Search in the Presence of Uncertainty

1. Search in the Presence of Uncertainty • Uses in A.I. • Inference (as we did for Belief Networks) • Parameter estimation (learning) • Model class selection (selecting model dimensionality) • Historical foundations in the simulation of physical systems: particularly systems of particles • Gibbs • Metropolis CSI 661 - Uncertainty in A.I. Lecture 11

2. BBN Learning Example CSI 661 - Uncertainty in A.I. Lecture 11

3. Statistical Physics - Background • Micro-state versus Macro-state • Micro-state unknown, partial knowledge • P(s) = 1/Z . Exp(-E(s) / T), Z = Sum_s exp(-E(s) / T • Known as the Gibbs, Boltzmann, canonical, equilibrium distribution • Equivalent to what? • Intensive versus Extensive quantities (grow linearly with system size) • Extensive quantities per unit/particle reach constant limits • Interested in systems at thermodynamic equilibrium • Macroscopic properties can be expressed as expectations CSI 661 - Uncertainty in A.I. Lecture 11

4. Ising Spin Glass Model Phase transitions CSI 661 - Uncertainty in A.I. Lecture 11

5. Free Energy of a SystemRelationship to A.I. • Free energy F = -T.log(Z) = <E> - T.H • Z is the partition function, T temperature • H the system entropy • F and H are extensive values • (cf. Slide 1) What are the analagous particles for: • Parameter estimation (learning) • Inference • Model class selection CSI 661 - Uncertainty in A.I. Lecture 11

6. Next Lecture • Read, Neal, Chapter 2 CSI 661 - Uncertainty in A.I. Lecture 11