Artificial Intelligence on the Web

1. Artificial Intelligence on the Web Wednesday, Week 9

2. Intelligence Exercise • What is Intelligence? • What activities require intelligence?

3. AI Definition #1 • “The automation of activities that we associate with human thinking, activities such as decision-making, problem solving, learning…”

4. AI Definition #2 • “The study of how to make computers do things at which, at the moment, people are better.”

5. AI Definition #3 • “The study of computations that make it possible to perceive, reason, and act.”

6. AI Definition #4 • “The branch of computer science that is concerned with the automation of intelligent behavior.”

7. Main AI Definitions • Systems that think like humans • Systems that act like humans • Systems that act rationally

8. Thinking humanly: • Problem is figuring out how humans think. • This is an interesting question apart from AI. • We are concerned with solving the problem as a human would.

9. Acting humanly: • This idea is pretty much summed up in the Turing Test. • Can we get a program to seem human enough to fool a human interrogator?

10. Acting Rationally: • “Acting to achieve one’s goals, given one’s beliefs.” • So, based on what we know about the world, we should always do the right thing. • It is generally too difficult to find the right thing to do.

11. AI Topics • Let’s focus on Definition #2: Getting computers to do things that human’s are currently better at. • This sweeps away troubling philosophical questions, and allows us to take an engineering perspective.

12. Search Problems • Many AI problems involve finding a sequence of actions to reach a goal. • Chess - find a series of moves to win a game. • Robot control - find a series of movements that leads to a particular room.

13. Search Problems • We formalize search by dividing the world into a set of states and actions. • States: • Chess - legal board positions. • Robot navigation - the robot’s current room. • Actions: • Chess - Legal chess moves. • Robot - move East, West, North or South.

14. Search Problems • We need to know two more things: • The successor function tells us how actions change the state. • The goal state tells us where we are trying to get.

15. Robot Example • Our robot is trying to get from A to P. A B C D E F G H I J K L M N O P

16. Search Tree • Each of our four actions will result in a new state. • From each of those new states, we again have four possible actions to choose from. • The process can be viewed as a tree…

17. Search Tree A North West East South A E B A North West East South … … A I E F

18. Navigating a Search Tree • We can move through a search tree in different ways. • One possibility: Breadth First Search • First consider every possible action sequence of length N. • Then move on to every possible action sequence of length N+1. • We’ll consider other options in lab.

19. Search Efficiency • With breadth first search, how large will our tree get before we reach P? • 46 = 4096. • In general? • BD • B is the branching factor - The number of actions. • D is the depth - The number of steps to the goal.

20. Making Search More Efficient • We can do better if we have an evaluation function - something that tells us if one state is better than another. • Chess is a good example: • Branching factor is around 35. • Number of moves until goal is about 100. • Search tree size: 35100 • We can do much better by using board evaluation - some configurations are clearly better than others.

21. Speaking of Chess… • This is an example of an adversarial game. • In this sort of search we need to consider: • The results of our own actions AND • The possible responses of our opponent. • What would the tree look like? • …

22. General Reasoning • Our two examples so far don’t really feel like intelligence. • What if our states are sets of logical claims? • Germany is a country. • If something is a country, it has a flag. • Our goals are to answer logical questions: • Does Germany have a flag? • Actions are logical operators: • (A AND A->B) -> B

23. General Reasoning • Intelligence through theorem proving. • This was a popular idea early in the history of AI. • Can you guess what problems arise? • The state space is huge. • The action space is big. • It relies on statements being either true or false, when we usually don’t know for sure.

24. A Big Stumbling Block • Our discussion so far has pre-supposed that the world is deterministic and knowledge is certain: • If the robot tries to move North, he always succeeds. • Every country ALWAYS has a flag. • In fact, we almost never have determinism or certainty.

25. Probability as a Tool in AI • Probability theory gives us a formal framework for reasoning under uncertainty. • Some notation: • P(A) = the probability that statement A is true. • P(SNOW_TOMORROW) = .4 • 40% chance it will snow. 60% chance it will not. • P(A | B) = the probability that A is true if we know B to be true. • P(SNOW_TOMORROW | SUMMER) = .001

26. Bayes’ Rule • Let’s say I have a fever. I want to know the following: • P(PNEUMONIA | FEVER) • I do know this: • P(FEVER | PNEUMONIA) = .9 • P(PNEUMONIA) = .001 • P(FEVER) = .1

27. Bayes’ Rule P(E | H) * P(H) P(H | E) = P(E) • Where H is a hypothesis and E is evidence. • P(PNEU. | FEV.)= P(FEV. | PNEU.) * P(PNEU.) • P(PNEU. | FEV.) = .9 * .001 / .1 = .009 • Why is Bayes’ rule helpful? • We want one probability, we need three others to get it. P(FEV.)

28. Bayes’ Rule • Let’s ask a doctor: • How likely is it that a patient with pneumonia has a fever? • “Very likely. I’d say 90%” EASY • What is the probability that a patient with fever has pneumonia? • “I dunno. People get fevers for all sorts of reasons. Flu, infections, etc…” HARD • This happens all the time. It is often easy to estimate a conditional probability in one direction, and not the other.

29. Bayes’ Nets • A nice approach to handling general reasoning while taking probabilities into account. • Here is an example…