Quantile Regression using Random Forest Proximities

ArXiv ID: 2408.02355 “View on arXiv”

Authors: Unknown

Abstract

Due to the dynamic nature of financial markets, maintaining models that produce precise predictions over time is difficult. Often the goal isn’t just point prediction but determining uncertainty. Quantifying uncertainty, especially the aleatoric uncertainty due to the unpredictable nature of market drivers, helps investors understand varying risk levels. Recently, quantile regression forests (QRF) have emerged as a promising solution: Unlike most basic quantile regression methods that need separate models for each quantile, quantile regression forests estimate the entire conditional distribution of the target variable with a single model, while retaining all the salient features of a typical random forest. We introduce a novel approach to compute quantile regressions from random forests that leverages the proximity (i.e., distance metric) learned by the model and infers the conditional distribution of the target variable. We evaluate the proposed methodology using publicly available datasets and then apply it towards the problem of forecasting the average daily volume of corporate bonds. We show that using quantile regression using Random Forest proximities demonstrates superior performance in approximating conditional target distributions and prediction intervals to the original version of QRF. We also demonstrate that the proposed framework is significantly more computationally efficient than traditional approaches to quantile regressions.

Keywords: Quantile regression forests (QRF), Uncertainty quantification, Random Forest proximities, Corporate bonds, Conditional distribution estimation, Fixed Income (Corporate Bonds)

Complexity vs Empirical Score

• Math Complexity: 5.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper introduces a novel algorithmic modification to quantile regression forests, involving non-trivial statistical mechanics and proximity metrics, but grounds it in practical implementation with computational efficiency benchmarks, dataset applications, and performance comparisons on real-world financial data.

  flowchart TD
    A["<b>Research Goal</b><br/>Quantify uncertainty in corporate bond<br/>volume forecasting via novel<br/>Random Forest proximities"] --> B["<b>Methodology: Proximity-Based<br/>Quantile Regression</b><br/>Leverage RF distance metrics to<br/>infer conditional distribution<br/>(Single model vs. per-quantile)"]
    B --> C["<b>Data Inputs</b><br/>Public Datasets &<br/>Corporate Bond Volume Data"]
    C --> D["<b>Computational Process</b><br/>Train RF → Compute Proximities<br/>→ Aggregate Residuals →<br/>Estimate Conditional Quantiles"]
    D --> E["<b>Key Findings</b><br/>1. Superior distribution approximation<br/>2. Better prediction intervals<br/>3. Higher computational efficiency<br/>vs. traditional QRF"]