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$L_0$ Feature Selection via Monte Carlo Tree Search in High-Dimensional Financial Regression

Cameron Mouangue, Tristan Cazenave · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.13574 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

La selección potencial de funciones es un problema central en la suboptimización de datos financieros de alta dimensión, donde un gran número de variables de ingeniería y una fuerte correlación entre los predictores reducen la estabilidad y la interpretación del riesgo del modelo. La regularización de $L_1$ (Lasso) se utiliza ampliamente para la regresión escasa, pero su encogimiento puede ser restrictivo cuando las señales informativas se distribuyen a través de las variables correlacionadas. La regresión exacta de los espacios evita este encogimiento, pero requiere la solución de un problema de optimización de valores combinatorios que es computacionalmente difícil y generalmente es adecuado para minimizar el error de regresión en la muestra en lugar de en la muestra. Este documento presenta un marco de selección de características basado en la búsqueda de Monte Carlo Tree basado

Machine translation (Meta M2M100); the English original follows.

Abstract

Feature selection is a central problem in high-dimensional financial regression, where large numbers of engineered variables and strong correlations among predictors reduce model stability and interpretability. $L_1$ regularization (Lasso) is widely used for sparse regression, but its shrinkage can be restrictive when informative signals are spread across correlated variables. Exact sparse regression avoids this shrinkage but requires solving a combinatorial optimization problem that is computationally difficult and is typically fit to minimize in-sample rather than out-of-sample error. This paper presents a feature selection framework based on Monte Carlo Tree Search with Generalized Nested Rollout Policy Adaptation (GNRPA). Feature selection is formulated as a sequential decision process, and candidate subsets are scored by their out-of-sample validation performance rather than training error. The method also supports a lexicographic objective accounting for subset size and multicollinearity. We study this approach on a contemporaneous explanatory regression task: explaining the weekly return of the NASDAQ-100 index from 1,072 engineered features spanning market, macroeconomic, and factor data. This isolates the value of subset selection under multicollinearity from the separate problem of predictive forecasting. On this task, the proposed method identifies sparse feature subsets with higher out-of-sample explanatory power than an optimized Lasso baseline, reaching an out-of-sample $R^2$ of 0.6961 versus 0.6313 for Lasso. These results suggest that Monte Carlo Tree Search is a practical alternative to convex regularization for sparse explanatory feature selection in financial regression, with potential value for factor attribution and risk decomposition where transparency matters as much as out-of-sample fit.

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Topics: Feature selection, Lasso (programming language), Multicollinearity, Monte Carlo method, Mathematics, Computer science

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