Part 1 : Introduction to this class

• Examples of graphical systems :

  • Automatic Diagnosis of Complex Systems
  • Autonomous Driving
  • Automatic Aircraft Tracking
  • Speech Recognition and Voice control
• Graphical models

  • Receiver information about its environment, at regular or irregular intervals
  • Must identify objects, classify situations, make predictions, take decision
  • information may be incomplete/wrong/noisy
• Probalistic Models:

  • represent knowledge about the world and about its uncertainty
  • support logical and probabilistic inference (decision-making)
  • can be learned from example observations
  • (graphical representations of factorised probability distributions
• Declarative modeling (general approach)

  • construct a model of the world
  • devise general inference algortihms
  • declarative approach to model solving
• Advantages of declarative approach :

  • clear separation of knowledge
  • representation has a clear, well-defined semantics, independant of the alogrtihms that operate on it
  • inference algorithms can be entirely generic and independant
  • can adapt a system simply by chaning the knowledge base (model)
• Proablistic Graphical Models :

  • a formalism for modelling the structure of a world
  • quantifying the degree of uncertainty

  probalistic --> represent probaility distributions

  graphical --> make dependencies explicit in a graph structure
• Central issues of Probalistic Graphical Models :

  1. Modelling : representing the relevant aspects of a given world + connections
  2. Inference : taking (messy/noisy/uncertain) observations about the world
  3. Learning : automatically building models of complex worlds from observations
• Statis Models

  Bayesian Networks
• Temporal models


  Dynamic Bayes Nets, HMMs, Kalman Filters
• Inference 


  how to use models to answer questions --> determinsitic and/or probalistic algorithms
• Learning : how to learn models from data --> parameter and structure learning
• A model : first part is the variables, second part is the (Full) Joint Distribution (covering all possible cases)
• Problems :

  1. Representational Complexity : large number of variables is too large to store
  2. Computational Complexity : requires exponential time
  3. Modelling Complexity : valid model for a complex world is difficult