Documents

Bayesian Networks

Description
Bayesian Networks Recap of Last Lecture  Probability: Precise representation of uncertainty.  Probability Theory: Optimal updating of knowledge bared on new information.  Bayesian Inference  Conditional Probability ( | )  Product Rule (  Chain Rule ( ) ) ( | ) ( ) ( ) ( | ) ( | ∏ ( |  x, y independent iff ( ) ( ) ( ) ) ) ( ( ) )  x and y are conditionally independent of z iff ( | ) | ( | ) ( | ) Probabilistic Models  Models describe how (a portion of) the world works.  Models are al
Categories
Published
of 14
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  Bayesian Networks Recap of Last Lecture    Probability: Precise representation of uncertainty.    Probability Theory: Optimal updating of knowledge bared onnew information.    Bayesian Inference    Conditional Probability (|)()()      Product Rule ()(|)()      Chain Rule (        )(  )(  |  )(  |    )   ∏(  |        )       x, y independent iff  ()()()      x and y are conditionally independent of z iff  (|)(|)(|)     |    Probabilistic Models    Models describe how (a portion of) the world works.    Models are always simplifications    May not account for every variable    May not account for all interactions between variables    What do we do with probabilistic models?    We (or the agents) need to reason about the unknownvariables, given evidence.    Example:a)   Explanation (diagnostic reasoning)b)   Prediction (causal reasoning)c)   Value of information Probabilistic Reasoning    Suppose we go to my house and see that the door is open.    What’s the cause? Is it a burglar? Should we go in? Call the police?    Then again, it could be just be my wife. Maybe she camehome early.    How should we represent these relationships?  Bayes’ Nets: Big Picture      Two problems with using full joint distribution / tree tables asour probabilistic models. o   Unless there are only a few variables, the joint is way toobig to represent explicitly. For  variables with domainsize  joint tables has   entries. o   Hard to learn (estimate) anything empirically about morethan a few variables at a time.    Bayes’ nets: a technique for describing complex joint distributions (models) using simple local distributions(conditional probabilities) o   More properly called graphical models . o   We describe how variables locally interact. o   Local interactions chain together to give global indirectinteractions.  Graphical Model Notation    Causal relationships are represented in directed acyclic graphs.    Arrows (Arcs) indicates relationships between nodes.    For now: image that arrows mean direct causation (in global, they don’t)   Types of Probabilistic Relationships 1.   Independent ( |)()   (| )()  2.   Direct Cause (| )     opendoor wife burglar ABAB
Search
Tags
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x