M J Pazzani and W Sarrett. A framework for the average case analysis of conjunctive learning algorithms. Machine Learning, 9:349--372, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....favor difficult inputs for the algorithm to be tested. Since algorithmic learning has a lot of practical applications it is of great interest to analyze the average case performance, too, and to obtain tight bounds that say something about the typical behavior in practice. Pazzani and Sarrett [17] have proposed a framework for analyzing the average case behavior of learning algorithms. Several authors have followed their approach (cf. e.g. 15, 16] Their main goal is to predict the expected accuracy of the hypothesis produced with respect to the number of training examples. However, ....

....have been obtained showing that worst case bounds differ exponentially from the average case behavior in the particular setting of learning under binomially distributed input data. Within our framework, we could completely overcome the drawbacks of the approach undertaken by Pazzani and Sarrett [17]. In particular, our analysis is fully analytical and does not involve any computer simulation. The results obtained provide a general overview about the average case behavior of the Wholist algorithm for the class of binomial distributions. The influence of the parameter p determining the ....

M.J. Pazzani and W. Sarrett, A framework for average case analysis of conjunctive learning algorithms. Machine Learning 9:349--372, 1992.

....favor difficult inputs for the algorithm to be tested. Since algorithmic learning has a lot of practical applications it is of great interest to analyze the average case performance, too, and to obtain tight bounds that say something about the typical behavior in practice. Pazzani and Sarrett [17] have proposed a framework for analyzing the average case behavior of learning algorithms. Several authors have followed their approach (cf. e.g. 15, 16] Their main goal is to predict the expected accuracy of the hypothesis produced with respect to the number of training examples. However, ....

....have been obtained showing that worst case bounds differ exponentially from the average case behavior in the particular setting of learning under binomially distributed input data. Within our framework, we could completely overcome the drawbacks of the approach undertaken by Pazzani and Sarrett [17]. In particular, our analysis is fully analytical and does not involve any computer simulation. The results obtained provide a general overview about the average case behavior of the Wholist algorithm for the class of binomial distributions. The influence of the parameter p determining the ....

M.J. Pazzani and W. Sarrett, A framework for average case analysis of conjunctive learning algorithms. Machine Learning 9:349--372, 1992.

....in practice. As a result, the link between theory and experiment in machine learning has become tenuous, leading some researchers to explore other paths. An alternative approach involves the average case analysis of specific induction algorithms on domains with known characteristics. For example, Pazzani and Sarrett (1992) report early results of this sort for a conjunctive learning method, and similar studies have been done for decision stumps (Iba Langley, 1992) the naive Bayesian classifier (Langley, Iba, Thompson, 1992) 1 nearest neighbor (Langley Iba, 1992) and k nearest neighbor (Okamoto Nobuhiro, ....

....completely independent given the class (Domingos Pazzani, 1997) but this does not mean that the analysis will accurately predict its learning curve under such conditions. In our future work, we should run experiments with domains that violate the independence assumption to varying degrees, as Pazzani and Sarrett (1992) did for their analysis of conjunctive learning. They reported good fits to observed learning curves despite strong dependencies, and we anticipate similar results for naive Bayes. Average Case Analysis of Naive Bayes 9 We also hope to extend our approach to the averagecase analysis of other ....

Pazzani, M., & Sarrett, W. (1992). A framework for average-case analysis of conjunctive learning algorithms. Machine Learning , 9 , 349-372.

....proved within the PAC model are usually worst case bounds. Since experimental studies have shown quite often a large gap between the worst case bounds proved and the actual runtime observed, several authors advocated to analyze the average case behavior of learning algorithms (cf. e.g. [7, 10, 12, 14, 15, 16, 17, 18]) We continue along this line of research. Within this paper we deal with the problem to learn eciently univariate integer valued polynomials as well as univariate polynomials over nite elds from two different sources of information. The underlying model is Gold [9] style learning in the ....

M.J. Pazzani and W. Sarrett, A framework for average case analysis of conjunctive learning algorithms. Machine Learning 9:349-372, 1992.

....that favor difficult inputs for the algorithm to be tested. Since algorithmic learning has a lot of practical applications it is of great interest to analyze the average case performance, too, and to obtain tight bounds that say something about the typical behavior in practice. Pazzani and Sarret [17] have proposed a framework for analyzing the average case behavior of learning algorithms. Several authors have followed their approach (cf. e.g. 15, 16] Their main goal is to predict the expected accuracy of the hypothesis produced with respect to the number of training examples. However, ....

....have been obtained showing that worst case bounds differ exponentially from the average case behavior in the particular setting of learning under binomially distributed input data. Within our framework, we could completely overcome the drawbacks of the approach undertaken by Pazzani and Sarret [17]. In particular, our analysis is fully analytical and does not involve any computer simulation. The results obtained provide a general overview about the average case behavior of the Wholist algorithm for the class of binomial distributions. The influence of the parameter p determining the ....

M.J. Pazzani and W. Sarrett, A framework for average case analysis of conjunctive learning algorithms. Machine Learning 9:349--372, 1992.

....that favor difficult inputs for the algorithm to be tested. Since algorithmic learning has a lot of practical applications it is of great interest to analyze the average case performance, too, and to obtain tight bounds that say something about the typical behavior in practice. Pazzani and Sarrett [17] have proposed a framework for analyzing the average case behavior of learning algorithms. Several authors have followed their approach (cf. e.g. 15, 16] Their main goal is to predict the expected accuracy of the hypothesis produced with respect to the number of training examples. However, ....

....have been obtained showing that worst case bounds differ exponentially from the average case behavior in the particular setting of learning under binomially distributed input data. Within our framework, we could completely overcome the drawbacks of the approach undertaken by Pazzani and Sarrett [17]. In particular, our analysis is fully analytical and does not involve any computer simulation. The results obtained provide a general overview about the average case behavior of the Wholist algorithm for the class of binomial distributions. The influence of the parameter p determining the ....

M.J. Pazzani and W. Sarrett, A framework for average case analysis of conjunctive learning algorithms. Machine Learning 9:349--372, 1992.

....performance of a learner, rather than its worst case behavior. Since algorithmic learning has a lot of practical applications it is of great interest to analyze the average case performance, and to obtain tight bounds saying something about the typical behavior in practice. Pazzani and Sarrett [14] have proposed a framework for analyzing the averagecase behavior of learning algorithms. Several authors have followed their approach (cf. e.g. 12, 13] Their main goal is to predict the expected accuracy of the hypothesis produced with respect to the number of training examples. However, the ....

M.J. Pazzani and W. Sarrett, A framework for average case analysis of conjunctive learning algorithms. Machine Learning 9:349--372, 1992.

....slowly with the number of irrelevant attributes. Theoretical results for algorithms that search restricted hypothesis spaces are encouraging. For instance, the worst case number of errors made by Littlestone s (1987) Winnow method grows only logarithmically with the number of irrelevant features. Pazzani and Sarrett s (1992) average case analysis for Wholist, a simple conjunctive algorithm, and Langley and Iba s (1993) treatment of the naive Bayesian classifier, suggest that their sample complexities grow at most linearly with the number of irrelevant features. However, the theoretical results are less optimistic ....

Pazzani, M. J., & Sarrett, W. (1992). A framework for the average case analysis of conjunctive learning algorithms. Machine Learning , 9 , 349--372.

....that favor difficult inputs for the algorithm to be tested. Since algorithmic learning has a lot of practical applications it is of great interest to analyze the average case performance, too, and to obtain tight bounds that say something about the typical behavior in practice. Pazzani and Sarrett [17] have proposed a framework for analyzing the average case behavior of learning algorithms. Several authors have followed their approach (cf. e.g. 15, 16] Their main goal is to predict the expected accuracy of the hypothesis produced with respect to the number of training examples. However, ....

....have been obtained showing that worst case bounds differ exponentially from the average case behavior in the particular setting of learning under binomially distributed input data. Within our framework, we could completely overcome the drawbacks of the approach undertaken by Pazzani and Sarrett [17]. In particular, our analysis is fully analytical and does not involve any computer simulation. The results obtained provide a general overview about the average case behavior of the Wholist algorithm for the class of binomial distributions. The influence of the parameter p determining the ....

M.J. Pazzani and W. Sarrett, A framework for average case analysis of conjunctive learning algorithms. Machine Learning 9:349--372, 1992.

....of PAC identification assuming a strategy of lower consistency. We would also like to gain a theoretical understanding of why GABIL improves its predictive accuracy when using lower levels of consistency on more complex target concepts and noisier data. Perhaps an average 22 case analysis (Pazzani Sarrett, 1992) would be appropriate for this task. Finally, we would like to mention that although our experimental results are preliminary, we hope that they will inspire others to further investigate the regions of appropriateness of varied levels of consistency. For some systems, simplicity is a much tougher ....

Pazzani, P. & Sarrett, W. (1992). A framework for average case analysis of conjunctive learning algorithms. Machine Learning, 9.

....Reich June, 1994 the conclusions obtained from these experiments. ffl (Linster, 1992) This edited volume contains the solution of several research groups to the same knowledge acquisition problems. It represents an attempt to improve the evaluation of different knowledge acquisition approaches. (Pazzani and Sarrett, 1992) This paper presents an average, rather than worst, case analysis of some simple ML programs in an attempt to better tie the predictions of ML theories and practical results. 6 Social science (Blumberg and Pringle, 1983) This paper criticizes empirical manipulation as the solution to the how to ....

Pazzani, M. J. and Sarrett, W. (1992). "A framework for average case analysis of conjunctive learning algorithms." Machine Learning, 9(4):349--372.

....of learning rate are much slower than those observed in practice. As a result, the link between theory and experiment in machine learning has become tenuous. An alternative approach involves the average case analysis of specific induction algorithms on domains with known characteristics. Pazzani and Sarrett (1992) report early results of this sort for a conjunctive learning method, and similar studies have been done for decision stumps (Iba Langley, 1992) the naive Bayesian classifier (Langley, Iba, Thompson, 1992) 1 nearest neighbor (Langley Iba, 1992) and k nearest neighbor (Okamoto Nobuhiro, ....

....not completely independent given the class (Domingos Pazzani, 1997) but this does not mean that the analysis will accurately predict its learning curve under such conditions. In future work, we should run experiments with domains that violate the independence assumption to varying degrees, as Pazzani and Sarrett (1992) did in their analysis of conjunctive learning. They reported good fits to observed learning curves despite dependencies, and we anticipate similar results for naive Bayes. We also hope to extend our new analytic techniques to other induction algorithms, including nearest neighbor and methods that ....

Pazzani, M., & Sarrett, W. (1992). A framework for average-case analysis of conjunctive learning algorithms. Machine Learning , 9 , 349-372.

....observations are consistent with Aha s (1990) reports on the sensitivity of nearest neighbor methods to the number of irrelevant attributes. We can also compare the behavior of the nearest neighbor algorithm to that of other induction methods for which average case analyses exist. In particular, Pazzani and Sarrett (1992) have studied the Wholist algorithm, which initializes its concept description to the conjunction of features in the first positive training instance, then removes any feature that fails to occur in later positive instances. Similarly, Langley, Iba, and Thompson (1992) have analyzed the behavior ....

Pazzani, M. J., & Sarrett, W. (1992). A framework for the average case analysis of conjunctive learning algorithms.

.... learning intersections of halfspaces in constant dimensional spaces (Blumer et al. 1989) and algorithms for learning DNF formulas in n O(log n) time under the uniform distribution (Verbeurgt, 1990) The above results for the greedy set cover method are distribution free and worst case, but Pazzani and Sarrett (1992) report an average case analysis of even simpler methods for conjunctive learning that imply logarithmic growth for certain product distributions. Similar operations for adding and removing features form the core of methods for inducing more complex logical concepts, but these methods also involve ....

Pazzani, M. J., & Sarrett, W. (1992). A framework for the average case analysis of conjunctive learning algorithms. Machine Learning , 9 , 349--372.

....Bayesian classifier s average case behavior for insufficient samples (i.e. samples not including all possible examples) was analyzed by Langley et al. 1992) who plotted sample cases and found the rate of convergence to 100 accuracy to be quite rapid. 7 Comparing Langley et al. s results with Pazzani and Sarrett s (1990) average case formulas for the classical wholist algorithm for learning conjunctions shows that the latter converges faster, which is not surprising, considering that it was specifically designed for this concept class. On the other hand, as Langley et al. 1992) point out, the Bayesian classifier ....

Pazzani, M., & Sarrett, W. (1990). A framework for average case analysis of conjunctive learning algorithms. Machine Learning, 9, 349--372.

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M J Pazzani and W Sarrett. A framework for the average case analysis of conjunctive learning algorithms. Machine Learning, 9:349--372, 1992.

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