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46 Cards in this Set
- Front
- Back
Random Variables
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Take on one more more values (Ex Roll for a dice can be 1, 2 ,3 ..)
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Joint Variables
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Multiple Variable probabilities P(A, B)
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Marginialization
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Sum accross a row or column
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COnditional Probability
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Whats the probability of even A given that I know event B is true.
P(A|B) = P(A | B) / P(B) |
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Marginilization General Rule
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P(X,Y,Z) and want P(X,Y) sum over Z
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Bayes Rule
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P(B|A) = [P(A|B) * P(B)] / P(A)
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Indepence
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P(A,B) = P(A) * P(B)
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Conditional Indepence
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P(A | B,C) =
[P(B | A) * P(C | A) * P(A)] / P(B,C) |
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Naive Bayes
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P(Cause) * Prod(P(Event | Cause)) / [ Summation Over Cause (P(Cause) * Prod(P(Event | Cause))
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Iterative Vs. Search Solutions
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Iterative returns the goal as a solution while searches return the path
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Hill Climbing
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One dimension for each variable, try to find global max or global min, evaluation function says how good point is
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HIll Climbing - Random Restart
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Randomly restart each time
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Simulated Annealing
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Shake surface to move out of local mini/maxi and accept new state if better or based on decreasing probability if worse
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Beam Search
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Start multiple instances
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Genetic Algorithm
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Fitness Function - Increases!
Selection - Choose which parents based on fitness probability Crossover - Choose a cut on parents and swap to make two new Mutation - Randomly Flip bits |
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Syntax
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How to construct sentences, their structure
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Semantics
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What the meaning of a sentnce is
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Atomic Sentence
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Truth value is assigned directly by model
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Complex Sentence
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Truth value assigned by the rules
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Valid Sentence
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Sentence true under all conditions
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Satisfiable Sentence
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Sentence is true under some conditions
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Unsatisfiable Sentence
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Sentence can never be true
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Inference
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Antecedent / Consequent
if we contain the Antecedent, we get the consequent |
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A=>B Equivalent
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~A v B
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Modus Ponens
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A=>B, A
B |
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And Introduction
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A,B
A & B |
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Modus Tolens
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A=>B, ~B
~A |
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Or Introduction
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A
A v B |
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Unit Resolution
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A v B, ~B
A |
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And Elimination
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A & B
A,B |
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Forward Inference
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Insert something into KB, then derive all consequences
KB Tell is Slow, Ask is quick |
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Backward Inference
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To see if Q is true, see if antecedents are truee
KB tesll is quick, ask is slow |
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COnjunctive Normal Form
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X1 & X2 & X3
S.T. X1 only contains ~, v |
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Resolution
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Must be in conjunctive normal form, add opposite of what you want to KB, find contradiction using only unit resolution
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Constants
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Refer to exactly one thing
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Variables
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Reference constants
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Relational Predicates
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Return true or false:
MarriedTo(John,Doe) |
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Functinoal Predicates
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Return an entity
FatherOf(John) = Joe |
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For All Statements
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Always an impllication
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There Exists Statement
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Always an And statement
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For all and There Exists Equivalence
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~For All (Sentence)
There Exists ~(Sentence) |
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For All Introduction
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Can substitue any term into for all statement
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There Exists Introduction - Skoelemizatino
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Can itnroduce one new constant into KB for there exists
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Propositionalization
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Make all possible isntantiations, hard to do
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Planning Languages
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State, Goal, Actions {Name, Parms, Precondition, Effect}
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Pllanning languages - Backward vs. Forward
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Start from goal vs start from initial
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