Artificial Intelligence Lecture 1

Transcription

1 Artificial Intelligence Lecture 1

2 istrative Matters Webpage: Examiner: Mathias Broxvall Assistant: Lia Susana d.c. Silva Lopez Schedule 20 hours/week on this course. 4 hours lectures, and ~4 hours preparations for lectures Read slides from previous lectures. Read course book. Prepare questions. Think! Discuss! 3 hours assisted labs (Thursdays ) 9 hours left Prepare for labs. Read instructions, make designs, lookup functions.. Labs on your own time. You must be able to debug your own code! 2

3 istrative Matters Course book: Alison Cawsey, The essence of Artificial Intelligence Recommended reading: (Python) 1.Zelle, Python Programming (AI) 1.Russel, Norvig, Artificial Intelligence a modern approach. 2.Rich, Knight, Artificial Intelligence, 2:nd ed. 3. Internet there much high quality free material available. 3

4 What is Artificial Intelligence? Artificial: Not natural or real, made by the art of man Intelligence: 1) The power of perceiving, learning, understanding and knowing; mental ability. 2) News, information. (Oxford Advanced Learners Dictionary of Current English) Artificial Intelligence is the design and study of computer programs that behave intelligently. (Dean, Allen.) The branch of computer science that is concerned with the automation of intelligent behavior. (Luger, Stubblefield) Artificial Intelligence is the art of making computers work the way they do in the movies. (Unknown) 4

5 What is Artificial Intelligence? AI as a broad field involving research in numerous other areas Computer Science Psychology Neuroscience Linguistics Philosophy 5

6 What is Artificial Intelligence Weak AI: Machines can be made to act as if they were intelligent. Ex: Eliza, A.L.I.C.E, expertsystems etc. Strong AI: Machines that act intelligently have real, conscious minds. Ex: human-like AI, the movie A.I. etc. non-human-like HAL in the movie

7 What is Artificial Intelligence? Even if we make the great AI Machine, how do we test if it can think? The Turing test: First described by Alan Turing, If an impartial judge communicating with a human and/or with a computer both attempting to pass as a human and he cannot see the difference between them, then the machine passes the turing test. The Chinese room: Thought experiment by John Searly (1980) debunking strong AI and the Turing test. The Loebner price competition: The Loebner Prize is an annual competition that awards prizes to the Chatterbot considered the most humanlike for that year. The format of the competition is much like that of a standard Turing test. (wikipedia) 7

8 What is Artificial Intelligence? 8

9 What is Artificial Intelligence? 9

10 What is Artificial Intelligence? 10

11 What is Artificial Intelligence? 11

12 What is Artificial Intelligence In this course AI looks a bit different.. 12

13 Course contents Search Expert Systems Natural Language Processing Machine Learning Knowledge Representation and Inference Agents and Robotics Laboratory exercises Search, Game playing, Neural networks

14 What is Artificial Intelligence? But you can still do some cool things. The water jug problem: Suppose you are given 1 jug (3L) and 1 jug (4L). You also have a tap With which you can fill the jugs. Goal: Get exactly 2L in the 4L jug. 4L 3L 14

15 Representation From AI admirers to AI programmers. Step 1: Represent the problem so that it is computerfriendly. Step 2: Code the problem in a programming language. Step 3: Develop/code an algorithm to find a solution. Step 4: Represent the solution so that it is humanfriendly. 15

16 Representation Step 1: Representing the problem for a machine. We represent the amount of water in the jugs with (X,Y) 1.(X,Y) > (4,Y) Fill the 4 liter jug. 2.(X,Y) > (X,3) Fill the 3 liter jug. 3.(X,Y) > (0,Y) Empty the four liter jug 4.(X,Y) if X+Y >= 4 and Y > 0 > (4,Y (4 X)) Fill the 4 liter jug with water from the 3 liter jug. 16

17 Representation 17

18 (4,2) (0,2) (2,0) 18

19 Starting with Python Python is a object oriented, functional,interpretative and incremental programming language. Object oriented: it has classes / methods etc. Interpretative: It it not compiled but interpretative during run-time. (Some Just In Time compilation done) Incremental: You can mix development and test running, just enter functions as the commandline. Simplifies development. Functional: Functions are objects that can be manipulated like everything else. Gives a lot of power, especially for AI applications 19

20 Python Integers, Strings, Lists, Tuples, Dictionaries 42 foo 'foo' [1,2,3] [[1,2],[3,4] (1,2) { foo : 42} List operations X[0] = 3 ; Y[1] = [1,2,3] ; Y[1][1] = 2 ; Z[-1] Slices X[0:2] = [1], X[1:] ; X[-1] Function definitions and conditionals def abs(x): if x > 0: else: return x return x Python is sensitive to indentation level! 20

21 def fac(n): res=1 for i in range(2,n+1): res=res*i return res def fac2(n): if n==1: return 1 else: return n*fac2(n 1) 21

22 General idea of recursion Make the program work for a base case (eg. N=1) For complex cases, decompose into simpler cases and call yourself (eg. fac(n) = N*fac(N-1) for N>1) This is similar to the idea of PROOF BY INDUCTION Prove that the base-case is true Prove that the recursive cases are true 22

23 How can we come up with a recursive algorithm? First, find the simplest trivial cases for which you know the answer immediately. Eg. Check if an element is part of a list: Base case 1) The element occurs first in the list (return True) Base case 2) The list is empty (return False) Figure out how to solve all other cases by calling yourself Eg. Check if an element is part of a list Recursive case 1) If neither case 1 or 2 holds then call yourself recursively on the rest of the list and return that answer 23

24 How can we come up with a recursive algorithm? Example: make a list flat moving the content of all sublist into the main list Base case 1: The list is empty return empty list Recursive case 1: The first element is not a list return this element appended in front of the result of flattening the rest of the list Recursive case 2: The first element is list flatten the first element and append the result to what you get by flattening the rest of the list 24

25 a more advanced example Flattening a list def flatten(l): if L==[]: return [] elif isinstance(l[0],list): return flatten(l[0])+flatten(l[1:]) else: return L[:1]+flatten(L[1:]) >>> flatten([1,[2,3],4]) [1,2,3,4] 25

26 Why is recursion important for AI? Many AI problems can be solved with recursive algorithms. Different cases can correspond to the different choices of the AI algorithm Eg. in the water jug problem: A base case is if we found the solution. Recursive case(s): one for each possible action that can be done. See if the recursive call found the solution, otherwise try the next possible action. Nb. we have to avoid infinite recursion! 26

27 Exercise Create a function that sums all numbers contained in a list, or inside lists inside that list, or inside lists inside lists inside lists... >>> mysum([1,2,3]) 6 >>> mysum([[1,2],[3,[4]]]) 10 27

28 Computational complexity Big O notation Ignores constant values, concentrate on the cost in terms of parameters of the problem. Shows the worst case growth, especially for large n. O(1) = O(2) etc. O(n) = O(2n) O(n + 3n 2 ) = O(n 2 ) O(2 n )!= O(3 n ) etc. Ordo complexity of a problem. eg: O(n 2 ) Complexity of the best known algorithm solving the problem Lower bound complexity of a problem. eg: (n) Proven lower bound for all algorithms solving the problem 28

29 Computational complexity: examples for i in range(0,n): some constant cost function O(n) for i in range(0,n): for j in range(0,n): some constant cost function O(n 2 ) for i in range(0,n): for j in range(0,i): some constant cost function O(n 2 ) 29

30 Computational complexity: examples for i in range(0,7*n*n): some constant cost function O(n 2 ) for i in range(0,pow(2,n)): some constant cost function O(2 n ) for i in range(0,pow(3,n)): for j in range(0,5): some constant cost function O(3 n ) 30

31 Computational Complexity What is the computational complexity of the following function: def f(n): if N==1: return 1 else return f(n-1) + f(n-1) 31

32 Categorization of complexity of problems Polynomial: can be solved in polynomial time with respect to the size of the input. constant time O(1): eg. hash table lookup linear time O(n): eg. checking if element in list logarithmic time O(log(n)): eg. checking if element is present in a sorted list O(n*log(n)): eg. sorting a list Exponential: O(2 n ): eg. satisfiability problem Determines if a boolean formula is true for atleast one assignment of variables 32

33 Classes of complexity P: Polynomial time NP: plus all problems for which the best algorithm found up to now is exponential, but the solution can be verified in polynomial time. NP-complete: sub-class of NP of specially important (and difficult) problems. If one could find an algorithm that solves a problem in the NP-complete class in polynomial time, it would be possible to solve all the problems in NP in polynomial time Holy grail of computer science: NP = P??? 33

34 Higher order functions Functions are objects like anything else! >>> fac <function fac at 0xb75e36bc> def myapply(f,l): if L!=[]: print F(L[0]) myapply(f,l[1:]) >>>myapply(fac,[1,2,3])

35 Church's calculus Mathematical framework for describing computation Created in the 1930's Pythons 'lambda' inspired by this calculus Creates an unnamed (anonymous) function >>> lambda x: x+2 <function <lambda> at 0xb6f12764> >>> myapply(lambda x: x+2, [1,2,3])

36 Built-in higher order functions Higher order functions Functions that accept other functions as arguments >>> map(fac,[1,2,3]) [1, 2, 6] >>> filter(lambda x: x>1, [1,2,3]) [2, 3] >>> all(map(lambda x: x>1, [1,2,3])) False >>> any(map(lambda x: x>1, [1,2,3])) True >>> sorted([[1,2], [3], [4,5,6]],lambda x,y: len(x) len(y)) [[3], [1,2], [4,5,6]] 36

37 Generators >>> [ fac(x) for x in range(1,5) ] [1, 2, 6, 24] >>> [ fac(x) for x in range(1,10) if x%2 == 0 ] [2, 24, 720, 40320] >>> [(x,y) for x in range(1,4) for y in range(1,4) if x>y] [(1, 0), (2, 0), (2, 1), (3, 0), (3, 1), (3, 2)] 37