Machine Learning - DISCo

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Cup C [2+,3-I I( i \ Cup C Fragile ... Cup C BottamlsFlal, I2++l Light, HmConcnvity, ConcavifyPointsUp [4+.2-I Cup C HasConcavity, ConcavityPointsUp HandleOnTop [0+,2-I Cup C BonomlsFlat, Light, HasConcaviry, ConcavifyPoinfsUp, 1 ~andleon~o~ Cup C BottomlsFlof, Light, HasConcavity, W+&I FIGURE 12.8 Hypothesis space search in FOCL. To learn a single rule, FOCL searches from general to increasingly specific hypotheses. Two kinds of operators generate specializations of the current hypothesis. One kind adds a single new literal (solid lines.in the figure). A second kind of operator specializes the rule by adding a set of literals that constitute logically sufficient conditions for the target concept, according to the domain theory (dashed lines in the figure). FOCL selects among all these candidate specializations, based on their performance over the data. Therefore, imperfect domain theories will impact the hypothesis only if the evidence supports the theory. This example is based on the same training data and domain theory as the earlier KBANN example. primitive attributes of the instances, are considered nonoperational. An example of a nonoperational attribute in this case is the attribute Stable. At each point in its general-to-specific search, FOCL expands its current hypothesis h using the following two operators: , 1. For each operational literal that is not part of h, create a specialization of h by adding this single literal to the preconditio s. This is also the method used by FOIL to generate candidate successors. P he solid arrows in Figure 12.8 denote this type of specialization.
CHAPTER 12 COMBINING INDUCTIVE AND ANALYTICAL LEARNING 359 2. Create an operational, logically sufficient condition for the target concept according to the domain theory. Add this set of literals to the current preconditions of h. Finally, prune the preconditions of h by removing any literals that are unnecessary according to the training data. The dashed arrow in Figure 12.8 denotes this type of specialization. The detailed procedure for the second operator above is as follows. FOCL first selects one of the domain theory clauses whose head (postcondition) matches the target concept. If there are several such clauses, it selects the clause whose body (preconditions) have the highest information gain relative to the training examples of the target concept. For example, in the domain theory and training data of Figure 12.3, there is only one such clause: Cup t Stable, Lifable, Openvessel The preconditions of the selected clause form a logically sufficient condition for the target concept. Each nonoperational literal in these sufficient conditions is now replaced, again using the domain theory and substituting clause preconditions for clause postconditions. For example, the domain theory clause Stable t BottomIsFlat is used to substitute the operational BottomIsFlat for the unoperational Stable. This process of "unfolding" the domain theory continues until the sufficient conditions have been restated in terms of operational literals. If there are several alternative domain theory clauses that produce different results, then the one with the greatest information gain is greedily selected at each step of the unfolding process. The reader can verify that the final operational sufficient condition given the data and domain theory in the current example is BottomIsFlat , HasHandle, Light, HasConcavity , ConcavityPointsUp As a final step in generating the candidate specialization, this sufficient condition is pruned. For each literal in the expression, the literal is removed unless its removal reduces classification accuracy over the training examples. This step is included to recover from overspecialization in case the imperfect domain theory includes irrelevant literals. In our current example, the above set of literals matches two positive and two negative examples. Pruning (removing) the literal HasHandle results in improved performance. The final pruned, operational, sufficient conditions are, therefore, BottomZsFlat , Light, HasConcavity , ConcavityPointsUp This set of literals is now added to the preconditions of the current hypothesis. Note this hypothesis is the result of the search step shown by the dashed arrow in Figure 12.8. Once candidate specializations of the current hypothesis have been generated, using both of the two operations above, the candidate with highest information gain is selected. In the example shown in Figure 12.8 the candidate chosen at the first level in the search tree is the one generated by the domain theory. The search then proceeds by considering further specializations of the theory-suggested
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Machine Learning Tom M. Mitchell Pr
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xvi PREFACE A third principle that
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CHAPTER INTRODUCTION Ever since com
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CHAPTER 1 INTRODUCITON 3 0 Learning
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CHAFTlB 1 INTRODUCTION 5 that allow
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1.2.2 Choosing the Target Function
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CHAPTER I INTRODUCTION 9 x5: the nu
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Thus, we seek the weights, or equiv
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could involve creating board positi
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the available training examples. Th
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0 Chapter 10 covers algorithms for
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ination of board features of your c
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CHAFER 2 CONCEm LEARNING AND THE GE
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When learning the target concept, t
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CHAPTER 2 CONCEPT LEARNING AND THE
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is needed. In the general case, as
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2.5 VERSION SPACES AND THE CANDIDAT
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{ 1 FIGURE 2.3 A version space w
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CHAPTER 2 CONCEET LEARNJNG AND THE
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C H m R 2 CONCEPT LEARNING AND THE
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CH.4PTF.R 2 CONCEFT LEARNING AND TH
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the power set of X? In general, the
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CHAFI%R 2 CONCEPT LEARNING AND THE
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CHAPTER 2 CONCEPT. LEARNING AND THE
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CHAFTER 2 CONCEPT LEARNING AND THE
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Hirsh, H. (1991). Theoretical under
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CHAPTER 3 DECISION TREE LEARNING 53
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CHAPTER 3 DECISION TREE LEARMNG 55
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High wx CHAPTER 3 DECISION TREE LEA
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{Dl, D2, ..., Dl41 P+S-I Which attr
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3.6 INDUCTIVE BIAS IN DECISION TREE
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3.6.2 Why Prefer Short Hypotheses?
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easonable strategy, in fact it can
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Although the first of these approac
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multiple ways, then averaging the r
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CHAFER 3 DECISION TREE LEARNING 77
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C m 3 DECISION TREE LEARNING 79 Fay
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CHAPTER ARTIFICIAL NEURAL NETWORKS
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at normal speeds on public highways
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~t is also applicable to problems f
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FIGURE 43 A perceptron. A single pe
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this example. Notice the training r
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Gradient descent search determines
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- - CHAF'l'ER 4 ARTIFICIAL NEURAL N
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C H m R 4 ARTIFICIAL NEURAL NETWORK
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CHAPTER 4 ARTIFICIAL NEURAL NETWORK
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and combining this with Equations (
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Inputs Outputs Input 10000000 0 100
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FIGURE 4.8 Learning the 8 x 3 x 8 N
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30 x 32 resolution input images lef
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left, (0,1,0,O) to encode a face lo
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close to zero, as the bright face w
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4.8.2 Alternative Error Minimizatio
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BACKPROPAGATION searches the space
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4.6. Explain informally why the del
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Mitchell, T. M., & Thrun, S. B. (19
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the impact of possible pruning step
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Here the notation Pr denotes that t
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a A random variable can be viewed a
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5.3.2 The Binomial Distribution A g
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In case the random variable Y is go
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which is wide enough to contain 95%
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intervals for discrete-valued hypot
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Then as n + co, the distribution go
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we might observe this difference in
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1. Partition the available data Do
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perfectly fits the form of the abov
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CHAFER 5 EVALUATING HYPOTHESES 151
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Geman, S., Bienenstock, E., & Dours
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CHAFER 6 BAYESIAN LEARNING 155 U Fo
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CHAPTER 6 BAYESIAN LEARNING 157 As
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. - Product rule: probability P(A A
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CHAPTER 6 BAYESIAN LEARNING 161 Rec
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CHAPTER 6 BAYESIAN LEARNING 163 of
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CHAPTER 6 BAYESIAN LEARNING 165 a l
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CHAPTER 6 BAYESIAN LEARNING 167 the
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CHAPTER 6 BAYESIAN LEARNING 169 doe
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CIUPlER 6 BAYESIAN LEARNING 171 sub
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CHAPTER 6 BAYESIAN LEARNING 173 0 T
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CHAFER 6 BAYESIAN LEARNING 175 the
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6.9 NAIVE BAYES CLASSIFIER CHAPTJZR
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CHAETER 6 BAYESIAN LEARNING 179 Sim
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-a- CHAPTER 6 BAYESIAN LEARNING 181
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CHAPTER 6 BAYESIAN LEARNING 183 Exa
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CHAPTER 6 BAYESIAN LEARNING 185 In
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C H m R 6 BAYESIAN LEARNING 187 Fir
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CHAPTER 6 BAYESIAN LEARNING 189 For
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CHAPTER 6 BAYESIAN LEARNING 191 ord
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CHAPTER 6 BAYESIAN LEARNING 193 max
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CHAPTER 6 BAYESIAN LEARNING 195 Ste
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6.13 SUMMARY AND FURTHER READING Th
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CHAPTER 6 BAYESIAN LEARNING 199 pro
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CHAPTER COMPUTATIONAL LEARNING THEO
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CHAPTER 7 COMPUTATIONAL LEARNING TH
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C Instance space X Where c and h di
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usually more concerned with the num
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are drawn. Haussler (1988) provides
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CHAPTER 7 COMPUTATIONAL LEARNING TH
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C that contains every teachable con
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Instance space X FIGURE 73 A set of
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can show that it is at least 3, as
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The following theorem bounds the VC
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FIND-S: C CHAPTER 7 COMPUTATIONAL L
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We define the optimal mistake bound
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log' Rearranging terms yields which
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Current research on computational l
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(b) You now draw a new set of 100 i
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CHAPTER 8 INSTANCE-BASED LEARNING 2
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(i.e., on all axes in the Euclidean
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8.3.1 Locally Weighted Linear Regre
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C H m R 8 INSTANCE-BASED LEARNING 2
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CHAPTER 8 INSTANCEBASED LEARNING 24
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CHAPTER 8 INSTANCE-BASED LEARMNG 24
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A thorough discussion of radial bas
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CHAPTER GENETIC ALGORITHMS Genetic
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Fitness: A function that assigns an
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can then be represented by the foll
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the crossover point n is chosen at
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value of the target attribute c. Th
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In the above experiment, the two ne
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The second step above follows from
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FIGURE 9.2 Crossover operation appl
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0 (DU x y) (do until), which execut
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9.6.2 Baldwin Effect Although Lamar
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iteration, the most fit members of
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Belew, R. K., & Mitchell, M. (Eds.)
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Tumey, P. D., Whitley, D., & Anders
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As an example of first-order rule s
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10.2.1 General to Specific Beam Sea
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A few remarks on the LEARN-ONE-RULE
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decisions regarding preconditions o
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10.4 LEARNING FIRST-ORDER RULES In
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Every well-formed expression is com
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eralize the current disjunctive hyp
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Here let us also make the closed wo
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In the case of noise-free training
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(e.g., neural network) fits the dat
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C : KnowMaterial v -Study C: KnowMa
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CHAPTER 10 LEARNING SETS OF RULES 2
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In contrast, the generate-and-test
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which enable the user to specify th
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Wrobel (1992) use rule schemata in
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De Raedt, L., & Bruynooghe, M. (199
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Page 403 and 404: APPENDIX NOTATION Below is a summar
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Page 417 and 418: Probability distribution, 133. See
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