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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

Korean

특성 선택은 고차원적 재정적 회귀에서 핵심적인 문제이며, 예측자들 사이의 대규모 엔지니어링 변수와 강력한 상관 관계가 모델 안정성과 해석성을 감소시킨다. $L_1$ 정규화 (Lasso)는 광범위하게 희귀 회귀를 위해 사용되지만, 소규모 데이터 최적화는 상관 관계 변수에 기반한 정보적 신호가 확산될 때 제한적일 수 있습니다. 정확한 정규 회귀는 예측자들 사이의 안정성을 감소시킬 수 있지만 계산적으로 어려운 조합적 값 최적화 문제를 해결할 필요가 있으며, 일반적으로 샘플 오프 라인 오프 라인 오프 라인 오프 라인 오프 라인 오프 라인 오프 라인 오프 라인 오

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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