Teaching a Course in Applied Statistics

Chatfield, Chris

doi:10.2307/2348001

Cited by 31 publications

(34 citation statements)

References 17 publications

(11 reference statements)

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“…Among these 12 domains, LBR has lower error rates than NB in 9 domains, the same error rate in 2 domains, and a slightly higher error rate in one domain. The (product moment) correlation coefficient based on these 12 data points is 0.92, indicating a highly significant correlation (Chatfield, 1978). When considering only significant error differences, C4.5 is significantly more accurate than NB in 6 domains.…”

Section: When Does Lbr Outperform the Naive Bayesian Classifier?mentioning

confidence: 94%

“…An error rate ratio, for example for LBR vs NB, presents a result for LBR divided by the corresponding result for NB-a value less than 1 indicates an improvement due to LBR. To compare the error rates of two algorithms in a domain, a one-tailed pairwise t-test (Chatfield, 1978) on the error rates of the 20 trials is carried out. The difference is considered as significant, if the significance level of the t-test is better than 0.05.…”

Section: Experimental Domains and Methodsmentioning

confidence: 99%

“…In Table 5, boldface (italic) font, for example for LBR vs NB, indicates that LBR is significantly more (less) accurate than NB. The fourth and third last rows in Table 5 show the numbers of wins, ties, and losses between the error rates of the corresponding two algorithms in the 29 domains, and the significance level of a one-tailed pairwise sign-test (Chatfield, 1978) on these win/tie/loss records. 6 The second last and the last rows in this table present similar comparison results but treating insignificant wins and losses in individual domains as ties.…”

Section: Experimental Domains and Methodsmentioning

confidence: 99%

“…To these are added the errors of the existing local naive Bayesian classifier on the remaining local training examples. 5 If this measure is lower than the errors of the local naive Bayesian classifier of the current Bayesian rule at a significance level better than 0.05 using a one-tailed pairwise sign-test (Chatfield, 1978), this attribute-value pair becomes a candidate condition to be added to the current Bayesian rule. The sign-test is used to control the likelihood of adding conditions that reduce error by chance.…”

Section: An Operational Description Of Lbrmentioning

confidence: 99%

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Abstract. The naive Bayesian classifier provides a simple and effective approach to classifier learning, but its attribute independence assumption is often violated in the real world. A number of approaches have sought to alleviate this problem. A Bayesian tree learning algorithm builds a decision tree, and generates a local naive Bayesian classifier at each leaf. The tests leading to a leaf can alleviate attribute inter-dependencies for the local naive Bayesian classifier. However, Bayesian tree learning still suffers from the small disjunct problem of tree learning. While inferred Bayesian trees demonstrate low average prediction error rates, there is reason to believe that error rates will be higher for those leaves with few training examples. This paper proposes the application of lazy learning techniques to Bayesian tree induction and presents the resulting lazy Bayesian rule learning algorithm, called LBR. This algorithm can be justified by a variant of Bayes theorem which supports a weaker conditional attribute independence assumption than is required by naive Bayes. For each test example, it builds a most appropriate rule with a local naive Bayesian classifier as its consequent. It is demonstrated that the computational requirements of LBR are reasonable in a wide cross-section of natural domains. Experiments with these domains show that, on average, this new algorithm obtains lower error rates significantly more often than the reverse in comparison to a naive Bayesian classifier, C4.5, a Bayesian tree learning algorithm, a constructive Bayesian classifier that eliminates attributes and constructs new attributes using Cartesian products of existing nominal attributes, and a lazy decision tree learning algorithm. It also outperforms, although the result is not statistically significant, a selective naive Bayesian classifier.

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Section: When Does Lbr Outperform the Naive Bayesian Classifier?mentioning

confidence: 94%

Section: Experimental Domains and Methodsmentioning

confidence: 99%

Section: Experimental Domains and Methodsmentioning

confidence: 99%

Section: An Operational Description Of Lbrmentioning

confidence: 99%

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“…For convenience, the remainder of this work is mainly focussed on the optimal setting of N F = 31. The analytic expression P Table 3.3 from [108], where f i,j is the jth real-valued feature vector of subject i, N s is the number of subjects, N i is the number of samples or feature vectors of subject i and N t is the total number of samples N t = Ns i=1 N i . This table is also used in ANOVA (analysis of variance) models and describes the method for computing the sum of squares of the source of the within-class (SSW), between-class (SSB), and the total (SST) variation.…”

Section: Biometric Databases and Feature Extractionmentioning

confidence: 99%