Active Learning Theory

Active learning optimizes labeling budgets by selecting the most informative samples for human annotation.

The Active Learning Loop

┌──────────────────────────────────────────────┐
│                                              │
▼                                              │
Unlabeled Pool → Query Strategy → Oracle → Labeled Set
                      │              │           │
                      │         (Human)          │
                      │                          │
                      └─────────────────────────┘
                           Train Model

Why Active Learning?

Same accuracy with 80% fewer labels.

Query Strategies

1. Uncertainty Sampling

Select samples where model is most uncertain:

Least Confidence:

x* = argmax_x (1 - P(ŷ|x))

Margin Sampling:

x* = argmin_x (P(ŷ₁|x) - P(ŷ₂|x))

Entropy:

x* = argmax_x H(P(y|x)) = argmax_x (-Σ P(y|x) log P(y|x))

2. Query-by-Committee (QBC)

Train multiple models, select where they disagree:

Models: M₁, M₂, ..., Mₙ
Vote entropy: x* = argmax_x H(votes)

3. Expected Model Change

Select samples that would change model most:

x* = argmax_x ||∇L(x)||

Gradient magnitude indicates influence.

4. Diversity Sampling

Ensure selected samples cover feature space:

Cluster unlabeled data
Select one sample per cluster

5. Hybrid Strategies

Combine uncertainty and diversity:

Score(x) = α · Uncertainty(x) + (1-α) · Diversity(x)

Batch Active Learning

Select multiple samples per round:

Greedy: Select top-k by score Diverse: Cluster-based selection Batch-mode: Joint optimization over batch

Cold Start Problem

Initial model has no training data:

Solutions:

1. Random initial batch
2. Diversity-based selection
3. Transfer from related task
4. Self-supervised pre-training

Stopping Criteria

When to stop querying:

Pool-Based vs Stream-Based

Pool-Based:

• Access to entire unlabeled pool
• Can compare and rank samples
• Common in research

Stream-Based:

• Samples arrive sequentially
• Must decide immediately
• Common in production

References

• Settles, B. (2012). "Active Learning." Morgan & Claypool.
• Sener, O., & Savarese, S. (2018). "Active Learning for Convolutional Neural Networks: A Core-Set Approach." ICLR.