CS 380: ARTIFICIAL INTELLIGENCE MACHINE LEARNING. Santiago Ontañón
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1 CS 380: ARTIFICIAL INTELLIGENCE MACHINE LEARNING Santiago Ontañón
2 Summary so far: Rational Agents Problem Solving Systematic Search: Uninformed Informed Local Search Adversarial Search Logic and Knowledge Representation Predicate Logic First-order Logic Today: Machine Learning
3 What is Learning?
4 Machine Learning Computational methods for computers to exhibit specific forms of learning. For example: Learning from Examples: Supervised learning Unsupervised learning Reinforcement Learning Learning from Observation (demonstration/imitation)
5 Examples Supervised Learning: learning to recognize writing
6 Examples Supervised Learning: image classification
7 Examples Unsupervised Learning: clustering observations into meaningful classes
8 Examples Reinforcement Learning: learning to walk
9 Examples Learning from demonstration: performing tasks that other agents (or humans) can do
10 Examples Reinforcement Learning: Learning from demonstration:
11 Inductive learning (a.k.a. Science) Simplest form: learn a function from examples (tabula rasa) f is the target function An example is a pair x, f(x), e.g., O O X X X, +1 Problem: find a(n) hypothesis h such that h f given a training set of examples (This is a highly simplified model of real learning: Ignores prior knowledge Assumes a deterministic, observable environment Assumes examples are given Assumes that the agent wants to learn f why?) Chapter 18, Sections 1 3 6
12 Inductive learning method Construct/adjust h to agree with f on training set (h is consistent if it agrees with f on all examples) E.g., curve fitting: f(x) x Chapter 18, Sections 1 3 7
13 Inductive learning method Construct/adjust h to agree with f on training set (h is consistent if it agrees with f on all examples) E.g., curve fitting: f(x) x Chapter 18, Sections 1 3 8
14 Inductive learning method Construct/adjust h to agree with f on training set (h is consistent if it agrees with f on all examples) E.g., curve fitting: f(x) x Chapter 18, Sections 1 3 9
15 Inductive learning method Construct/adjust h to agree with f on training set (h is consistent if it agrees with f on all examples) E.g., curve fitting: f(x) x Chapter 18, Sections
16 Inductive learning method Construct/adjust h to agree with f on training set (h is consistent if it agrees with f on all examples) E.g., curve fitting: f(x) x Chapter 18, Sections
17 Inductive learning method Construct/adjust h to agree with f on training set (h is consistent if it agrees with f on all examples) E.g., curve fitting: f(x) x Ockham s razor: maximize a combination of consistency and simplicity Chapter 18, Sections
18 Attribute-based representations Examples described by attribute values (Boolean, discrete, continuous, etc.) E.g., situations where I will/won t wait for a table: Example Attributes Target Alt Bar F ri Hun P at P rice Rain Res T ype Est WillWait X 1 T F F T Some $$$ F T French 0 10 T X 2 T F F T Full $ F F Thai F X 3 F T F F Some $ F F Burger 0 10 T X 4 T F T T Full $ F F Thai T X 5 T F T F Full $$$ F T French >60 F X 6 F T F T Some $$ T T Italian 0 10 T X 7 F T F F None $ T F Burger 0 10 F X 8 F F F T Some $$ T T Thai 0 10 T X 9 F T T F Full $ T F Burger >60 F X 10 T T T T Full $$$ F T Italian F X 11 F F F F None $ F F Thai 0 10 F X 12 T T T T Full $ F F Burger T Classification of examples is positive (T) or negative (F) Chapter 18, Sections
19 Decision trees One possible representation for hypotheses E.g., here is the true tree for deciding whether to wait: Patrons? None Some Full F T WaitEstimate? > F Alternate? Hungry? T No Yes No Yes Reservation? Fri/Sat? T Alternate? No Yes No Yes No Yes Bar? T F T T Raining? No Yes No Yes F T F T Chapter 18, Sections
20 Expressiveness Decision trees can express any function of the input attributes. E.g., for Boolean functions, truth table row path to leaf: A B A xor B F F F F T T T F T T T F F F B A F T B T F T T T F Trivially, there is a consistent decision tree for any training set w/ one path to leaf for each example (unless f nondeterministic in x) but it probably won t generalize to new examples Prefer to find more compact decision trees Chapter 18, Sections
21 Hypothesis spaces How many distinct decision trees with n Boolean attributes?? Chapter 18, Sections
22 Hypothesis spaces How many distinct decision trees with n Boolean attributes?? = number of Boolean functions Chapter 18, Sections
23 Hypothesis spaces How many distinct decision trees with n Boolean attributes?? = number of Boolean functions = number of distinct truth tables with 2 n rows Chapter 18, Sections
24 Hypothesis spaces How many distinct decision trees with n Boolean attributes?? = number of Boolean functions = number of distinct truth tables with 2 n rows = 2 2n Chapter 18, Sections
25 Hypothesis spaces How many distinct decision trees with n Boolean attributes?? = number of Boolean functions = number of distinct truth tables with 2 n rows = 2 2n E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees Chapter 18, Sections
26 Hypothesis spaces How many distinct decision trees with n Boolean attributes?? = number of Boolean functions = number of distinct truth tables with 2 n rows = 2 2n E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees How many purely conjunctive hypotheses (e.g., Hungry Rain)?? Chapter 18, Sections
27 Hypothesis spaces How many distinct decision trees with n Boolean attributes?? = number of Boolean functions = number of distinct truth tables with 2 n rows = 2 2n E.g., with 6 Boolean attributes, there are 18,446,744,073,709,551,616 trees How many purely conjunctive hypotheses (e.g., Hungry Rain)?? Each attribute can be in (positive), in (negative), or out 3 n distinct conjunctive hypotheses More expressive hypothesis space increases chance that target function can be expressed increases number of hypotheses consistent w/ training set may get worse predictions Chapter 18, Sections
28 Decision tree learning Aim: find a small tree consistent with the training examples Idea: (recursively) choose most significant attribute as root of (sub)tree function DTL(examples, attributes, default) returns a decision tree if examples is empty then return default else if all examples have the same classification then return the classification else if attributes is empty then return Mode(examples) else best Choose-Attribute(attributes, examples) tree a new decision tree with root test best for each value v i of best do examples i {elements of examples with best = v i } subtree DTL(examples i, attributes best, Mode(examples)) add a branch to tree with label v i and subtree subtree return tree Chapter 18, Sections
29 Choosing an attribute Idea: a good attribute splits the examples into subsets that are (ideally) all positive or all negative Patrons? Type? None Some Full French Italian Thai Burger P atrons? is a better choice gives information about the classification Chapter 18, Sections
30 Information answers questions Information The more clueless I am about the answer initially, the more information is contained in the answer Scale: 1 bit = answer to Boolean question with prior 0.5, 0.5 Information in an answer when prior is P 1,..., P n is H( P 1,..., P n ) = Σ n i = 1 P i log 2 P i (also called entropy of the prior) Chapter 18, Sections
31 Entropy Given a set of symbols S, drawn from an alphabet B Entropy: expected number of bits needed to encode the next symbol (amount of information that knowing one more symbol provides us) If S are drawn at random from B, entropy is maximal If S is always the same symbol from B, entropy is minimal (we know which symbol will come next, so, no new information)
32 Entropy H(X) = X i p(x i )log p(x i ) Example for binary variable: 1.0 Entropy(S) p +
33 Information contd. Suppose we have p positive and n negative examples at the root H( p/(p+n), n/(p+n) ) bits needed to classify a new example E.g., for 12 restaurant examples, p = n = 6 so we need 1 bit An attribute splits the examples E into subsets E i, each of which (we hope) needs less information to complete the classification Let E i have p i positive and n i negative examples H( p i /(p i +n i ), n i /(p i +n i ) ) bits needed to classify a new example expected number of bits per example over all branches is Σ i p i + n i p + n H( p i/(p i + n i ), n i /(p i + n i ) ) For P atrons?, this is bits, for T ype this is (still) 1 bit choose the attribute that minimizes the remaining information needed Chapter 18, Sections
34 Entropy for Attribute Selection Information Gain: reduction gain in Entropy due to selecting attribute A Gain(S, A) =H(S) X v2values(a) S v S H(S v) Idea: the best attribute is the one that maximizes information gain
35 Example contd. Decision tree learned from the 12 examples: Patrons? None Some Full F T Hungry? Yes No Type? F French Italian Thai Burger T F Fri/Sat? T No Yes F T Substantially simpler than true tree a more complex hypothesis isn t justified by small amount of data Chapter 18, Sections
36 ID3 Does Best-First Search A1 + + A2... Search in the hypothesis space, starting from a tree with a single node, and using Information Gain as the heuristic function A2 + + A2... We can conceive better search strategies (e.g. A*), but the computational cost might be too large (although it might learn much better!) + + A A
37 ID3 Better heuristics than Information Gain exits: E.g. Gain Ratio, GINI index, RLDM distance, etc. Many alternative search strategies (e.g. decision forests) Over-fitting: What happens if we have an example in the training set that is noise? (e.g. that is mislabeled) ID3 will try to force it into the decision tree! Over-fitting strategies exist to avoid this (e.g. prevent leaves that have only a very small number of examples)
38 ID3 Converting a tree to rules: Each branch of the tree is a rule A decision tree is just a compact way to represent a set of rules Outlook Humidity Sunny Overcast Yes Rain Wind Outlook = rain and Wind = strong " playtennis = no High Normal Strong Weak No Yes No Yes
39 Performance measurement How do we know that h f? (Hume s Problem of Induction) 1) Use theorems of computational/statistical learning theory 2) Try h on a new test set of examples (use same distribution over example space as training set) Learning curve = % correct on test set as a function of training set size % correct on test set Training set size Chapter 18, Sections
40 Performance measurement contd. Learning curve depends on realizable (can express target function) vs. non-realizable non-realizability can be due to missing attributes or restricted hypothesis class (e.g., thresholded linear function) redundant expressiveness (e.g., loads of irrelevant attributes) % correct 1 realizable redundant nonrealizable # of examples Chapter 18, Sections
CS 380: ARTIFICIAL INTELLIGENCE
CS 380: ARTIFICIAL INTELLIGENCE MACHINE LEARNING 11/11/2013 Santiago Ontañón santi@cs.drexel.edu https://www.cs.drexel.edu/~santi/teaching/2013/cs380/intro.html Summary so far: Rational Agents Problem
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