Bayesian Active Learning

Information Theory and Uncertainty Quantification

Andreas Kirsch, 2024

About Me

Andreas Kirsch

• DPhil (Oxford, 2023) on Active Learning, Information Theory and Uncertainty Quantification (Kirsch 2024)
• Researcher at Midjourney, now DeepMind
• Prior: Research Engineer at DeepMind

• Welcome to Bayesian Active Learning
• This course builds on recent advances in deep active learning, information theory and uncertainty quantification
• We’ll focus on both theoretical foundations and practical implementations

Kirsch, Andreas. “Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions.”, DPhil Thesis, University of Oxford, 2024, 10.5287/ora-koewoxvaw.

Outline Now

1. What you’ll learn here and the big picture
2. What active learning is (and isn’t) and why it matters
3. Course logistics

• This is an intensive 30-hour course over 3 weeks
• We’ll move from fundamentals to cutting-edge research
• Balance between theory and hands-on implementation
• Course designed to build practical skills while understanding deep theoretical foundations

Empowerment Promise

By the end of this course, you’ll be able to:

• Design AI systems that learn efficiently from minimal labeled data
• Quantify and reason about uncertainty in deep learning models
• Apply information theory to guide optimal data selection
• Implement and scale active learning for real scientific applications

• These skills directly address key challenges in modern ML
• BatchBALD and similar methods show we can reduce labeled data needs by 60-80%
• Understanding uncertainty is crucial for deploying ML safely
• Information theory provides principled ways to reason about data value

The Big Picture

Key Question

How can we make AI systems learn more efficiently from less data?

Consider training a medical imaging AI system:

• Each labeled example requires expert radiologist time ($200+/hour)
• Need thousands of examples for good performance

Key Insight: Not all examples are equally valuable for learning

• Medical example connects to real costs ($200+/hour for radiologists)
• Similar challenges in drug discovery, protein folding
• Key insight from BatchBALD: naive batch acquisition often selects redundant points
• Need theoretical framework to understand data value

What Active Learning Is (And Isn’t)

Active Learning IS:

• Strategic data selection
• Interactive learning
• Uncertainty-guided sampling

Active Learning IS NOT:

• Data augmentation
• Semi-supervised learning
• Transfer learning

• Strategic selection: Based on information theory principles from your work
• Interactive: Builds on human-in-the-loop systems
• Important to distinguish from other data-efficient methods
• Common misconceptions lead to inefficient implementations

Our Journey Together

1. Foundations (Weeks 1 & 2)

   • Active learning fundamentals
   • Information theory basics
   • Bayesian neural networks and uncertainty

2. Advanced Methods (Weeks 3)

   • Batch acquisition strategies
   • Prediction-oriented selection
   • Scalable approximations

• Foundations draw from information theory framework
• Advanced methods include BatchBALD and causal extensions
• Applications based on real deployment experience
• Progressive building of concepts

Course Goals

1. Build strong information-theoretic foundations for active learning
2. Master uncertainty quantification methods for deep learning
3. Understand modern active learning approaches like BatchBALD and EPIG
4. Develop practical skills in scaling active learning to large datasets
5. Ability to apply active learning to real scientific problems

• Goal 1: We’ll start with Shannon entropy and mutual information, building up to acquisition functions
• Goal 2: Cover both aleatoric and epistemic uncertainty, Bayesian neural networks, and ensemble methods
• Goal 3: These methods represent key advances in batch acquisition and information-theoretic selection
• Goal 4: Focus on practical implementations using PyTorch, handling large unlabeled pools efficiently

Key message: Balance between theoretical depth and practical implementation skills

Prerequisites and Support

Expected Background

• Basic probability theory
• Python programming
• Machine learning fundamentals

Available Support

• Office hours
• Tutors
• Extra reading material

• Probability theory needed for information-theoretic framework
• Python skills for implementing active learning loops
• Support available for bridging any gaps
• Extra reading includes key papers from thesis bibliography

• quizzes before lectures on the previous lecture (ungraded)
• 2 weekly assignments (graded)
  • for non-coding questions:
    • hand-written solutions to be handed in
  • for coding questions:
    • hand-written overview to be handed in
    • Python code for implementation tasks to be sent in
• 1 final exam (graded)

• Assignments designed to build both theoretical understanding and practical skills
• Hand-written solutions for theory questions encourage deeper engagement with concepts
• Coding tasks will use real datasets and implement key algorithms from scratch
• First assignment focuses on information theory fundamentals and non-Bayesian active learning
• Second covers uncertainty quantification in Bayesian neural networks and Bayesian active learning
• Quizzes assess understanding of core concepts and ability to reason about trade-offs
• Format may evolve based on class progress and interests

Note: all subject to updates

Why This Course Matters

Real-World Impact

• Drug discovery: Each experiment costs thousands of dollars
• Protein folding: “One PhD student per protein structure”
• Climate modeling: Limited high-quality historical data
• AI safety: Collecting human feedback is expensive

For Your Future

• Growing demand for efficient ML in scientific domains
• Critical skill for research and industry
• Bridges theory and practical implementation

• Drug discovery example from your thesis collaboration with pharma companies
• Protein folding connects to work with DeepMind
• Climate modeling shows need for efficient data use
• AI safety ties to uncertainty quantification work

This Week’s Goals

1. Understand why active learning matters
2. See how information theory guides data selection
3. Implement a simple active learning loop
4. Connect theory to practical applications

Success Strategy

• Focus on intuition before formalism
• Engage with assignments and coding exercises
• Connect concepts to your background
• Ask questions early and often
• Participate in discussions

• Simple example shows core active learning loop
• Information theory introduced gradually
• Implementation builds intuition
• Applications maintain motivation

How to Succeed in This Course

1. Engage Actively

   • Complete weekly assignments
   • Participate in discussions
   • Work through code examples

2. Build Foundations

   • Master information theory basics
   • Understand uncertainty types
   • Practice implementing methods

3. Connect Ideas

   • Link theory to applications
   • Relate to your research interests
   • Share insights with classmates

• Active engagement mirrors active learning principles
• Foundation building follows thesis structure
• Connecting ideas across domains is crucial

Let’s Begin: A Simple Example

This simple example will grow into sophisticated active learning strategies throughout the course.

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_classification
from sklearn.ensemble import RandomForestClassifier

# Generate synthetic data
np.random.seed(1337)
X, y = make_classification(n_samples=1000, n_features=20)

# Start with a small labeled set
labeled_idx = np.random.choice(len(X), 10, replace=False)
unlabeled_idx = np.setdiff1d(np.arange(len(X)), labeled_idx)

# Plot the data
plt.scatter(X[unlabeled_idx, 0], X[unlabeled_idx, 1], c='blue', label='Unlabeled', s=2)
plt.scatter(X[labeled_idx, 0], X[labeled_idx, 1], c='red', label='Labeled', s=10)
plt.legend()
plt.show()

Think About

How would you choose which points to label next?

• Code demonstrates basic active learning setup
• Shows why random sampling is suboptimal
• Sets up later discussion of acquisition functions
• Visualizes the core problem

Let’s Begin: A Simple Example

Questions to Ponder

1. Why might random sampling be inefficient?
2. How do humans choose what data to learn from?
3. What makes some examples more informative than others?

• Links to fundamental questions in your research
• Connects to information theory framework
• Prepares for deeper theoretical discussion

Other Questions?

Important

Remember: Your questions help everyone learn!

• Encourage specific technical questions
• Link to research examples when possible
• Use questions to preview coming material

Preview

Next lectures:

1. A deep dive into active learning fundamentals
2. A unified framework for information theory
3. Your first active learning implementation

Key Message

Active learning isn’t just about saving resources—it’s about making AI systems more efficient and effective learners.

• Next lectures build theoretical framework
• Information theory ties everything together
• Implementation details matter for scaling

Summary

This overview:

• Established the core problem: learning efficiently from minimal labeled data
• Clarified what active learning is (and isn’t) from a high-level perspective
• Connected theory to real applications in drug discovery, protein folding, and climate modeling
• Set up the learning path through foundations, methods, and applications

• Frames course in broader research context
• Shows practical impact of theoretical work
• Sets expectations for learning outcomes

References

Kirsch, Andreas. 2024. “Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions.” arXiv Preprint arXiv:2401.04305.