Paper: arXiv 2310.12428

Abstract

We initiate a novel approach to explain the predictions and out of sample performance of random forest (RF) regression and classification models by exploiting the fact that any RF can be mathematically formulated as an adaptive weighted K nearest-neighbors model. Specifically, we employ a recent result that, for both regression and classification tasks, any RF prediction can be rewritten exactly as a weighted sum of the training targets, where the weights are RF proximities between the corresponding pairs of data points. We show that this linearity facilitates a local notion of explainability of RF predictions that generates attributions for any model prediction across observations in the training set, and thereby complements established feature-based methods like SHAP, which generate attributions for a model prediction across input features. We show how this proximity-based approach to explainability can be used in conjunction with SHAP to explain not just the model predictions, but also out-of-sample performance, in the sense that proximities furnish a novel means of assessing when a given model prediction is more or less likely to be correct. We demonstrate this approach in the modeling of US corporate bond prices and returns in both regression and classification cases.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced statistical concepts like GAP proximities and matrix expansions, requiring dense mathematical notation. It is highly data-driven with a specific case study on corporate bond modeling, but lacks the full backtest implementation details typical of Street Traders.

Research Flowchart

  flowchart TD
  Goal["Research Goal: Explain Random Forest predictions & out-of-sample performance using proximities"]
  
  Input["Data Input: US Corporate Bond Prices & Returns"]
  
  Method["Methodology: Re-formulate RF as adaptive weighted KNN"]
  Prox["Compute RF Proximities between data points"]
  
  Process1["Local Explainability: Generate attributions across training observations"]
  Process2["Trust Scoring: Assess likelihood of prediction correctness"]
  
  SHAP["Integration: Combine with SHAP (feature-based) for holistic explanation"]
  
  Out1["Finding: RF proximities provide novel interpretability layer"]
  Out2["Finding: Enables assessment of prediction reliability out-of-sample"]
  
  Goal --> Input
  Input --> Method
  Method --> Prox
  Prox --> Process1
  Prox --> Process2
  Process1 --> SHAP
  Process2 --> SHAP
  SHAP --> Out1
  SHAP --> Out2