Project 11: Resampling and Modern Methods Lab

Build a lab for bootstrap, permutation tests, cross-validation, and Monte Carlo risk simulation.

Quick Reference

Attribute Value
Difficulty Level 3: Advanced
Time Estimate 2 weeks
Main Programming Language Python
Alternative Programming Languages R
Coolness Level Level 4: Hardcore Tech Flex
Business Potential 1. The “Resume Gold”
Prerequisites Projects 7-10
Key Topics Bootstrap, permutation tests, CV, Monte Carlo

1. Learning Objectives

  1. Estimate uncertainty with bootstrap replicates.
  2. Build permutation-based significance logic.
  3. Design leakage-safe cross-validation workflows.
  4. Use Monte Carlo to stress policy decisions.

2. All Theory Needed (Per-Concept Breakdown)

2.1 Bootstrap and Permutation Logic

  • Fundamentals: Resampling approximates unknown sampling distributions from observed data.
  • Deep Dive into the concept: Bootstrap and permutation answer different questions; choosing the wrong one can invalidate conclusions.

2.2 Cross-Validation and Simulation

  • Fundamentals: CV estimates generalization; Monte Carlo explores uncertain scenarios.
  • Deep Dive into the concept: Fold leakage and weak scenario design are the most common failure modes.

3. Project Specification

3.1 What You Will Build

A command-line lab that compares model metrics with bootstrap intervals, permutation p-values, repeated CV, and scenario simulations.

3.2 Functional Requirements

  1. Bootstrap CI module for arbitrary metrics.
  2. Permutation test module for model delta significance.
  3. Repeated CV module with split registry.
  4. Monte Carlo scenario engine for decision risk.

3.3 Non-Functional Requirements

  • Deterministic runs and replicate logs.
  • Convergence diagnostics for replicate count.

3.4 Example Usage / Output

$ python resampling_lab.py --task model_compare
Bootstrap AUC CI A: [0.782, 0.811]
Bootstrap AUC CI B: [0.776, 0.807]
Permutation p-value: 0.118
Recommendation: no strong evidence A > B

3.5 Real World Outcome

You produce robust model-comparison decisions that include uncertainty rather than point-score overconfidence.

4. Solution Architecture

Input task -> resampling orchestrator -> metric distribution store -> decision report

5. Implementation Guide

5.1 Development Environment Setup

pip install numpy scipy scikit-learn

5.2 Project Structure

P11/
  resampling_lab.py
  scenarios/
  outputs/

5.3 The Core Question You Are Answering

“How likely is this model difference to persist beyond this sample?”

5.4 Concepts You Must Understand First

  1. Bootstrap interval construction
  2. Exchangeability in permutation testing
  3. Cross-validation leakage patterns
  4. Monte Carlo scenario design

5.5 Questions to Guide Your Design

  1. How many replicates are enough for stable estimates?
  2. Which metric is decision-critical?
  3. How will you detect leakage early?

5.6 Thinking Exercise

Design a scenario where naive random CV would be invalid and explain a safer split strategy.

5.7 The Interview Questions They’ll Ask

  1. Why does bootstrap not fix sampling bias?
  2. When is permutation invalid?
  3. How do you know if replicates are enough?
  4. Why can CV overestimate production performance?
  5. What decisions does Monte Carlo improve?

5.8 Hints in Layers

  • Hint 1: Start with one scalar metric.
  • Hint 2: Add permutation null generation.
  • Hint 3: Add repeated CV and split logging.
  • Hint 4: Add replicate convergence plots.

5.9 Books That Will Help

Topic Book Chapter
Bootstrap Efron & Tibshirani Ch. 1-3
Resampling in ML ISLR resampling chapter
Simulation Think Stats simulation chapters

6. Testing Strategy

  • Deterministic seed tests.
  • Known synthetic effect recovery tests.
  • Leakage injection tests.

7. Common Pitfalls & Debugging

Pitfall Symptom Solution
Too few replicates unstable CI endpoints increase B, monitor convergence
Leakage across folds inflated CV metrics strict split registry and pipeline isolation
Wrong null in permutation misleading p-values explicit hypothesis encoding

8. Extensions & Challenges

  • Add block bootstrap for time dependence.
  • Add Bayesian bootstrap comparison.

9. Real-World Connections

  • Model selection for fraud detection.
  • Risk-adjusted launch decisions.

10. Resources

  • Efron & Tibshirani
  • ISLR

11. Self-Assessment Checklist

  • I can choose the right resampling method by question type.
  • I can explain uncertainty in model comparisons.
  • My pipeline catches leakage risks.

12. Submission / Completion Criteria

Minimum: bootstrap + permutation + repeated CV on one dataset.

Full: includes Monte Carlo policy simulation and convergence diagnostics.