REVIEW SHEET. CIS 140. Winter 2007.  Robert Levinson

OBJECTIVES
-----------------
Course Objectives:
1. Learn Fundamentals of Classical AI.
2. Prepare for doing Research.
   a. Hot topics/Perspectives. Critical Analysis.
      b. Instructor's Research
		reinforcement learning
			ii.a.
			   c. Critical/analytical approach as opposed to
			   "Show-and-Tell".
3.  Relationship of Mathematics, Information Theory to AI issues.

4. Hands-on experience through Programming Project:

5.   "Stock Market".  Prisoner's Dilemma.

TOPICS
-----------------
     AI vs. Cognitive Science.
 
  Agents:
     Search and Planning:
     SINGLE-AGENT SEARCH ALGORITHMS:
	  3 types:
		   a. UNINFORMED
		  Breadth first search      No commit
		 Depth first search        High Commit

                       BFS vs. DFS vs. DFID

		 Iterative deepening
	      [bi-directional]
	  b. (mildly) INFORMED an
		 heuristic function h
	  that estimates distance to the goal is defined.

	 Best-first search f = h
		 A*   f=g^ + h
		 A*-Admissible h<=h*i: guarantees find optimal
		 A*-Monotone Restriction. h=0 at goal, |h(i)-h(j)| <=1
			  allows algorithm to be streamlined.
                   Theorems and proofs

                  [IDA* - much more efficient]
   c.  [ PLANNING]            /* not covered  *?
(agent is given rules of problem domain)
               [  Means-Ends-Analysis
		    Macros
		    Subgoals
		    Abstract States
                 MacroTables vs. PWs   ]

     Machine Learning:
	  Decision Tree
	     finding smallest is NP-hard.]
	  Emas
          Reinforcement Learning
              [Temporal Difference Learning]
	     Dynamic Learning rate
             NNC, K-NNC
	      NNC

	   Version Spaces

          Perceptrons
	     Perceptron Learning Theorem
	     (one simple layer can't do XOR).
	       (add non-linear terms for more power!)

          Gradient Descent

        [  Linear Regression --->  Logistic Regression
	      ----> Kernel Regression  ---> Support Vector Machines]

	  Decision Trees
	     How to generate, compress, measure cost

          Statistics 


   [   briefly mentioned:
   
	  Panel of Experts

          Genetic Algorithms 

          Genetic Programming  ]

	    
      Representation:
        [  Hypergraphs ]
	  Propositional Logic
	  Predicate Logic
	  Existential Graphs
	  SAT matrices
	  Truth Tables

  

        Game Tree Searching
	-------------------
	 Minimax
	 Minimax Alpha-Beta
	      major problem with minimax:
		(is just worst case guarantee)
		strategic
         How computers play chess.
	     4 stage search, quiescence
	[[     singular extension ]
	     Strengths and weaknesses.
	     <How to beat>
	     [Aspiration window]
	   [  Killer Heuristic ]
	     [History Heuristic]
	     [Null-Move
	     Transposition Table, Piece Square Table. ]]
       [ GO vs. chess.]
	  [ Hypergraph TTT ]

        Simultaneous Play Payoff Matrices
	   dominant strategies or else stochastic (nash)
	   equilbrium

     Inference:    
         Resolution (prove by contradiction) 
	 Unification 
	 Skolemization
	 Clausification
         EGs: Deiteration (deletion), Double Neg Removal, [Bob's Rule.]
	     Existential Graphs
	    

     Retrieval: 
	    [K-D-Tries for Nearest Neighbor]
	    Lisp sort function



DEFINITIONS 
-----------------
     Knowledge is Information Processed for further use.

     Informal Defintion of Intelligence #1:
	  Optimal problem-solving in pursuit of goals
	  under resource constraints.
            (making cost-effective descisions)

     Informal Defintion of Intelligence #2: 
	  Exploitation, creation of order (redundancy=mutual information).

    summary: Wise Autonomous Decision Making!

     Subsumes:  A subsumes B iff B is true whenever A is true.
	      synonymous with implies

     State Space Search Problem: 
	 (Initial State, Operators, and Goals).
	   Operator = preconditions, adds and deletes. 

     Meta = One system or degree of freedom above or beyond

     Meta-Reasoning = Reasoning about Reasoning

     Abstraction = Hide irrelevant details.
     Generalization = Hide hopefully irrelevant details.

     NP-hard (completeness).
	 Input must be unbounded in size.

     "Commit": Prune a potential solution path - burn a bridge.

      Mathematical Objects:
	     Set
	       Intensional Def.
	       Extensional Def.
	   [    Recursively Enumerable 
	 [      Recursive
	 [    Tuple
	     Relation
              Binary
		Reflexive   Anti-reflexive  Areflexive...
		Symmetric  etc.
		Transitive etc.
		Equivalence Relation: R,S,T
		Partial Order: R,AntiS,T
		    Ex: Subsumption
			Easier-Than
		  Total Order     ] ]
      [     Hypergraphs = set + subsets of the set ].
	   [Nested Directed Hypergraphs] ]

           Isomorphic = same after mathematical abstratcion.

        [  5 measures of information:
	     ,amt. of raw materials,cost, utility, surprise reduction, 
	     gain ratio. ]

         Quantity of Information in Event E of Prob. P:
	     H(E)=I(E)=-log2(P)

              Knowing value of a variable of N values is:
		  -summation(Pilog2(Pi)) i=1,..n

           [   Mutual Information = Symmetry between U and X:
		    I(U:X) = H(U) - H(U|X). ]

              Complexity = Amount of Information required
	      to compute the value of a variable or predicate.

            [  Gain Ratio = Utility Aft - Utility Bef
			   -------------------------
				 Complexity(Cost)   ]

            [  Variable P fully determines variable Q iff I(Q:P)=I(Q).
	    ]

               Note: "Fully determines" subsumes "subsumes".

              Credibilty of an agent = inverse of its error.

               Universal Greedy Algorithm
		   (minimize entropy on each step). 


	 
CONCEPTUAL TOOLS/FRAMEWORKS

    [ World as Predicates + Actions with grounding in sense predicates. ]
     

     Agent-Environment relationship

  [   Partial Order of Predicates by Subsumption(POPS) ]

[*     Partial Order of State Spaces by Easier-Than] 

     NNC tables vs. Decision Trees.
	 rote  vs. compress and generalize

     4 main approaches to computer chess/ AI:
	  Brute force vs. Human Oriented (schematic
	  approach) vs. Mathematical Abstraction  vs. Statistics
	  (Morph)
------------------


APPLICATIONS
-----------------
     Nim: There is an optimal rule
     Chess:
       [  Rules
	 3 stages
         2 main strategies
	 tactics vs. positional
	 Values of Pieces
	 Simple Mates
	 King opposition
	 Hypermodern School
	 gambit
	 main  principles. ]

     Computer Chess
	 Deep Blue versus Kasparov
	 Shannon A (full depth search)_, Shannon B(selective search)
	 [Quiescence: wait until positions are quiet before evaluating 

          MORPH - experience-based learner.

     8 puzzle (CSP)   nxn puzzles are NP hard
              Determining solvability
[              Using macro table  ]
	      Manhattan Distance
	      [Wheel Problem 
	      PathMax]
     SAT  NP hard 
   [  Towers of Hanoi]
     Missionaries and Cannibals  
     Tic-Tac-Toe   
     Eight Puzzle
	 only half the states solvable (cycle algorithm)
         nxn is NP-complete
	 Manhattan Distance is admissible and monotone heuristic
         No simple optimal rule even known for 3x3.
      Stock Market, PD , - exploit other agents patterns/success.
      Stock Market
	 Rule 1. If doesn't work , do opposite!
	 Rule 2. Don't follow Rule 1

          Technical Analysis = black box analysis of price behavior
	  Fundamental Analysis = model of economy and stock prices.
	  


LISP
-------
Recursion
Core functions: first, rest, cons, if, null, setf, quote,eval.
some functions to practice on:
parencount mymapcar reverse append snoc mid flatten length sortedp merge myor. 
Functions as parameters.
reading and writing files:

PRINCIPLES
-----------------

Everything is relative:
        Information, Complexity, Similarity, and Utility are
	all domain-dependent.

symmetry=mutual information=structure=relationships=relatedness
=correlation=goodstufftofind.

Maximize agent uncertainty - Minimize environment uncertainty:

Tension: Uncertainty/Combinatorial Explosion vs. Commitment

Tension: Knowledge vs. Search (each can replace the other).
   Search is used as a last resort.

Maximize Entropy (don't make an unnecessary commitment): Occam'z Razor.
Prefer simplest (least complex) explanation.

[*Distance Heuristic for Chess:
     minimize short safe path distance to opponents pieces etc.]

*** Efficiency is gained by exploiting mutual information = symmetry
=structure.

Fundamental Problem of Learning:
     Extensional Def. ---> Intensional Def.

Fundamental Problem of Search:
    Binary Relation ---> Path Distance Function  

Parity is often useful predicate (e.g. Nim, 8puzzle, mutilated
checkerboard )

Total Information = Diversity + Symmetry.

Law 1: Amount of information constant in a closed system.

Law 2: Symmetry never decreases in a closed system.

[Law 3: Trade off between risk and reward.]

[Information/Energy Chart.]