Uncertainty, Probability, and Bayesian Inference
Why Probability Is Central to AI
Modeling uncertainty
Real-world AI systems face incomplete observability, noisy sensors, and ambiguous labels. Probability provides a principled language for uncertainty, belief updating, and rational decision-making.
Bayesian basics
Bayes' rule
Bayes' theorem is . In AI, it underpins learning, diagnosis, and sequential belief updating.
Probabilistic graphical models
| Model | Structure | Inference notes |
|---|---|---|
| Bayesian network | Directed acyclic graph | Exact inference can be hard |
| Markov random field | Undirected graph | Useful for symmetric dependencies |
| Hidden Markov model | Temporal latent-state model | Dynamic programming enables efficient inference |
| Conditional random field | Discriminative structured model | Popular for sequence labeling |
What is the role of the evidence term in Bayes' rule?
The evidence makes the posterior integrate to one.
Correct answer: It normalizes the posterior distribution
Why are exact inference algorithms often infeasible in large graphical models?
Graph topology and variable count can cause combinatorial blow-up, motivating approximate inference.
Correct answer: Because marginalization over many hidden variables can be computationally intractable, often exponential in graph structure.
Inference strategies
Exact inference
- Provides exact marginals
- Often exponential in worst case
- Useful for small or structured models
Approximate inference
- Scales to larger models
- Includes variational and sampling methods
- Introduces bias or variance
Research frontier
Modern AI increasingly combines probabilistic reasoning with deep representations, but calibration, uncertainty quantification, and robust posterior approximation remain open problems.