QuadraticDiscriminantAnalysis / Classifier Layer

Quadratic Discriminant Analysis Classification: A classifier with a quadratic decision boundary, generated by fitting class conditional densities to the data and using Bayes’ rule.

Mathematical formulation: where:

  • P(x|y) has class-specific covariance matrices
  • Each class modeled as Gaussian:
  • Results in quadratic decision boundaries

Key characteristics:

  • Class-specific covariances
  • Quadratic boundaries
  • No covariance sharing
  • More flexible than LDA
  • Higher variance estimator

Advantages:

  • Handles non-linear separation
  • Class-specific scatter
  • Better when variances differ
  • Natural probability estimates
  • No distribution assumptions between classes

Common applications:

  • Medical diagnosis
  • Signal classification
  • Pattern recognition
  • Spectral analysis
  • Biometric identification

Outputs:

  1. Predicted Table: Results with predictions
  2. Validation Results: Cross-validation metrics
  3. Test Metric: Hold-out performance
  4. ROC Curve Data: Classification analysis
  5. Confusion Matrix: Class predictions
  6. Feature Importances: Discriminant coefficients
Table
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Predicted Table
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Validation Results
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Test Metric
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ROC Curve Data
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4
Confusion Matrix
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5
Feature Importances

SelectFeatures

[column, ...]

Feature column selection for Quadratic Discriminant Analysis:

Data requirements:

  1. Statistical assumptions:

    • Class-wise Gaussian distribution
    • Independent features preferred
    • Sufficient samples per class
    • Non-singular class covariances

  2. Preprocessing needs:

    • Standardization recommended
    • Outlier treatment important
    • Missing value handling
    • Feature scaling beneficial

  3. Feature considerations:

    • Check class-wise correlations
    • Monitor feature variance
    • Assess discriminative power
    • Consider interactions

  4. Sample size guidelines:

    • n_samples_per_class > n_features
    • More samples for stability
    • Class-balanced preferred
    • Consider dimensionality

  5. Quality checks:

    • Class-wise distributions
    • Covariance stability
    • Feature relevance
    • Numerical conditioning

Note: If empty, automatically uses all suitable numeric columns except target

Target column specification for QDA classification:

Requirements:

  1. Data structure:

    • Categorical labels
    • Unique class values
    • No missing labels
    • Clear class definitions

  2. Class characteristics:

    • Two or more classes
    • Adequate samples per class
    • Distinct covariance structures
    • Well-defined boundaries

  3. Statistical considerations:

    • Class-wise normality
    • Covariance differences
    • Sample size requirements
    • Prior probabilities

  4. Practical aspects:

    • Label encoding
    • Class separation
    • Error costs
    • Prediction goals

  5. Validation needs:

    • Stratified sampling
    • Performance metrics
    • Model evaluation
    • Generalization assessment

Note: Must be a single column containing class labels

Params

oneof
DefaultParams

Default configuration for Quadratic Discriminant Analysis:

Core settings:

  1. Covariance estimation:

    • No regularization (reg_param = 0.0)
    • Class-specific matrices
    • Maximum likelihood estimation

  2. Numerical parameters:

    • Tolerance: 1e-4
    • Automatic prior estimation
    • Standard precision

  3. Memory settings:

    • No covariance storage
    • Minimal memory usage
    • Efficient computation

Best suited for:

  • Well-separated classes
  • Sufficient samples per class
  • Different class variances
  • Initial modeling phase

Customizable parameters for Quadratic Discriminant Analysis:

Parameter categories:

  1. Regularization control:

    • Covariance stability
    • Numerical conditioning
    • Variance reduction

  2. Estimation settings:

    • Prior probabilities
    • Covariance computation
    • Numerical precision

  3. Memory management:

    • Storage options
    • Computation efficiency
    • Resource utilization

Trade-offs:

  • Stability vs flexibility
  • Memory vs computation
  • Precision vs generalization
0

Covariance regularization parameter:

Mathematical form: where:

  • α is reg_param
  • Σ is sample covariance
  • I is identity matrix

Impact:

  • Controls matrix conditioning
  • Reduces estimation variance
  • Improves numerical stability
  • Prevents singularity

Typical values:

  • None: 0.0
  • Weak: 0.01-0.1
  • Moderate: 0.1-0.3
  • Strong: 0.3-0.9

Guidelines:

  • Increase for small sample sizes
  • Adjust for feature correlation
  • Monitor performance impact
  • Consider class sample sizes

Hyperparameter optimization for Quadratic Discriminant Analysis:

Search space organization:

  1. Regularization search:

    • Covariance stability
    • Numerical robustness
    • Model complexity

  2. Performance criteria:

    • Metric selection
    • Evaluation strategy
    • Model comparison

Computational impact:

  • Time: O(n_params * n_classes * n_features²)
  • Memory: O(n_classes * n_features²)
  • Storage: O(n_params * n_classes * n_features²)

RegParam

[f64, ...]
0

Regularization parameter search space:

Search strategies:

  1. Logarithmic scale:

    • [0.0, 0.01, 0.1, 0.3]
    • Covers wide range
    • Standard approach

  2. Fine-grained:

    • [0.0, 0.05, 0.1, 0.15, 0.2]
    • Detailed exploration
    • Precise tuning

  3. Problem-specific:

    • Small samples: [0.1, 0.3, 0.5]
    • Large samples: [0.0, 0.01, 0.1]

Selection impact:

  • Model stability
  • Prediction accuracy
  • Generalization
  • Numerical behavior
Accuracy

Performance evaluation metrics for QDA classification:

Purpose:

  • Model evaluation
  • Performance comparison
  • Model selection
  • Quality assessment

Selection criteria:

  • Class distribution
  • Problem objectives
  • Error sensitivity
  • Application requirements
Default ~

Native QDA scoring method:

Properties:

  • Based on accuracy
  • Fast computation
  • Standard metric
  • Equal error weights

Best for:

  • Initial evaluation
  • Quick assessment
  • Balanced datasets
  • General comparison
Accuracy ~

Standard classification accuracy:

Formula:

Properties:

  • Range: [0, 1]
  • Intuitive metric
  • Equal weighting
  • Simple calculation

Best for:

  • Balanced classes
  • Equal error costs
  • Overall performance
  • Standard comparison
BalancedAccuracy ~

Class-normalized accuracy score:

Formula:

Properties:

  • Range: [0, 1]
  • Class-wise normalization
  • Imbalance robust
  • Fair evaluation

Best for:

  • Imbalanced datasets
  • Varying class sizes
  • Fair comparison
  • Minority class focus
LogLoss ~

Logarithmic loss metric:

Formula:

Properties:

  • Range: [0, ∞)
  • Probability sensitive
  • Penalizes confidence errors
  • Information theoretic

Best for:

  • Probability estimation
  • Confidence assessment
  • Risk modeling
  • Calibration needs
RocAuc ~

Area Under ROC Curve score:

Measurement:

Properties:

  • Range: [0, 1]
  • Threshold invariant
  • Ranking quality
  • Discrimination power

Best for:

  • Binary classification
  • Ranking problems
  • Threshold optimization
  • Performance curves

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.

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
98

Random seed for reproducible splits. Ensures:

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

Same seed guarantees identical splits across runs.

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
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
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

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
3

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.

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
5

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.

98

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.

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

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
5

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
98

Seed for reproducible stratified splits. Ensures:

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

Fixed seed guarantees identical stratified splits.

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.

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
5

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.

98

Random seed for reproducible shuffling. Controls:

  • Split randomization
  • Sample selection
  • Result reproducibility

Important for:

  • Debugging
  • Comparative studies
  • Result verification
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.

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
5

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
98

Seed for reproducible stratified sampling. Ensures:

  • Consistent class proportions
  • Reproducible splits
  • Comparable experiments

Critical for:

  • Benchmarking
  • Research studies
  • Quality assurance
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.

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.

5

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
0

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
0

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
0

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
Model data using QuadraticDiscriminantAnalysis: Graph Dataflow Studio -->
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