Motivation and Overview Probabilistic Graphical Models Introduction Motivation and Overview

millions of pixels or thousands of superpixels predisposing factors symptoms test results diseases treatment outcomes each needs to be labeled {grass, sky, water, cow, horse, …}

Probabilistic Graphical Models

Models Data Model domain expert Declarative representation Learning elicitation Algorithm Algorithm Algorithm

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

Probability Theory Declarative representation with clear semantics Powerful reasoning patterns Established learning methods *** Reasoning with probabilities *** Well understood and useful for modeling uncertainty: dealing with noise, for modeling phenomenon not in our model, and uncertainty inherent in the system *** We can learn probabilities from sets of observations

Complex Systems Random variables X1,…, Xn predisposing factors symptoms test results diseases treatment outcomes class labels for thousands of superpixels Random variables X1,…, Xn Joint distribution P(X1,…, Xn)

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

Graphical Models

Graphical Representation Intuitive & compact data structure Efficient reasoning using general-purpose algorithms Sparse parameterization feasible elicitation learning from data

Many Applications Medical diagnosis Computer vision 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

Image Segmentation

Medical Diagnosis -

Textual Information Extraction Mrs. Green spoke today in New York. Green chairs the finance committee. Person Location Person

Multi-Sensor Integration: Traffic Trained on historical data Learn to predict current & future road speed, including on unmeasured roads Dynamic route optimization Multiple views on traffic Weather Learned Model Incident reports I95 corridor experiment: accurate to 5 MPH in 85% of cases Fielded in 72 cities So far, we have focused on perception from a single source. There are also many cases where we have data streaming in from multiple sensors and information sources, often very heterogeneous in nature. Machine learning provides us with the tools to integrate those different sensors into a coherent picture. For example, a recently fielded traffic system. Thanks to: Eric Horvitz, Microsoft Research

Speech Recognition K O N F I D E N S [Source: http://www-g.eng.cam.ac.uk/125/now/speech2.html]

Biological Network Reconstruction 1 2 3 CD3 CD28 LFA-1 L A T PI3K RAS Cytohesin JAB-1 Zap70 VAV SLP-76 10 6 4 Lck PKC PLCg PIP3 Akt 7 5 PIP2 PKA Raf 8 MAPKKK MAPKKK Mek1/2 9 MEK4/7 MEK3/6 Erk1/2 Causal protein-signaling networks derived from multiparameter single-cell data Sachs et al., Science 2005 JNK p38

Overview Representation Inference Learning Directed and undirected Temporal models More compact representations Inference Exact Approximate Learning Parameters and structure With and without complete data