Paper: arXiv 2610.13574

Authors: Cameron Mouangue, Tristan Cazenave

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel application of Monte Carlo Tree Search to a challenging financial feature selection problem, demonstrating strong empirical results against a robust baseline. The methodology is well-articulated, and the focus on out-of-sample performance is highly relevant for quantitative finance.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve Feature Selection in High-Dimensional Financial Regression] --> B{Formulate Feature Selection as Sequential Decision Process};
    B --> C[Methodology: Monte Carlo Tree Search with GNRPA];
    C --> D{Inputs: NASDAQ-100 Weekly Returns & 1072 Engineered Features};
    D --> E[Computational Process: Out-of-Sample Validation & Lexicographic Objective];
    E --> F[Outcome 1: MCTS Identifies Sparse Subsets with Higher Out-of-Sample R^2 (0.6961)];
    E --> G[Outcome 2: Outperforms Optimized Lasso Baseline (R^2 0.6313)];
    F & G --> H[Conclusion: MCTS is Practical Alternative for Sparse Explanatory Feature Selection in Finance];