LinearSvr / Regressor Layer

Linear Support Vector Regression: Similar to SVR with parameter kernel='linear', but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples.

Mathematical formulation: $f (x) = w^{T} x + b$ with loss function: $L (y, f (x)) = ma x (0, ∣ y - f (x) ∣ - ϵ)$

Key characteristics:

Linear model architecture
Efficient optimization
Scalable to large datasets
Flexible loss functions

Advantages:

Fast training speed
Low memory usage
Good generalization
Linear interpretability

Common applications:

High-dimensional data
Large-scale regression
Real-time prediction
Feature importance

Outputs:

Predicted Table: Results with predictions
Validation Results: Cross-validation metrics
Test Metric: Hold-out performance
Feature Importances: Feature weights

Note: Optimized implementation using liblinear

Table

Predicted Table

Validation Results

Test Metric

Feature Importances

SelectFeatures

[column, ...]

Feature selection for Linear SVR:

Requirements:

Data properties:
- Numeric features
- No missing values
- Finite numbers
- Linear relationships
Preprocessing needs:
- Feature scaling crucial
- Outlier removal
- Correlation check
- Dimensionality check
Model considerations:
- Feature relevance
- Linear separability
- Memory constraints
- Training speed

Best practices:

Scale to [-1, 1] or [0, 1]
Remove redundant features
Check multicollinearity
Consider feature selection

Note: If empty, uses all numeric columns except target

SelectTarget

column

Target variable for Linear SVR:

Requirements:

Data type:
- Numeric continuous
- No missing values
- Finite values
- Real-valued
Distribution properties:
- Consider scaling
- Check outliers
- Assess skewness
- Note range
Model implications:
- Error tolerance (ε)
- Loss function choice
- Scale sensitivity
- Performance metrics

Preprocessing tips:

Scale if needed
Handle outliers
Check distribution
Document transformations

Note: Must be a single numeric column

Params

oneof

DefaultParams

Default Linear SVR configuration:

Model parameters:
- C = 1.0 (regularization)
- ε = 0.0 (error tolerance)
- Squared ε-insensitive loss
Training settings:
- tol = 0.0001 (precision)
- max_iter = 1000
- fit_intercept = true
Model structure:
- intercept_scaling = 1.0
- Random initialization
- Linear architecture

Best suited for:

Initial modeling
Large datasets
Linear patterns
Quick baselines

CustomParams

Customizable Linear SVR parameters:

Parameter categories:

Model complexity:
- Regularization strength
- Loss function
- Error tolerance
Training control:
- Convergence criteria
- Iteration limits
- Numerical precision
Model structure:
- Intercept fitting
- Feature scaling
- Initialization

Trade-offs:

Speed vs accuracy
Memory vs precision
Bias vs variance

Epsilon

f64

Error tolerance (ε) parameter:

Function:

Defines insensitive region
Controls prediction tolerance
Affects model sparsity

Guidelines:

ε = 0.0: No tolerance
ε > 0.0: Sparse solutions
Scale with target variance

Note: Depends on target scale

Loss

enum

SquaredEpsilonInsensitive

Loss function selection:

Mathematical forms:

L1 (Epsilon-insensitive): $L (y, f) = ma x (0, ∣ y - f ∣ - ϵ)$
L2 (Squared Epsilon-insensitive): $L (y, f) = ma x (0, ∣ y - f ∣ - ϵ)^{2}$

Properties:

L1: More robust to outliers
L2: Smoother solutions

Impact on model:

Training stability
Solution sparsity
Prediction behavior

EpsilonInsensitive ~

L1 Epsilon-insensitive loss:

Properties:

Linear penalty beyond ε
Robust to outliers
Sparse solutions
Standard SVR choice

Best for:

Noisy data
Outlier presence
Memory constraints
Sparse models

SquaredEpsilonInsensitive ~

L2 Squared epsilon-insensitive loss:

Properties:

Quadratic penalty beyond ε
Smooth solutions
Dense coefficients
Stable gradients

Best for:

Clean data
Smooth transitions
Stable predictions
Fine regression

Tol

f64

0.0001

Convergence tolerance:

Controls:

Solution precision
Training duration
Optimization stopping

Typical values:

Strict: 1e-5
Standard: 1e-4
Relaxed: 1e-3

Trade-off: Precision vs speed

CFactor

f64

Regularization strength (C):

Impact:

Small C: Strong regularization
Large C: Weak regularization

Selection guide:

Low noise: C > 1.0
High noise: C < 1.0
Balanced: C = 1.0

Note: Inversely proportional to strength

FitIntercept

bool

true

Intercept calculation control:

Model formulation:

With intercept: $f (x) = w^{T} x + b$
Without intercept: $f (x) = w^{T} x$

Mathematical impact:

Extends feature space: $x_{n e w} = [x, 1]$
Regularization: $\frac{λ}{2} (∣∣ w ∣ ∣^{2} + b^{2})$
Loss computation: $L (y, w^{T} x + b)$

Effects when True:

Affine transformation
Bias correction
Translation invariance
Complete linear model

Best practices:

True: Standard regression
False: Origin-centered data
Consider with scaling
Check data centering

InterceptScaling

f64

Intercept regularization scaling:

Function:

Scales synthetic feature
Controls intercept strength
Affects regularization

Usage:

Large values: Less regularization
Small values: More regularization
Default: Balanced (1.0)

Note: Only used with fit_intercept=true

RandomState

u64

Random number generator seed:

Controls:

Data shuffling
Initialization
Reproducibility

Settings:

0: System random
Fixed value: Reproducible
Different: Ensemble creation

MaxIter

i64

1000

Maximum iterations limit:

Purpose:

Controls training time
Prevents infinite loops
Resource management

Guidelines:

Small data: 500-1000
Large data: 1000-2000
Complex: 2000+

Note: May affect convergence

GridSearch

Linear SVR hyperparameter optimization:

Search dimensions:

Model complexity:
- Regularization (C)
- Error tolerance (ε)
- Loss function type
Training control:
- Convergence criteria
- Iteration limits
- Numerical precision
Model structure:
- Intercept handling
- Feature scaling
- Initialization

Best practices:

Log-scale for C, ε
Compare loss functions
Monitor convergence
Resource awareness

Epsilon

[f64, ...]

Error tolerance (ε) search:

Search patterns:

No tolerance: [0.0]
- Exact fitting
- Maximum precision
Standard range:
- [0.1, 0.2, 0.5]
- Scale with target
Fine-grained:
- [0.01, 0.05, 0.1]
- Precision study

Loss

[enum, ...]

SquaredEpsilonInsensitive

Loss function selection:

Mathematical forms:

L1 (Epsilon-insensitive): $L (y, f) = ma x (0, ∣ y - f ∣ - ϵ)$
L2 (Squared Epsilon-insensitive): $L (y, f) = ma x (0, ∣ y - f ∣ - ϵ)^{2}$

Properties:

L1: More robust to outliers
L2: Smoother solutions

Impact on model:

Training stability
Solution sparsity
Prediction behavior

EpsilonInsensitive ~

L1 Epsilon-insensitive loss:

Properties:

Linear penalty beyond ε
Robust to outliers
Sparse solutions
Standard SVR choice

Best for:

Noisy data
Outlier presence
Memory constraints
Sparse models

SquaredEpsilonInsensitive ~

L2 Squared epsilon-insensitive loss:

Properties:

Quadratic penalty beyond ε
Smooth solutions
Dense coefficients
Stable gradients

Best for:

Clean data
Smooth transitions
Stable predictions
Fine regression

Tol

[f64, ...]

0.0001

Convergence tolerance search:

Search spaces:

High precision:
- [1e-5, 1e-4, 1e-3]
- Exact solutions
Balanced:
- [1e-4, 1e-3]
- Speed vs accuracy
Quick convergence:
- [1e-3, 1e-2]
- Faster training

CFactor

[f64, ...]

Regularization strength search:

Search patterns:

Log-scale:
- [0.1, 1.0, 10.0]
- Wide exploration
- Common range
Fine-tuning:
- [0.8, 1.0, 1.2]
- Around optimal
- Local search

Impact:

Model complexity
Generalization
Fitting precision

FitIntercept

[bool, ...]

true

Intercept fitting evaluation:

Search options:

Standard: [true]
- With bias term
- General case
- Complete model
Compare: [true, false]
- Model flexibility
- Bias importance
- Structure impact

Consider with:

Data centering
Feature scaling
Target distribution

InterceptScaling

[f64, ...]

Intercept scaling search:

Search ranges:

Standard:
- [1.0, 2.0, 5.0]
- Regular scaling
- Common values
Wide range:
- [0.1, 1.0, 10.0]
- Impact study
- Full exploration

Effects:

Bias strength
Regularization impact
Model flexibility

MaxIter

[i64, ...]

1000

Maximum iterations search:

Search spaces:

Standard range:
- [500, 1000, 2000]
- Common scenarios
- Balanced choice
Extended search:
- [1000, 2000, 5000]
- Complex problems
- Full convergence
Quick trials:
- [100, 500]
- Initial testing
- Fast iteration

RandomState

u64

Random seed control:

Applications:

Reproducibility:
- Fixed seed
- Consistent results
- Debug support
Stability analysis:
- Multiple seeds
- Variance study
- Robustness check

Values:

0: System random
Fixed: Reproducible runs

RefitScore

enum

R2score

Regression model evaluation metrics:

Purpose:

Model performance evaluation
Error measurement
Quality assessment
Model comparison

Selection criteria:

Error distribution
Scale sensitivity
Domain requirements
Business objectives

Default ~

Model's native scoring method:

Typically R² score
Model-specific implementation
Standard evaluation
Quick assessment

R2score ~

Coefficient of determination (R²):

Formula: $R^{2} = 1 - \frac{\sum ( y _{i} - y ^ _{i} ) ^{2}}{\sum ( y _{i} - y ˉ ) ^{2}}$

Properties:

Range: (-∞, 1]
1: Perfect prediction
0: Constant model
Negative: Worse than mean

Best for:

General performance
Variance explanation
Model comparison
Standard reporting

ExplainedVariance ~

Explained variance score:

Formula: $1 - \frac{Va r ( y - y ^ )}{Va r ( y )}$

Properties:

Range: (-∞, 1]
Accounts for bias
Variance focus
Similar to R²

Best for:

Variance analysis
Bias assessment
Model stability

MaxError ~

Maximum absolute error:

Formula: $max (∣ y_{i} - \overset{y}{^}_{i} ∣)$

Properties:

Worst case error
Original scale
Sensitive to outliers
Upper error bound

Best for:

Critical applications
Error bounds
Safety margins
Risk assessment

NegMeanAbsoluteError ~

Negative mean absolute error:

Formula: $- \frac{1}{n} \sum ∣ y_{i} - \overset{y}{^}_{i} ∣$

Properties:

Linear error scale
Robust to outliers
Original units
Negated for optimization

Best for:

Robust evaluation
Interpretable errors
Outlier presence

NegMeanSquaredError ~

Negative mean squared error:

Formula: $- \frac{1}{n} \sum (y_{i} - \overset{y}{^}_{i})^{2}$

Properties:

Squared error scale
Outlier sensitive
Squared units
Negated for optimization

Best for:

Standard optimization
Large error penalty
Statistical analysis

NegRootMeanSquaredError ~

Negative root mean squared error:

Formula: $- \frac{1}{n} \sum (y_{i} - \overset{y}{^}_{i})^{2}$

Properties:

Original scale
Outlier sensitive
Interpretable units
Negated for optimization

Best for:

Standard reporting
Interpretable errors
Model comparison

NegMeanSquaredLogError ~

Negative mean squared logarithmic error:

Formula: $- \frac{1}{n} \sum (lo g (1 + y_{i}) - lo g (1 + \overset{y}{^}_{i}))^{2}$

Properties:

Relative error scale
For positive values
Sensitive to ratios
Negated for optimization

Best for:

Exponential growth
Relative differences
Positive predictions

NegMedianAbsoluteError ~

Negative median absolute error:

Formula: $- m e d ian (∣ y_{i} - \overset{y}{^}_{i} ∣)$

Properties:

Highly robust
Original scale
Outlier resistant
Negated for optimization

Best for:

Robust evaluation
Heavy-tailed errors
Outlier presence

NegMeanPoissonDeviance ~

Negative Poisson deviance:

Formula: $- 2 \sum (y_{i} lo g (\frac{y _{i}}{y ^ _{i}}) - (y_{i} - \overset{y}{^}_{i}))$

Properties:

For count data
Non-negative values
Poisson assumption
Negated for optimization

Best for:

Count prediction
Event frequency
Rate modeling

NegMeanGammaDeviance ~

Negative Gamma deviance:

Formula: $- 2 \sum (lo g (\frac{y _{i}}{y ^ _{i}}) + \frac{y _{i} - y ^ _{i}}{y ^ _{i}})$

Properties:

For positive continuous data
Constant CV assumption
Relative errors
Negated for optimization

Best for:

Positive continuous data
Multiplicative errors
Financial modeling

NegMeanAbsolutePercentageError ~

Negative mean absolute percentage error:

Formula: $- \frac{100}{n} \sum ∣ \frac{y _{i} - y ^ _{i}}{y _{i}} ∣$

Properties:

Percentage scale
Scale independent
For non-zero targets
Negated for optimization

Best for:

Relative performance
Scale-free comparison
Business metrics

D2AbsoluteErrorScore ~

D² score with absolute error:

Formula: $1 - \frac{\sum ∣ y _{i} - y ^ _{i} ∣}{\sum ∣ y _{i} - y ˉ ∣}$

Properties:

Range: (-∞, 1]
Robust version of R²
Linear error scale
Outlier resistant

Best for:

Robust evaluation
Non-normal errors
Alternative to R²

D2PinballScore ~

D² score with pinball loss:

Properties:

Quantile focus
Asymmetric errors
Risk assessment
Distribution modeling

Best for:

Quantile regression
Risk analysis
Asymmetric costs
Distribution tails

D2TweedieScore ~

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

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