vs quality
MaxLeafNodes
u32Maximum leaf node count:
Growth control:
- 0: Unlimited leaves
- >0: Best-first growth
Effects:
- Tree size limitation
- Memory control
- Complexity bound
Alternative to max_depth
Minimum impurity decrease:
Purpose:
- Prevents weak splits
- Controls growth
- Pre-pruning method
RandomState
u64Controls the randomness of the estimator. The features are always randomly permuted at each split, even if splitter is set to 'best'. When max_features < n_features, the algorithm will select max_features at random at each split before finding the best split among them.
Controls:
- Split selection
- Feature sampling
- Tree structure
Usage:
- Fixed: Reproducible results
- Different: Model variation
- 0: System random
CcpAlpha
f64Cost-complexity pruning alpha:
Pruning criterion: where:
- R(T): Tree error
- |T|: Number of leaves
- α: Complexity parameter
Effect:
- Larger α: More pruning
- Smaller α: Less pruning
- 0: No pruning
Decision Tree hyperparameter optimization:
Search dimensions:
-
Tree structure:
- Growth controls
- Node constraints
- Split criteria
-
Complexity control:
- Depth/leaves limits
- Sample thresholds
- Pruning parameters
-
Split quality:
- Feature selection
- Impurity measures
- Splitting strategy
Best practices:
- Start coarse-grained
- Focus on key parameters
- Monitor complexity
- Consider interactions
Criterion
[enum, ...]Split quality measurement:
Available criteria:
-
Mean Squared Error:
- Variance reduction
- L2 loss minimization
- Standard choice
-
Friedman MSE:
- MSE with improvements
- Better split selection
- Potential gains
-
Absolute Error:
- L1 loss minimization
- Median-based splits
- Robust to outliers
-
Poisson:
- Deviance reduction
- Count data
- Non-negative targets
Mean squared error criterion:
Formula: Gain:
Properties:
- Minimizes variance
- Sensitive to outliers
- Mean-based splits
Best for:
- Normal distributions
- Continuous targets
- General regression
Friedman's MSE criterion:
Formula:
Properties:
- Enhanced MSE
- Split potential
- Local improvements
- Better splits
Best for:
- Complex patterns
- Gradient boosting
- Refined splitting
Mean absolute error criterion:
Formula: Gain:
Properties:
- Median-based splits
- Outlier resistant
- Robust predictions
Best for:
- Skewed distributions
- Outlier presence
- Robust modeling
Poisson deviance criterion:
Formula:
Properties:
- Count data modeling
- Non-negative targets
- Rate prediction
Best for:
- Count outcomes
- Event rates
- Frequency data
Splitter
[enum, ...]Split selection strategy:
-
Best splits:
- Exhaustive search
- Optimal local decisions
- Maximum gain selection
-
Random splits:
- Random feature subset
- Faster computation
- More diverse trees
Trade-offs:
- Computation vs optimality
- Deterministic vs random
- Speed vs precision
Best split selection:
Process:
- Evaluates all possible splits
- Chooses maximum gain
- Deterministic choices
Best for:
- Small to medium datasets
- Optimal local decisions
- Reproducible results
Random split selection:
Process:
- Random feature sampling
- Best split within subset
- Stochastic decisions
Best for:
- Large datasets
- Faster training
- Ensemble methods
MaxDepth
[u32, ...]Tree depth search:
Search patterns:
-
Simple trees:
- [3, 5, 7]
- Fast training
- Good generalization
-
Complex trees:
- [10, 15, 20, None]
- Detailed patterns
- More capacity
MinSamplesSplit
[u32, ...]Split threshold search:
Common ranges:
-
Fine-grained:
- [2, 5, 10]
- Detailed splits
-
Coarse-grained:
- [10, 20, 50]
- Stable splits
- Prevent overfitting
MinSamplesLeaf
[u32, ...]Leaf size search:
Search spaces:
-
Detailed leaves:
- [1, 3, 5]
- Fine predictions
-
Stable leaves:
- [5, 10, 20]
- Robust predictions
- Smoother regions
MinWeightFractionLeaf
[f64, ...]Leaf weight fraction search:
Ranges:
-
No constraint: [0.0]
-
Light constraint:
- [0.0, 0.1, 0.2]
- Balanced trees
-
Heavy constraint:
- [0.2, 0.3, 0.4]
- Force larger leaves
MaxFeatures
[enum, ...]Feature subset size for splits:
Options:
- All features: n_features
- Square root: √n_features
- Log base 2: log₂(n_features)
- Custom count: user-defined
Impact:
- Split quality
- Training speed
- Tree diversity
- Memory usage
Use all features:
Properties:
- Maximum information
- Slower computation
- Optimal splits
Best for:
- Small feature sets
- Important decisions
- Single trees
Square root of features:
Formula:
Benefits:
- Balanced selection
- Reduced computation
- Common default
Best for:
- Random forests
- General usage
- Medium feature sets
Log base 2 of features:
Formula:
Benefits:
- Smaller subsets
- Faster splitting
- High dimensions
Best for:
- Many features
- Quick training
- Feature sampling
User-defined feature count:
Properties:
- Flexible control
- Manual optimization
- Problem-specific
Best for:
- Expert tuning
- Known requirements
- Special cases
MaxFeaturesF
[u32, ...]Custom feature count search:
Search patterns:
-
Small subsets:
- [2, 4, 6]
- Fast training
-
Large subsets:
- [0.3n, 0.5n, 0.7*n]
- Better splits
Note: Used with max_features=Custom
MaxLeafNodes
[u32, ...]Leaf count search:
Search ranges:
-
Simple trees:
- [10, 20, 30]
- Basic patterns
-
Complex trees:
- [50, 100, None]
- Detailed patterns
Alternative to max_depth search
MinImpurityDecrease
[f64, ...]Impurity threshold search:
Ranges:
-
Fine splits:
- [0.0, 1e-4, 1e-3]
- Detailed trees
-
Coarse splits:
- [1e-3, 1e-2, 1e-1]
- Pre-pruning effect
- Prevent weak splits
RandomState
u64Random seed control:
Usage patterns:
-
Development:
- Fixed seed
- Reproducible results
-
Production:
- Multiple seeds
- Stability check
CcpAlpha
[f64, ...]Cost-complexity search:
Search patterns:
-
No pruning: [0.0]
-
Light pruning:
- [0.001, 0.01, 0.1]
- Maintain complexity
-
Heavy pruning:
- [0.1, 0.2, 0.3]
- Simplify tree
RefitScore
enumRegression model evaluation metrics:
Purpose:
- Model performance evaluation
- Error measurement
- Quality assessment
- Model comparison
Selection criteria:
- Error distribution
- Scale sensitivity
- Domain requirements
- Business objectives
Model's native scoring method:
- Typically R² score
- Model-specific implementation
- Standard evaluation
- Quick assessment
Coefficient of determination (R²):
Formula:
Properties:
- Range: (-∞, 1]
- 1: Perfect prediction
- 0: Constant model
- Negative: Worse than mean
Best for:
- General performance
- Variance explanation
- Model comparison
- Standard reporting
Explained variance score:
Formula:
Properties:
- Range: (-∞, 1]
- Accounts for bias
- Variance focus
- Similar to R²
Best for:
- Variance analysis
- Bias assessment
- Model stability
Maximum absolute error:
Formula:
Properties:
- Worst case error
- Original scale
- Sensitive to outliers
- Upper error bound
Best for:
- Critical applications
- Error bounds
- Safety margins
- Risk assessment
Negative mean absolute error:
Formula:
Properties:
- Linear error scale
- Robust to outliers
- Original units
- Negated for optimization
Best for:
- Robust evaluation
- Interpretable errors
- Outlier presence
Negative mean squared error:
Formula:
Properties:
- Squared error scale
- Outlier sensitive
- Squared units
- Negated for optimization
Best for:
- Standard optimization
- Large error penalty
- Statistical analysis
Negative root mean squared error:
Formula:
Properties:
- Original scale
- Outlier sensitive
- Interpretable units
- Negated for optimization
Best for:
- Standard reporting
- Interpretable errors
- Model comparison
Negative mean squared logarithmic error:
Formula:
Properties:
- Relative error scale
- For positive values
- Sensitive to ratios
- Negated for optimization
Best for:
- Exponential growth
- Relative differences
- Positive predictions
Negative median absolute error:
Formula:
Properties:
- Highly robust
- Original scale
- Outlier resistant
- Negated for optimization
Best for:
- Robust evaluation
- Heavy-tailed errors
- Outlier presence
Negative Poisson deviance:
Formula:
Properties:
- For count data
- Non-negative values
- Poisson assumption
- Negated for optimization
Best for:
- Count prediction
- Event frequency
- Rate modeling
Negative Gamma deviance:
Formula:
Properties:
- For positive continuous data
- Constant CV assumption
- Relative errors
- Negated for optimization
Best for:
- Positive continuous data
- Multiplicative errors
- Financial modeling
Negative mean absolute percentage error:
Formula:
Properties:
- Percentage scale
- Scale independent
- For non-zero targets
- Negated for optimization
Best for:
- Relative performance
- Scale-free comparison
- Business metrics
D² score with absolute error:
Formula:
Properties:
- Range: (-∞, 1]
- Robust version of R²
- Linear error scale
- Outlier resistant
Best for:
- Robust evaluation
- Non-normal errors
- Alternative to R²
D² score with pinball loss:
Properties:
- Quantile focus
- Asymmetric errors
- Risk assessment
- Distribution modeling
Best for:
- Quantile regression
- Risk analysis
- Asymmetric costs
- Distribution tails
D² score with Tweedie deviance:
Properties:
- Compound Poisson-Gamma
- Flexible dispersion
- Mixed distributions
- Insurance modeling
Best for:
- Insurance claims
- Mixed continuous-discrete
- Compound distributions
- Specialized modeling
Split
oneofStandard 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.
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
u64Random seed for reproducible splits. Ensures:
- Consistent train/test sets
- Reproducible experiments
- Comparable model evaluations
Same seed guarantees identical splits across runs.
Shuffle
boolData 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
f64Proportion 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
boolMaintain 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
oneofStandard 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
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
u32Number 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.
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
u32Number 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
u64Random 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
boolWhether 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
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
u32Number 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
u64Seed for reproducible stratified splits. Ensures:
- Consistent fold assignments
- Reproducible results
- Comparable experiments
- Systematic validation
Fixed seed guarantees identical stratified splits.
Shuffle
boolData 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.
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
u32Number 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
u64Random seed for reproducible shuffling. Controls:
- Split randomization
- Sample selection
- Result reproducibility
Important for:
- Debugging
- Comparative studies
- Result verification
TestSize
f64Proportion 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.
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
u32Number 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
u64Seed for reproducible stratified sampling. Ensures:
- Consistent class proportions
- Reproducible splits
- Comparable experiments
Critical for:
- Benchmarking
- Research studies
- Quality assurance
TestSize
f64Fraction 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.
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 + 1
th 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
u32Number 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
u64Maximum 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
u64Number 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
u64Number 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