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Hypotheses, estimation of accuracy (continued) bias and variance in estimate, 129, 151, 152 errors in, 129-131, 151 evaluation of, 128-129 justification of, in inductive vs analytical learning, 334-336 representations of, 23 testing of, 144-145 Hypothesis space, 14-15 bias in, 40-42, 46, 129 finite, sample complexity for, 207-214, 225 infinite, sample complexity for, 214-220 VC dimension of, 214-217 Hypothesis space search by BACKPROPAGATION algorithm, 97, 106, 122-123 comparison with decision tree learning, 106 comparison with KBANN and TANGENTPROP algorithms, 350-35 1 by CANDIDATE-ELIMINATION algorithm, 64 in concept learning, 23-25, 46-47 constraints on, 302-303 by FIND-Salgorithm, 27-28 by FOIL algorithm, 286-287, 357-361 by genetic algorithms, 250, 259 by gradient descent, 90-91 by ID3 algorithm, 60-62,64, 76 by KBANN algorithm, 346 by learning algorithms, 24 by LEARN-ONE-RULE, 277 in machine learning, 14-15, 18 use of prior knowledge, 339-340, 362

I may as well nail my colors to the mast I don t use Shark. It is a venerable application and I m sure professional Cocoa developers use it all the time, but I personally find it a complex interface with not much useful information (by the way, a significant amount of the functionality of Shark is also available in the Time Profiler instrument, and you use it in much the same way as I describe Shark here). That disclaimer is out of the way; so, what is Shark In a nutshell, it s a tool for optimizing performance. You can use Shark to home in on parts of your program that represent performance problems or computational pinch points you can even get Shark to carry out a static analysis that can suggest better ways to approach particular parts of your program. To give you a picture of how Shark works, let s look at Fibonacci Fun again. Before doing this, it would be a good idea to load up the program a little more so that we get a better picture of what the program is doing. In startCalculation change the number of iterations in the main loop from 10 to 100 (see the bold code in Listing 12 5).

ID3 algorithm, 55-64,77 backtracking and, 62 CANDIDATE-ELIMINATION algorithm, comparison with, 61-62 choice of attributes in, 280-281 choice of decision tree, 63 cost-sensitive measures, 75-76 extensions to, 77 See also C45 algorithm

inductive bias of, 63-64, 76 LEARN-ONE-RULE, search comparison with, 277 limitations of, 61-62 overfitting in, 67-68 search of hypothesis space, 60-62, 64, 76 sequential covering algorithms, comparison with, 280-281 specialized for concept learning, 56 use of information gain in, 58-60 ID5R algorithm, comparison with GABIL, 258 ILP See Inductive logic programming Image encoding in face recognition, 114 Imperfect domain theory: in EBNN algorithm, 356 in explanation-based learning, 330 in FOCL algorithm, 360 in KBANN algorithm, 344-345 Incremental explanation methods, 328 Incremental gradient descent See Stochastic gradient descent INCREMENTAL VERSION SPACE MERGING algorithm, 47 Inductive-analytical learning, 334-363 advantages of, 362 explanation-based learning and, 330 learning problem, 337-338 prior knowledge methods to alter search, 339-340,362 properties of ideal systems, 337 weighting of components in EBNN algorithm, 351-352,355 weighting prior knowledge in, 338 Inductive bias, 39-45, 137-138 See also Occam's razor; Preference bias; Restriction bias of BACKPROPAGATION algorithm, 106 bias-free learning, 40-42 of CANDIDATE-ELIMINATION algorithm, 43-46, 63-64 in decision tree learning, 63-66 definition of, 43 in explanation-based learning, 322-323 of FIND-Salgorithm, 45 of ID3 algorithm, 63-64,76 of inductive learning algorithms, 42-46 of k-NEAREST NEIGHBOR algorithm, 234

Listing 12 5. Adding More Tterations to the Main Loop in Fibonacci Fun -(IBAction)startCalculation:(id)sender { NSAutoreleasePool *fibPool = [[NSAutoreleasePool alloc] init]; NSString *outputString; outputString = @"1: "; for (int x=1; x < 100; x++) { long long int fibValues[90]; fibValues[0] = 0; fibValues[1] = 1; for (int i=2; i < 90; i++) { fibValues[i] = fibValues[i-2] + fibValues[i-1]; NSString *thisFibString; thisFibString = [[NSString alloc] initWithFormat:@"%lli, ",fibValues[i]]; outputString = [outputString stringByAppendingFormat:@"%@", thisFibString]; // we're done with thisFibString now, so release [thisFibString release]; } outputString = [outputString stringByAppendingFormat:@"\n\n%i: ", x+1]; [outputField setStringValue:outputString]; } [fibPool drain]; }

of LMS algorithm, 64 of ROTE-LEARNER algorithm, 44-45 Inductive inference See Inductive learning Inductive learning, 42, 307-308 See also Decision tree learning; Genetic algorithms; Inductive logic programming; Neural network learning analytical learning, comparison with, 310, 328-329, 334-336, 362 inductive bias in, 4 2 4 6 Inductive learning hypothesis, 23 Inductive logic programming, 275,29 1 PROLOG-EBG, comparison with, 322 Information gain, 73 definition of, 57-58 in FOIL algorithm, 289 in ID3 algorithm, 5 5 , 5 8 4 0 Information theory: influence on machine learning, 4 Minimum Description Length principle and, 172 Initialize-thehypothesis approach, 339-346 Bayesian belief networks in, 346 Instance-based learning, 230-247 See also Case-based reasoning; k-NEAREST NEIGHBOR algorithm; Locally weighted regression advantages, 245-246 case-based reasoning, comparison with other methods, 240 limitations of, 23 1 Inverse entailment, 292, 302 first-order, 297 generate-and-test beam search, comparison with, 299 in PROGOL,300-302 Inverse resolution, 294-296, 302 first-order, 297-298 generate-and-test beam search, comparison with, 298-299 limitations of, 300 Inverted deduction, 291-293

Montr al (Qu bec)

Joint probability distribution, in Bayesian belief networks, 185-187