LassoLars / Regressor Layer

L1 regularization strength:

Mathematical impact: $$\underset{\beta }{\min }\frac{1}{2n}||y-X\beta |{|}_2^2+\alpha ||\beta |{|}_1$$

Effects:

• Controls sparsity
• Influences path length
• Affects solution stability
• Determines model complexity

Typical values:

• Weak: 0.01-0.1
• Standard: 1.0
• Strong: 10.0-100.0

Intercept calculation control:

Model forms: With intercept: $$y=X\beta +b+ϵ$$ Without intercept: $$y=X\beta +ϵ$$

Effects when True:

• Centers predictions
• Improves fit
• Handles bias
• Standard modeling

Effects when False:

• Origin-constrained
• Theory-driven
• Simpler model
• Domain-specific needs

Maximum number of iterations to perform.

Algorithm impact:

• Path length limit
• Computation bound
• Solution granularity
• Resource control

Typical ranges:

• Small problems: 100-300
• Standard: 500
• Complex: 1000+

Note: Each step adds one feature

Numerical precision parameter:

Usage: $$eps\times machine\_precision$$

Effects:

• Cholesky stability
• Numerical accuracy
• Computation reliability
• Ill-conditioning handling

Typical values:

• Standard: 1.0
• Ill-conditioned: 10-100
• Extreme cases: 100+

Solution path computation control:

When True:

• Computes full path
• Enables path analysis
• More memory usage
• Complete solution

When False:

• Final solution only
• Memory efficient
• Faster computation
• Large-scale problems

Trade-offs:

• Memory vs information
• Speed vs completeness
• Analysis vs efficiency

Noise addition parameter:

Purpose:

• Stability enhancement
• Tie breaking
• Degeneracy handling
• Numerical robustness

Effects:

• Adds U(-jitter, jitter) noise
• Affects path computation
• Influences selection
• Impacts reproducibility

Usage:

• 0: No jitter
• Small: 1e-6 to 1e-4
• Larger: Stability issues

Whether to restrict coefficients to be >= 0.

Mathematical impact: $$\underset{\beta \ge 0}{\min }\frac{1}{2n}||y-X\beta |{|}_2^2+\alpha ||\beta |{|}_1$$

Applications:

• Signal processing
• Image reconstruction
• Concentration studies
• Physical quantities

Effects:

• Modifies LARS path
• Constrains solutions
• Affects convergence
• Domain-specific meaning

Determines random number generation for jittering.

Controls:

• Jitter generation
• Tie breaking
• Stochastic processes

Usage patterns:

1. Development:

   • Fixed seed
   • Reproducible results
   • Debugging

2. Production:

   • Multiple seeds
   • Stability testing
   • Robustness checks

Regularization strength search space:

Search strategies:

1. Log scale (recommended):

   • [0.0001, 0.001, 0.01, 0.1, 1.0]
   • Wide coverage
   • Standard approach

2. Fine-tuning:

   • [0.1, 0.3, 0.7, 1.0]
   • Around promising values
   • Refined search

3. Problem-specific:

   • Based on data scale
   • Domain knowledge
   • Target sparsity

Intercept inclusion search space:

Options:

1. Standard: [true]

   • Default modeling
   • Centered data

2. Zero-intercept: [false]

   • Theory-driven
   • Origin-constrained

3. Complete: [true, false]

   • Model comparison
   • Impact analysis

Maximum steps search space:

Search patterns:

1. Basic range:

   • [100, 300, 500]
   • Standard problems

2. Extended search:

   • [500, 1000, 2000]
   • Complex problems

3. Path study:

   • Based on features
   • Solution granularity
   • Resource limits

Numerical precision search space:

Search ranges:

1. Standard conditions:

   • [1.0, 10.0]
   • Normal stability

2. Ill-conditioned:

   • [10.0, 100.0, 1000.0]
   • Numerical issues

3. Extreme cases:

   • Higher values
   • Stability critical

Path computation evaluation:

Options:

1. Full path: [true]

   • Complete analysis
   • Memory intensive

2. Final only: [false]

   • Resource efficient
   • Large problems

3. Compare: [true, false]

   • Trade-off study
   • Resource impact

Stability parameter search:

Search spaces:

1. No jitter: [0.0]

   • Default behavior
   • Clean data

2. Light jitter:

   • [1e-6, 1e-5, 1e-4]
   • Mild stability

3. Strong jitter:

   • [1e-4, 1e-3]
   • Severe issues

Positive constraint evaluation:

Search options:

1. Unconstrained: [false]

   • Standard modeling
   • Faster computation

2. Constrained: [true]

   • Physical meaning
   • Domain requirements

3. Compare: [true, false]

   • Impact analysis
   • Trade-off study

Random seed configuration:

Usage:

• Fixed: Reproducibility
• Varied: Stability tests
• Multiple: Robustness

Best practices:

• Document seeds
• Systematic testing
• Verify stability

Regression model evaluation metrics:

Purpose:

• Model performance evaluation
• Error measurement
• Quality assessment
• Model comparison

Selection criteria:

• Error distribution
• Scale sensitivity
• Domain requirements
• Business objectives

Random seed for reproducible splits. Ensures:

• Consistent train/test sets
• Reproducible experiments
• Comparable model evaluations

Same seed guarantees identical splits across runs.

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

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

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

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.

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.

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.

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

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

Seed for reproducible stratified splits. Ensures:

• Consistent fold assignments
• Reproducible results
• Comparable experiments
• Systematic validation

Fixed seed guarantees identical stratified splits.

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.

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.

Random seed for reproducible shuffling. Controls:

• Split randomization
• Sample selection
• Result reproducibility

Important for:

• Debugging
• Comparative studies
• Result verification

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.

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

Seed for reproducible stratified sampling. Ensures:

• Consistent class proportions
• Reproducible splits
• Comparable experiments

Critical for:

• Benchmarking
• Research studies
• Quality assurance

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.

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

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

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

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