Background: Meta-Labeling Method

"Not predicting up or down, but predicting 'whether this prediction is reliable.'"

The Problem with Traditional Methods

Scenario: You have a trend-following model that generates buy/sell signals

Traditional Flow:
Signal Generated -> Execute Directly -> Results are mixed

Problem:
  - Some signals have high win rate (when trend is clear)
  - Some signals have low win rate (in ranging markets)
  - The model cannot distinguish between these two situations

Result: Trading when you shouldn't, wasting costs, dragging down returns.

Core Idea of Meta-Labeling

Two-Stage Decision:

Detailed Process

Step 1: Primary Model Generates Signals

The primary model can be any strategy:

• Technical analysis rules
• Machine learning model
• Fundamental factors

Primary Model Output:
  +1 = Buy signal
  -1 = Sell signal
   0 = No signal

Step 2: Construct Meta Labels

For each primary model signal, determine whether that signal was correct:

Meta Label Definition:
  If primary signal direction is correct and profitable -> Meta Label = 1
  If primary signal direction is wrong or loses money -> Meta Label = 0

Combined with Triple Barrier:
  Primary model says "buy", triggers upper barrier (take-profit) -> Meta Label = 1
  Primary model says "buy", triggers lower barrier (stop-loss) -> Meta Label = 0

Step 3: Train Meta Model

The meta model learns to predict the success probability of primary model signals:

Features:
  - Primary model signal direction
  - Current volatility
  - Trend strength
  - Primary model historical accuracy
  - Market state indicators

Target:
  - Predict whether the signal will be profitable (binary classification)
  - Or predict confidence level (regression)

Step 4: Decision Execution

Final Decision = Primary Model Direction x Meta Model Confidence

Example:
  Primary Model: Buy (+1)
  Meta Model: Confidence 0.3 (low)

  Decision:
    Option A: Don't execute (confidence too low)
    Option B: Small position buy (30% of normal size)

Numerical Example

Setup: Trend-following primary model, 100 past signals

Statistics:

• Total signals: 100
• Profitable signals: 55 (55% win rate)
• Losing signals: 45

Meta Model Analysis:

High Confidence Signals (Meta Model > 0.7): 30
  - Profitable: 25 (83% win rate)
  - Losing: 5

Low Confidence Signals (Meta Model <0.3): 25
  - Profitable: 8 (32% win rate)
  - Losing: 17

Strategy: Only execute high confidence signals
  - Trading frequency reduced 70%
  - Win rate improved from 55% to 83%
  - Trading costs reduced

Feature Design for Meta Model

Market State Features

Primary Model Features

Time Features

Position Sizing

Meta model confidence can be directly used for position management:

Method 1: Linear Mapping
  Position = Confidence x Max Position

  Confidence 0.8 -> 80% position
  Confidence 0.3 -> 30% position

Method 2: Threshold Filtering
  Confidence > 0.6 -> Full position
  Confidence <0.6 -> No trade

Method 3: Convex Function Mapping
  Position = Confidence^2 x Max Position

  More aggressively reduce low confidence positions:
  Confidence 0.8 -> 64% position
  Confidence 0.5 -> 25% position
  Confidence 0.3 -> 9% position

Comparison with Direct Prediction

Key Insight:

Direct Prediction:
  100 trades, 55% win rate
  Expected profit = 55 x 1% - 45 x 1% = 10%

Meta-Labeling:
  30 high confidence trades, 80% win rate
  Expected profit = 24 x 1% - 6 x 1% = 18%

  Although fewer trades, returns are higher

Multi-Agent Perspective

Meta-Labeling naturally fits multi-agent architecture:

Signal Agent (Primary Model)
  |
  +- Output: Trading direction
  |
  v
Confidence Agent (Meta Model)
  |
  +- Input: Signal Agent's signal + market state
  +- Output: Confidence of that signal
  |
  v
Risk Agent
  |
  +- Adjust position based on confidence
  +- Low confidence -> Reject trade or small position
  +- High confidence -> Allow normal position

Meta Agent
  |
  +- Monitor Confidence Agent's accuracy
     -> If persistently failing, switch to conservative mode

Common Misconceptions

Misconception 1: Meta model will learn the same thing as primary model

Wrong. The two have different objectives:

• Primary model: Predict price direction
• Meta model: Predict when primary model is effective

Meta model can discover patterns like "primary model fails in high volatility."

Misconception 2: High confidence is always correct

Not guaranteed. Meta model also makes mistakes:

• Overfitting to historical patterns
• Market regime changes
• Insufficient sample size

Still need stop-losses and risk controls.

Misconception 3: Meta-Labeling can save a poor primary model

Limited. If primary model win rate is too low (<50%), meta model can only do so much:

• Can only reduce losses
• Cannot create positive expectancy

Primary model itself must have some predictive power.

Practical Recommendations

1. Verify Primary Model Has Base Alpha

First confirm:
  - Primary model win rate > 50%
  - Or win/loss ratio > 1
  - Positive returns out-of-sample

Without base Alpha, Meta-Labeling cannot create it

2. Keep Meta Model Simple

Recommended:
  - Logistic regression
  - Shallow decision trees
  - Simple neural networks (1-2 layers)

Avoid:
  - Deep models (easy to overfit)
  - Too many features (adds noise)

3. Independent Validation

Validation Process:
  1. Train primary model on training set
  2. Use primary model to generate signals on validation set
  3. Train meta model using validation set signal results
  4. Evaluate overall performance on test set

Key: Primary and meta models use different data

Summary