Daphne Koller Introduction Motivation and Overview Probabilistic Graphical Models

Daphne Koller Probabilistic Graphical Models

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 IntelligenceDifficulty Grade Letter SAT BD C A Bayesian networks Markov networks

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

Daphne Koller END END END

Template vertLeftWhite1 Suppose  is at a local minimum of a function. What will one iteration of gradient descent do? Leave  unchanged. Change  in a random direction. Move  towards the global minimum of J(  ). Decrease .

Template vertLeftWhite1 Consider the weight update: Which of these is a correct vectorized implementation?

Template vertLeftWhite2 Fig. A corresponds to  =0.01, Fig. B to  =0.1, Fig. C to  =1. Fig. A corresponds to  =0.1, Fig. B to  =0.01, Fig. C to  =1. Fig. A corresponds to  =1, Fig. B to  =0.01, Fig. C to  =0.1. Fig. A corresponds to  =1, Fig. B to  =0.1, Fig. C to  =0.01.

Template vertLeftWhite2

Template block2x2White1 Ordering of buttons is: 13 24