RETINA - Relevant Transformation of the Inputs Network Approach

A MATLAB implementation of the RETINA algorithm for automatic variable selection in statistical modeling with multicollinearity control.

Overview

RETINA is a model selection algorithm designed to automatically identify relevant predictors from a set of candidate variables while controlling for multicollinearity. It uses a stepwise approach with cross-validation to build parsimonious models that generalize well to new data.

Features

• Automatic variable selection with multicollinearity control
• Three algorithm variants:
  • Original PAGW (Perez-Amaral, Gallo, White) algorithm
  • PAGW with union model feature
  • Adaptive lambda grid search
• Cross-validation using three-way data splitting
• Multiple model selection criteria: AIC, AICC, BIC
• Efficient computation using sweep operations

Installation

Clone this repository:

git clone https://github.com/m-marinucci/RETINA.git
cd RETINA

Requirements

• MATLAB (tested on R2020a and later)
• Statistics and Machine Learning Toolbox (optional, for extended functionality)

Quick Start

% Clear workspace and initialize
clear all; close all; clc;

% Add RETINA to your MATLAB path
addpath('path/to/RETINA');

% Load your data or use the test example
[y, w, dataflag] = test1;  % Example data

% Set subsample proportions (must sum to less than 1)
pvec = [0.33; 0.33];  % 33% training, 33% validation, 34% test

% Run RETINA
[selected_model, subset_info] = RETINA(pvec, y, w, dataflag, 1, 1);

% selected_model contains the final selected variables
% subset_info contains detailed information about the selection process

Usage

Basic Usage

[c_retina, subset_retina] = RETINA(pvec, y, w, dataflag, procflag, verbose)

Parameters

• pvec: Vector of subsample proportions (must sum to less than 1, e.g., [0.33; 0.33] for equal splits)
• y: Response variable (n×1 column vector)
• w: Predictor matrix (n×p matrix)
• dataflag: Data type indicator (1 = actual data, 0 = simulated data)
• procflag: Algorithm variant:
  • 1: Original PAGW algorithm (fixed lambda grid search)
  • 2: PAGW with union model (includes all-predictor model)
  • 3: Adaptive lambda approach (adjusts grid based on data characteristics)
• verbose: Output verbosity (0 = silent, 1 = verbose)

Output

• c_retina: Selected model coefficients and statistics
• subset_retina: Detailed information about the model selection process

Algorithm Details

RETINA works in several stages with sophisticated model selection mechanisms:

Core Algorithm Flow

1. Data Splitting (datasubsets.m): Divides data into three subsamples for training, validation, and testing
2. Model Building (build_1.m, build_2.m, build_3.m): Constructs candidate models on the first subsample using stepwise addition of predictors with multicollinearity control via lambda threshold
3. Cross-Validation (crossub_1_2_2.m): Evaluates candidate models on the second subsample
4. Final Selection (evamod.m, evafinal.m): Tests the best models on the third subsample and selects the final model using information criteria (AIC, AICC, or BIC)

Key Components

• Model Building: Stepwise addition of predictors with multicollinearity control via lambda threshold
• Model Evaluation: Uses AIC, AICC, or BIC for model selection
• Efficient Computation: Uses sweep operations (sweep.m) for matrix calculations
• Duplicate Detection: compmod.m prevents redundant model evaluation

Algorithm Variants

The three procflag options provide different approaches:

• Procedure 1 (Original PAGW): Fixed lambda grid search with systematic exploration of predictor combinations
• Procedure 2 (PAGW with union model): Includes all-predictor model in addition to stepwise selection
• Procedure 3 (Adaptive lambda): Adjusts lambda grid based on data characteristics for more flexible multicollinearity control

Example

See example_usage.m for a complete working example with synthetic data.

File Structure

RETINA/
├── RETINA.m              # Main algorithm function
├── build_1.m             # Original PAGW algorithm
├── build_2.m             # PAGW with union model
├── build_3.m             # Adaptive lambda version
├── datasubsets.m         # Data splitting function
├── crossub_1_2_2.m       # Cross-validation function
├── evamod.m              # Model evaluation function
├── evafinal.m            # Final model selection
├── sweep.m               # Efficient matrix operations
├── test1.m               # Example data generator
└── run_RETINA.m          # Example runner script

Citation

If you use RETINA in your research, please cite:

@phdthesis{marinucci2008automatic,
  title={Automatic Prediction and Model Selection},
  author={Marinucci, Massimiliano},
  year={2008},
  school={Universidad Complutense Madrid},
  type={{PhD} dissertation}
}

Or in text format:

Marinucci, M. (2008). Automatic Prediction and Model Selection. 
PhD dissertation, Universidad Complutense Madrid.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Authors

• Massimiliano Marinucci

References

Core RETINA Publications

• Pérez-Amaral, T., Gallo, G. M., & White, H. (2003). A flexible tool for model building: the relevant transformation of the inputs network approach (RETINA). Oxford Bulletin of Economics and Statistics, 65(s1), 821-838.

• Pérez-Amaral, T., Gallo, G. M., & White, H. (2005). A comparison of complementary automatic modeling methods: RETINA and PcGets. Econometric Theory, 21(1), 262-277.

• Marinucci, M. (2010). Automatic Prediction and Model Selection. LAP Lambert Academic Publishing. ISBN: 978-3-8383-2689-4.

Related Automatic Model Selection Methods

• Hendry, D. F., & Krolzig, H. M. (1999). Improving on 'Data mining reconsidered' by K.D. Hoover and S.J. Perez. Econometrics Journal, 2(2), 202-219.

• Hoover, K. D., & Perez, S. J. (1999). Data mining reconsidered: encompassing and the general-to-specific approach to specification search. Econometrics Journal, 2(2), 167-191.

• Hendry, D. F., & Krolzig, H. M. (2001). Automatic Econometric Model Selection Using PcGets. London: Timberlake Consultants.

• Castle, J. L., Doornik, J. A., & Hendry, D. F. (2012). Model selection when there are multiple breaks. Journal of Econometrics, 169(2), 239-246.

Multicollinearity and Variable Selection

• Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B, 58(1), 267-288.

• Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B, 67(2), 301-320.

Acknowledgments

• Based on the PAGW algorithm by Perez-Amaral, Gallo, and White
• Developed as part of PhD research on automatic model selection methods