WK6: Bayesian Methods and Uncertainty in AI systems

Welcome to Week 6

Bayesian Methods and Uncertainty in AI systems

Module Lecturer: Dr Raghav Kovvuri

Email: [e-mail]

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 Introduction

Probability in AI

• A measure of how likely an event is to occur

            Scale: 0 (impossible) to 1 (certain)

Real-world analogy: Weather forecasting

• "70% chance of rain" - more likely to rain than not, but not certain

Why it matters in AI:

1. Handling uncertain data
2. Making decisions with incomplete information
3. Predicting outcomes

Basic Probability Concepts

Types of events:

• Independent: Outcome of one doesn't affect the other 

                 Example: Flipping a coin twice

• Dependent: Outcome of one affects the other

                 Example: Drawing cards from a deck without                                             replacement

Probability rules:

• Sum rule: P(A or B) = P(A) + P(B) - P(A and B)
• Product rule: P(A and B) = P(A) × P(B) (if independent)

Real-world AI analogy: Spam filter considering multiple features of an email

Formula: P(A|B) = P(B|A) × P(A) / P(B)

• P(A|B): Probability of A given B has occurred (Posterior)
• P(B|A): Probability of B given A (Likelihood)
• P(A): Initial probability of A (Prior)
• P(B): Probability of B occurring

Real-world analogy: Medical diagnosis

• Prior: General prevalence of a disease
  
• Likelihood: Accuracy of a medical test
  
• Posterior: Probability of having the disease given a positive test

Bayes' Theorem

Introduction Bayes' Theorem: A way to update beliefs based on new evidence

Bayes' Theorem in AI

Naive Bayes Classifier

Naive Bayes: A simple yet powerful classification algorithm

• "Naive" because it assumes features are independent (often not true in reality)

Common applications:

• Spam detection
• Sentiment analysis
• Document classification

Real-world analogy: Book categorization

Features: Words in the book

Classes: Genre (Mystery, Romance, Sci-Fi, etc.)

Naive assumption: Word occurrences are independent

Uncertainty in AI Systems

Types of uncertainty:

• Aleatory: Inherent randomness (e.g., rolling dice)
• Epistemic: Uncertainty due to lack of knowledge

Why uncertainty matters in AI:

1. Improves decision-making
2. Helps in risk assessment
3. Makes AI systems more robust

Real-world analogy: Self-driving cars

• Aleatory uncertainty: Random pedestrian movements
• Epistemic uncertainty: Limited sensor range or occlusions

Bayesian Networks

Bayesian Network: A graphical model representing probabilistic relationships

Components:

• Nodes: Variables
• Edges: Dependencies between variables
• Conditional Probability Tables (CPTs)

Real-world analogy: Detective's investigation board

• Pieces of evidence connected by strings
• Strength of connections represent probabilities

Applications in AI:

1. Diagnostic systems
2. Decision support tools
3. Predictive modeling

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Bayesian Network vs NN

Bayesian Inference in ML

Bayesian Inference: Using Bayes' theorem to update beliefs based on data

Process:

1. Start with prior beliefs
2. Collect data
3. Update beliefs (posterior)

Advantages in ML:

• Handles uncertainty in predictions
• Allows incorporation of prior knowledge
• Provides probability distributions instead of point estimates

Real-world analogy: Weather forecasting model Historical weather patterns (Prior), Current meteorological measurements (Data), Updated forecast (Posterior)

Bayesian Optimization in AI

Bayesian Optimization: A technique for optimizing expensive-to-evaluate functions

• Key idea: Use probabilistic model to guide the search for optimal parameters

Process:

Build

Build a probabilistic model of the objective function

Evaluate

Use this model to determine next points to evaluate

Update

Update the model with new results

Repeat

Repeat until convergence or budget exhausted

Real-world analogy: Finding the best recipe

1. Each ingredient combination is expensive (time-consuming to cook and taste)
   
2. Use feedback from previous attempts to guide next attempts
   
3. Gradually converge on the optimal recipe
   

Applications in AI:

• Hyperparameter tuning in ML, AutoML, R&D

Handling Uncertainty in DL

Sources of uncertainty in deep learning:

Model uncertainty: Uncertainty in model parameters

Data uncertainty: Noise or incompleteness in the training data

Techniques for uncertainty quantification:

1. Monte Carlo Dropout
2. Ensemble Methods
3. Bayesian Neural Networks

Real-world analogy: Weather ensemble forecasting

• Multiple models run with slightly different initial conditions
• Spread of predictions indicates uncertainty

In the context of Bayesian probability, what does the term "prior" refer to?

1. The initial probability estimate before considering new evidence
2. The final probability after considering all evidence
3. The probability of the evidence occurring
4. The difference between two probability estimates

Which of the following best describes the Naive Bayes assumption in classification tasks?

1. All features are equally important
2. The class is independent of the features
3. There must be an equal number of features and classes
4. Features are independent of each other given the class

In a Bayesian Network for a car starting problem, which of the following would most likely be a parent node to "Car Starts"?

1. Radio Works
2. Battery Charge
3. Car Color
4. Driver's Age

What is the primary advantage of using Bayesian Optimization in machine learning?

1. It always finds the global optimum
2. It requires no prior knowledge of the problem
3. It efficiently optimises expensive-to-evaluate functions
4. It guarantees the fastest convergence among all optimisation methods

In the context of uncertainty in AI systems, what does aleatory uncertainty refer to?

1. Uncertainty due to lack of knowledge
2. Uncertainty in the model parameters
3. Inherent randomness in the system
4. Uncertainty caused by measurement errors

Challenges

• Scalability of Bayesian methods to big data
• Integration with other AI techniques (e.g., reinforcement learning)
• Explainable AI through Bayesian frameworks

Real-world analogy: Evolution of weather forecasting

• From simple models to complex, probabilistic forecasts
• Increased computational power enabling more sophisticated methods
• Growing demand for explainable and reliable predictions

Conclusion and Takeaway

Key takeaways:

• Importance of probability in handling uncertainty in AI
• Bayes' theorem as a foundation for updating beliefs
• Applications of Bayesian methods in various AI domains

Practical applications recap:

• Naive Bayes for classification
• Bayesian networks for decision support
• Bayesian optimization for hyperparameter tuning
• Uncertainty quantification in deep learning