Linear Models, Variable Selection, Artificial Intelligence

Anton Westveld; By Riyadh Alrawkan; Edward Boone; Ryad Ghanam

arxiv: 2604.27191 · v1 · submitted 2026-04-29 · 📊 stat.ME · cs.LG· stat.ML

Linear Models, Variable Selection, Artificial Intelligence

By Riyadh Alrawkan , Edward Boone , Ryad Ghanam , Anton Westveld This is my paper

Pith reviewed 2026-05-07 09:52 UTC · model grok-4.3

classification 📊 stat.ME cs.LGstat.ML

keywords variable selectionartificial neural networkslinear regressionmodel selectionsimulation studyOLS estimateslife expectancy

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The pith

An artificial neural network trained on ordinary least squares estimates can identify significant variables for linear regression models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a method that uses an artificial neural network to perform variable selection in linear regression by training it to recognize which predictors are significant based on their ordinary least squares coefficient estimates. Simulations demonstrate that the network maintains accuracy across different sample sizes and levels of variance in the data. The authors compare this approach to conventional techniques including forward selection, backward elimination, AIC, BIC, and LASSO, finding competitive performance, and then apply it to a real dataset on life expectancy collected by the World Health Organization. This matters because choosing the right variables is a longstanding challenge in statistical modeling, and an AI-based tool trained once could offer a scalable alternative to iterative or penalty-based methods.

Core claim

The authors claim that training an artificial neural network on data generated from known linear models allows the network to learn to classify variables as significant or insignificant solely from their ordinary least squares estimates, and that this classifier performs well in simulations and can be used on real data.

What carries the argument

An artificial neural network that takes ordinary least squares estimates as input and outputs the significance of each variable.

If this is right

The method shows consistent accuracy in simulations for a range of sample sizes and error variances.
It performs at least as well as Forward, Backward, AIC, BIC, and LASSO selection methods in comparative simulations.
The pretrained network can be applied directly to datasets with up to 100 predictors, as illustrated with the WHO life expectancy data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the network generalizes beyond the training simulations, it could reduce the need for manual tuning of selection criteria in applied work.
Extending the training to include cases with correlated predictors might make the method robust to multicollinearity.
Using the network's output probabilities rather than hard classifications could provide a measure of inclusion uncertainty.

Load-bearing premise

That an ANN trained on simulated data with known true models will correctly identify significant variables when applied to real data where the true underlying model is unknown and OLS estimates may be biased or noisy.

What would settle it

Applying the method to a new set of simulated datasets with known ground-truth significant variables and verifying whether the selected variables match the true ones at high rates across varied conditions.

read the original abstract

Variable selection in linear regression models has been a problem since hypothesis testing began. Which variables to include or exclude from a model is not an easy task. Techniques such as Forward, Back ward, Stepwise Regression sequentially add or delete variables from a model. Penalized likelihood methods such as AIC, BIC, etc. seek to choose variables that have a significant contribution to the likelihood. Penalized sum of square methods such as LASSO and Elastic Net have been used to penalize small coefficients to only allow variables with large coefficients in the model. This work introduces an Artificial Intelligence approach to model selection where an ANN is trained to determine the significance of the variables based on OLS estimates. A simulation study shows the accuracy across various sample sizes and variances. Furthermore, a simulation study is conducted to compare the performance of the approach against Forward, Backward, AIC, BIC and LASSO. The approach is illustrated using a dataset from the World Health Organization regarding Life Expectancy. A github link is provided to the pretrained ANN that can handle up to 100 predictor variables, the original WHO dataset and the subset used in this work.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper trains an ANN on OLS estimates to pick significant variables in linear models, with simulation comparisons and a shared pretrained model, but the evaluation stays too clean to confirm real-data reliability.

read the letter

The main takeaway is that this work trains a neural net to take OLS coefficient estimates and output which variables matter, then tests it in simulations across sample sizes and variances while comparing to forward, backward, AIC, BIC, and LASSO. They also apply it to the WHO life expectancy data and release a pretrained model on GitHub that handles up to 100 predictors. That practical sharing is the clearest positive here; it gives applied users something they can actually download and try without rebuilding from scratch. The simulations show the approach holds up under the controlled conditions they set, which is a reasonable baseline check for a new wrapper method. The integration itself is new enough as a direct application to the OLS output vector rather than a full replacement of the regression step. The soft spots are straightforward. The description gives almost no architecture details, training protocol, or exact accuracy figures with error bars, so the central performance claim is hard to assess fully. More critically, the simulations use data generated with known truth and no mention of common real-world distortions like multicollinearity, heteroscedasticity, or non-Gaussian errors. Without those, the learned mapping risks being tuned to the simulation design rather than generalizing when OLS estimates are biased or noisy on actual data. The single WHO example does not close that gap. This is aimed at applied statisticians or analysts who run linear regressions and want another selection option they can plug in quickly. It is not reshaping theory but could serve as a handy tool if the robustness questions get answered. It deserves a serious referee because the code is shared and the comparisons exist, though any review would need to press for more methodological transparency and targeted stress tests on messy data.

Referee Report

3 major / 3 minor

Summary. The paper proposes an Artificial Intelligence method for variable selection in linear models by training an Artificial Neural Network (ANN) on ordinary least squares (OLS) coefficient estimates to identify significant variables. It presents simulation studies demonstrating the accuracy of this approach across various sample sizes and error variances, and compares its performance to Forward, Backward, AIC, BIC, and LASSO methods. The method is applied to the World Health Organization Life Expectancy dataset, and a pretrained ANN for up to 100 predictors is made available along with the data.

Significance. If the results hold, the approach offers a novel data-driven alternative to traditional variable selection techniques that could potentially handle complex patterns in OLS outputs without explicit penalty terms or sequential testing. The provision of a pretrained model and GitHub resources supports reproducibility and practical use. However, the current presentation limits the ability to assess its superiority or robustness beyond the specific simulations described.

major comments (3)

The abstract reports simulation accuracy and comparisons but provides no architecture details, training procedure, exact performance numbers, error bars, or data-generation protocol; without these, the central claim that the method works across sample sizes and variances cannot be fully evaluated.
The comparison to Forward, Backward, AIC, BIC and LASSO lacks specific quantitative results, tables, or figures showing performance metrics, making it difficult to verify the claim of outperformance or equivalence.
The ANN is trained exclusively on simulated data with known true models. The manuscript does not address whether the simulations include realistic violations such as multicollinearity, heteroscedasticity, omitted variables, or non-Gaussian errors that distort OLS estimates in real data (e.g., the WHO Life Expectancy dataset), raising doubts about generalization to cases where the true underlying model is unknown.

minor comments (3)

Typo in abstract: 'Back ward' should be 'Backward'.
The manuscript should include the specific GitHub link and details on how to use the pretrained ANN.
Consider adding more references to existing literature on machine learning for variable selection to contextualize the contribution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of clarity and robustness that we will address in the revision. We respond to each major comment below.

read point-by-point responses

Referee: The abstract reports simulation accuracy and comparisons but provides no architecture details, training procedure, exact performance numbers, error bars, or data-generation protocol; without these, the central claim that the method works across sample sizes and variances cannot be fully evaluated.

Authors: We agree that the abstract is brief and omits these specifics, which limits immediate evaluation. The full manuscript describes the ANN as a feedforward network taking OLS coefficient estimates as inputs, trained via backpropagation on simulated data generated from known linear models with varying sample sizes and error variances. Performance is quantified as the proportion of correctly identified significant variables. To improve the manuscript, we will revise the abstract to summarize the architecture, data-generation protocol, and key accuracy figures with standard errors from the simulations. revision: yes
Referee: The comparison to Forward, Backward, AIC, BIC and LASSO lacks specific quantitative results, tables, or figures showing performance metrics, making it difficult to verify the claim of outperformance or equivalence.

Authors: The manuscript conducts simulation comparisons and states that the ANN approach is competitive, but we acknowledge that consolidated quantitative metrics are not presented in a single table or figure. We will add a results table reporting accuracy, precision, and recall (with variability) for the ANN versus Forward, Backward, AIC, BIC, and LASSO across the simulated scenarios to allow direct verification. revision: yes
Referee: The ANN is trained exclusively on simulated data with known true models. The manuscript does not address whether the simulations include realistic violations such as multicollinearity, heteroscedasticity, omitted variables, or non-Gaussian errors that distort OLS estimates in real data (e.g., the WHO Life Expectancy dataset), raising doubts about generalization to cases where the true underlying model is unknown.

Authors: This observation is correct. The simulations assume standard conditions (independent Gaussian errors, no multicollinearity) to evaluate the method when the true model is known. The manuscript does not test or discuss performance under violations such as heteroscedasticity or omitted variables. In revision we will add a dedicated limitations subsection noting these assumptions, clarifying that the WHO application is illustrative only, and outlining plans for future work on more realistic data-generating processes. revision: partial

Circularity Check

0 steps flagged

No significant circularity: empirical ANN method with independent simulation evaluations

full rationale

The paper proposes training an ANN on simulated linear regression datasets (with known true models) to map OLS coefficient estimates to variable significance labels. Performance is then assessed via separate simulation studies that generate new data under varying n and sigma^2, comparing the ANN selector against Forward/Backward/AIC/BIC/LASSO, followed by an application to the real WHO Life Expectancy dataset. No equations, derivations, or theorems are presented that reduce any claimed accuracy or superiority to the training inputs by construction. There are no self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations. The simulation-based claims rely on out-of-sample test data distinct from training, rendering the approach self-contained and non-circular.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the ANN learning generalizable patterns of significance from OLS estimates. Free parameters include the network architecture, training hyperparameters, and choices of simulation settings for sample size and variance. Standard linear-model assumptions are invoked without new entities postulated.

free parameters (2)

ANN architecture and training hyperparameters
Number of layers, neurons per layer, activation functions, learning rate, and epochs are chosen or tuned to achieve reported accuracy on simulations.
Simulation data-generation parameters
Specific distributions and true coefficient values used to create training and test datasets across sample sizes and variances are selected by the authors.

axioms (2)

domain assumption Ordinary least squares estimates provide sufficient information for determining variable significance
The method feeds only OLS outputs into the ANN and assumes these capture the necessary signal.
standard math Linear regression model assumptions hold in the simulated and real data
OLS estimates are used throughout, relying on standard linearity, independence, and homoscedasticity conditions.

pith-pipeline@v0.9.0 · 5503 in / 1452 out tokens · 49951 ms · 2026-05-07T09:52:47.962454+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[1]

Steiner, B.,Tucker, P.,V asudevan, V.,W arden, P.,Wicke, M.,Yu, Y.andZheng, X. (2016). TensorFlow: A System for Large-Scale Machine Learning. In12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ’16)265–283

work page 2016
[2]

A New Look at the Statistical Model Identification.IEEE Transactions on Au- tomatic Control19716–723

Akaike, H.(1974). A New Look at the Statistical Model Identification.IEEE Transactions on Au- tomatic Control19716–723

work page 1974
[3]

Manning Publications

Chollet, F.(2021).Deep Learning with Python (2nd Edition). Manning Publications

work page 2021
[4]

R.andSmith, H.(1998).Applied Regression Analysis, 2nd ed

Draper, N. R.andSmith, H.(1998).Applied Regression Analysis, 2nd ed. Wiley

work page 1998
[5]

Chapman and Hall/CRC

Miller, A.(2002).Subset Selection in Regression, 2nd ed. Chapman and Hall/CRC

work page 2002
[6]

B.andChintala, S.(2019)

Tejani, A.,Chilamkurthy, S.,Steiner, B.,Lu F ang, J. B.andChintala, S.(2019). PyTorch: An Imperative Style, High-Performance Deep Learning Library. InAdvances in Neural Information Processing Systems (NeurIPS 32)(H. W allach,H. Larochelle,A. Beygelzimer,F. d'Alché- Buc,E. FoxandR. Garnett, eds.)32. Curran Associates, Inc

work page 2019
[7]

Effects of padding on LSTMs and CNNs

Reddy, D. M.andReddy, N. V. S.(2019). Effects of padding on LSTMs and CNNs. arXiv:1903.07288

work page Pith review arXiv 2019
[8]

Estimating the Dimension of a Model.The Annals of Statistics6461–464

Schwarz, G.(1978). Estimating the Dimension of a Model.The Annals of Statistics6461–464

work page 1978
[9]

Regression shrinkage and selection via the LASSO.Journal of the Royal Statistical Society: Series B (Methodological)58267–288

Tibshirani, R.(1996). Regression shrinkage and selection via the LASSO.Journal of the Royal Statistical Society: Series B (Methodological)58267–288

work page 1996
[10]

Regularization and variable selection via the elastic net.Journal of the Royal Statistical Society: Series B (Methodological)67301–320

Zou, H.andHastie, T.(2005). Regularization and variable selection via the elastic net.Journal of the Royal Statistical Society: Series B (Methodological)67301–320

work page 2005

[1] [1]

Steiner, B.,Tucker, P.,V asudevan, V.,W arden, P.,Wicke, M.,Yu, Y.andZheng, X. (2016). TensorFlow: A System for Large-Scale Machine Learning. In12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ’16)265–283

work page 2016

[2] [2]

A New Look at the Statistical Model Identification.IEEE Transactions on Au- tomatic Control19716–723

Akaike, H.(1974). A New Look at the Statistical Model Identification.IEEE Transactions on Au- tomatic Control19716–723

work page 1974

[3] [3]

Manning Publications

Chollet, F.(2021).Deep Learning with Python (2nd Edition). Manning Publications

work page 2021

[4] [4]

R.andSmith, H.(1998).Applied Regression Analysis, 2nd ed

Draper, N. R.andSmith, H.(1998).Applied Regression Analysis, 2nd ed. Wiley

work page 1998

[5] [5]

Chapman and Hall/CRC

Miller, A.(2002).Subset Selection in Regression, 2nd ed. Chapman and Hall/CRC

work page 2002

[6] [6]

B.andChintala, S.(2019)

Tejani, A.,Chilamkurthy, S.,Steiner, B.,Lu F ang, J. B.andChintala, S.(2019). PyTorch: An Imperative Style, High-Performance Deep Learning Library. InAdvances in Neural Information Processing Systems (NeurIPS 32)(H. W allach,H. Larochelle,A. Beygelzimer,F. d'Alché- Buc,E. FoxandR. Garnett, eds.)32. Curran Associates, Inc

work page 2019

[7] [7]

Effects of padding on LSTMs and CNNs

Reddy, D. M.andReddy, N. V. S.(2019). Effects of padding on LSTMs and CNNs. arXiv:1903.07288

work page Pith review arXiv 2019

[8] [8]

Estimating the Dimension of a Model.The Annals of Statistics6461–464

Schwarz, G.(1978). Estimating the Dimension of a Model.The Annals of Statistics6461–464

work page 1978

[9] [9]

Regression shrinkage and selection via the LASSO.Journal of the Royal Statistical Society: Series B (Methodological)58267–288

Tibshirani, R.(1996). Regression shrinkage and selection via the LASSO.Journal of the Royal Statistical Society: Series B (Methodological)58267–288

work page 1996

[10] [10]

Regularization and variable selection via the elastic net.Journal of the Royal Statistical Society: Series B (Methodological)67301–320

Zou, H.andHastie, T.(2005). Regularization and variable selection via the elastic net.Journal of the Royal Statistical Society: Series B (Methodological)67301–320

work page 2005