Probabilistic Graphical Models Introduction Motivation and Overview Daphne

Probabilistic Graphical Models Introduction Motivation and Overview Daphne Koller

Probabilistic Graphical Models Daphne Koller

Daphne Koller

Models Daphne Koller

Uncertainty • Partial knowledge of state of the world • Noisy observations • Phenomena not covered by our model • Inherent stochasticity Daphne Koller

Probability Theory • Declarative representation with clear semantics • Powerful reasoning patterns • Established learning methods Daphne Koller

Complex Systems Daphne Koller

Graphical Models Bayesian networks Difficulty Markov networks A Intelligence Grade Letter SAT D B C Daphne Koller

Graphical Models Daphne Koller

Graphical Models • Graphical representation: – intuitive & compact data structure – efficient reasoning using general algorithms – can be learned from limited data Daphne Koller

Many Applications • Medical diagnosis • Computer vision – Image segmentation • Fault diagnosis – 3 D reconstruction • Natural language – Holistic scene analysis processing • Speech recognition • Traffic analysis • Social network models • Robot localization & mapping • Message decoding Daphne Koller

END END Daphne Koller

Suppose q is at a local minimum of a function. What will one iteration of gradient descent do? Leave q unchanged. Change q in a random direction. Move q towards the global minimum of J(q). Decrease q.

Consider the weight update: Which of these is a correct vectorized implementation?

Fig. A corresponds to a=0. 01, Fig. B to a=0. 1, Fig. C to a=1. Fig. A corresponds to a=0. 1, Fig. B to a=0. 01, Fig. C to a=1. Fig. A corresponds to a=1, Fig. B to a=0. 01, Fig. C to a=0. 1. Fig. A corresponds to a=1, Fig. B to a=0. 1, Fig. C to a=0. 01.