Models Overview¶

Core distributional regression models in the DRN package. All models inherit from the common BaseModel interface and provide distributional predictions.

Model Hierarchy¶

classDiagram
    BaseModel <|-- GLM
    BaseModel <|-- DeepGLM
    BaseModel <|-- DRN
    BaseModel <|-- CANN
    BaseModel <|-- MDN
    BaseModel <|-- DDR
    BaseModel <|-- Constant

    class BaseModel {
        +fit(X, y)
        +predict(X)
        +quantiles(X, percentiles)
        +loss(x, y)
    }

    class GLM {
        +distribution: str
        +clone()
    }

    class DRN {
        +baseline: BaseModel
        +cutpoints: list
        +log_adjustments(x)
    }

Quick Reference¶

Model	Purpose	Key Features	Best For
BaseModel	Abstract base class	Common interface, PyTorch Lightning	All models inherit from this
GLM	Generalized Linear Models	Interpretable, statistical foundation	Baseline models, simple relationships
DeepGLM	Deep Generalized Linear Model	Neural feature learning + GLM head	Nonlinear relationships, distributional outputs
DRN	Distributional Refinement Network	Neural + interpretable baseline	Complex distributions with interpretability
CANN	Combined Actuarial Neural Network	Actuarial focus, separate parameter networks	Insurance and actuarial applications
MDN	Mixture Density Network	Multi-modal distributions	Complex, multi-peaked data
DDR	Deep Distribution Regression	Pure neural approach	Maximum flexibility, no baseline constraint
Constant	Constant prediction	Simple baseline	Benchmarking, ablation studies

Common Usage Patterns¶

Basic Model Training¶

from drn import GLM, DRN

# Train baseline
baseline = GLM('gamma')
baseline.fit(X_train, y_train)

# Train refined model
drn_model = DRN(baseline)
drn_model.fit(X_train, y_train)

Distribution Families¶

GLM Distributions¶

gaussian - Normal distribution for unbounded continuous data
gamma - Gamma distribution for positive continuous data
inversegaussian - Inverse Gaussian for positive data with right skew
lognormal - Log-normal for multiplicative processes

Advanced Distributions¶

Histogram - Flexible discrete distributions
Extended Histogram - Continuous extensions of histograms
Mixture Models - Multi-component distributions

Model Selection Guide¶

Start with GLM when:¶

You need interpretability
Data follows standard distributions
Baseline performance is adequate
Statistical inference is required

Use DRN when:¶

GLM baseline is reasonable but not sufficient
You need both flexibility and interpretability
Complex distributional shapes are present
Regularization control is important

Consider Advanced Models when:¶

CANN: Actuarial applications with domain knowledge
MDN: Multi-modal or mixture distributions expected
DDR: Maximum flexibility, no interpretability needed
Constant: Simple benchmarking baseline

Model Comparison¶

Performance Characteristics¶

Model	Training Speed	Inference Speed	Memory Usage	Interpretability	Flexibility
GLM	⭐⭐⭐⭐⭐	⭐⭐⭐⭐⭐	⭐⭐⭐⭐⭐	⭐⭐⭐⭐⭐	⭐⭐
DeepGLM	⭐⭐⭐	⭐⭐⭐⭐	⭐⭐⭐	⭐⭐⭐	⭐⭐⭐⭐
DRN	⭐⭐⭐	⭐⭐⭐⭐	⭐⭐⭐	⭐⭐⭐⭐	⭐⭐⭐⭐
CANN	⭐⭐	⭐⭐⭐	⭐⭐	⭐⭐	⭐⭐⭐⭐
MDN	⭐⭐	⭐⭐⭐	⭐⭐	⭐⭐	⭐⭐⭐⭐⭐
DDR	⭐⭐	⭐⭐⭐	⭐⭐	⭐	⭐⭐⭐⭐⭐