Machine Learning - DISCo

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Resolution rule, 293-294 first-order, 296-297 inverse entailment operator and, 294-296 propositional, 294 Restriction bias, 64 Reward function, in reinforcement learning, 368 Robot control: by BACKPROPAGATION and EBNN algorithms, comparison of, 356 genetic programming in, 269 Robot driving. See Autonomous vehicles Robot perception, attribute cost measures in, 76 Robot planning problems, explanationbased learning in, 327 ROTE-LEARNER algorithm, inductive bias of, 44-45 Roulette wheel selection, 255 Rule for estimating training values, 10, 383 Rule learning, 274-303 in decision trees, 71-72 in explanation-based learning, 311-3 19 by FOCL algorithm, 357-360 by genetic algorithms, 256-259, 269-270, 274 Rule post-pruning, in decision tree learning, 71-72 Rules: disjunctive sets of, learning by sequential covering algorithms, 275-276 first-order. See First-order rules propositional. See Propositional rules SafeToStack, 310-312 Sample complexity, 202. See also Training examples bound for consistent learners, 207-210, 225 equation for, 209 for finite hypothesis spaces, 207-214 for infinite hypothesis spaces, 214-220 of k-term CNF and DNF expressions, 213-214 of unbiased concepts, 212-213 Sample error, 130-131, 133-134, 143 training error and, 205 Sampling theory, 132-141 Scheduling problems: case-based reasoning in, 241 explanation-based learning in, 325 PRODIGY in, 327 reinforcement learning in, 368 Schema theorem, 260-262 genetic operators in, 261-262 Search bias. See Preference bias Search control problems: explanation-based learning in, 325-328, 329, 330 limitations of, 327-328 as sequential control processes, 369 Search of hypothesis space. See Hypothesis space search Sequential control processes, 368-369 learning task in, 370-373 search control problems in, 369 Sequential covering algorithms, 274, 275-279, 301, 313, 363 choice of attribute-pairs in, 280-282 definition of, 276 FOIL algorithm, comparison with, 287, 301-302 ID3 algorithm, comparison with, 280-28 1 simultaneous covering algorithms, comparison with, 280-282 variations of, 279-280, 286 Shattering, 214-215 Shepard's method, 234 Sigmoid function, 97, 104 Sigmoid units, 95-96, 115 Simultaneous covering algorithms: choice of attributes in, 280-281 sequential covering algorithms, comparison with, 280-282 Single-point crossover operator, 254, 261 SOAR, 327, 330 Specific-to-general search, 281 in FOIL algorithm, 287 Speech recognition, 3 BACKPROPAGATION algorithm in, 81 representation by multilayer network, 95, 96 VC dimension bound, 2 17-2 18 weight sharing in, 1 18
Split infomation, 73-74 Squashing function, 96 Stacking problems. See also SafeToStack analytical learning in, 310 explanation-based learning in, 3 10 genetic programming in, 263-265 PRODIGY in, 327 Standard deviation, 133, I 36-1 37 State-transition function, 380 Statistics: basic definitions, 133 influence on machine learning, 4 Stochastic gradient descent, 93-94, 98-100, 104-105 Student t tests, 147-150, 152 Substitution, 285, 296 Sum rule, 159 t tests, 147-150, 152 TANGENTPROP algorithm, 347-350, 362 BACKPROPAGATION algorithm, comparison with, 349 in EBNN algorithm, 352 search of hypothesis space Two-point crossover operator, 255, by KBANN and BACKPROPAGATION 257-258 algorithms, comparison with, Two-sided bounds, 141 350-35 1 tanh function, 97 Target concept, 22-23,4041 Unbiased estimator, 133, 137 PAC learning of, 211-213 Unbiased learners, 4042 Target function, 7-8, 17 sample complexity of, 212-2 13 continuous-valued. See Continuous- Uniform crossover operator, 255 valued target function Unifying substitution, 285, 296 representation of, 8-9, 14, 17 TD-GAMMON, 3, 14, 369, 383 TD(Q and BACKPROPAGATION algorithm in, 384 TD(h), 383-384, 387 Temporal credit assignment, in reinforcement learning, 369 Temporal difference learning, 383-384, 386-387 Terms, in logic, 284, 285 Text classification, naive Bayes classifier in, 180-184 Theorem of total probability, 159 0-subsumption, 302 with entailment and more-general-than partial ordering, 299-300 Tournament selection, 256 Training and validation set approach, 69. See also Validation set Training derivatives, 117-1 18 Training error: of continuous-valued hypotheses, 89-90 of discrete-valued hypotheses, 205 in multilayer networks, 98 alternative error functions, 117-1 18 Training examples, 5-6, 17, 23. See also Sample complexity explanation in PROLOG-EBG, 314-3 18 in PAC learning, 205-207 bounds on, 226 Voronoi diagram of, 233 Training experience, 5-6, 17 Training values, rule for estimation of, 10 True error, 130-131, 133, 137, 150, 204-205 of two hypotheses, differences in, 143-144 in version spaces, 208-209 Unsupe~ised learning, 191 Utility analysis, in explanation-based learning, 327-328 Validation set. See also Training and validation set approach cross-validation and, 111-1 12 error over, 110 Vapnik-Chervonenkis (VC) dimension. See VC dimension i I
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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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CHAPTER ANALYTICAL LEARNING Inducti
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What is interesting about this ches
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Given: rn Instance space X: Each in
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theories to automatically improve p
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Explanation: Training Example: FIGU
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FIGURE 11.3 Computing the weakest p
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example that is not yet covered by
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contain no description of such a pr
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additional detail that must be cons
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CHAPTER 11 ANALYTICAL LEARNING 325
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explaining to itself the reason for
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that fits the learner's prior knowl
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Height (Joe, Short) Height(Sue, Sho
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CHAF'TER 11 ANALYTICAL LEARNING 333
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CHAPTER 12 COMBINING INDUCTIVE AND
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CHAF'TER 12 COMBINING INDUCTIVE AND
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12.2.2 Hypothesis Space Search CAAP
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- KBANN(Domain-Theory, Training_Exa
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CHAF'TER 12 COMBINING INDUCTIVE AND
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Hypothesis Space Hypotheses that ma
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CHAFER 12 COMBINING INDUCTIVE AND A
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Page 403 and 404: APPENDIX NOTATION Below is a summar
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Page 417: Probability distribution, 133. See
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