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Table 1: Table of data describing who is and who is not sunburned, with attribute values (adapted from Winston, 1992). Consider the data in Table 1. Applying simple information-theoretic heuristics, the IDT in Figure 1 can be generated. Sunburned and non-sunburned individuals fall neatly into the same class at the leaves. This IDT can be used to generate four rules in a rule-based knowledge base, one for each path in the IDT: 1Note that there is no inconsistency between K1 and K2. 2
"... In PAGE 6: ...EDAGs) [22]. EDAGs can be interpreted as a set of rules with exceptions. The idea is that the root of the exception structure contains a default conclusion unless one of the children of the root contains a `concept apos; which leads to a conclusion which overrides the default conclusion. For instance, consider the four rules extracted from Table1 , i.e.... ..."
Table 4 Most Popular Names in the US
2001
"... In PAGE 16: ...0% and 12.7% of females and males born in 1800-1809 were named Mary and John, respectively, which were the most popular female and male names in those years (see Table4 ). The differences between the UK and the US, while deserving further study, might plausibly be related to their much different patterns of settlement and group formation.... In PAGE 55: ... The first part of the table presents data from the Census of 1880 (females ages 0-9 years), and the second part presents data from the Census of 1920 (females ages 40-49 years). Considering figures for individual years helps to show measurement variance about the long-term trends discussed in Section II A (text and Table4 ) and Section III B (text and Table 7). Comparing averages of individual years to figures based on a decade grouping indicates effects of aggregation across years.... ..."
Table 4 Most Popular Names in the US
"... In PAGE 16: ...ame. In the US, 15.0% and 12.7% of females and males born in 1800-1809 were named Mary and John, respectively, which were the most popular female and male names in those years (see Table4 ). The differences between England/Wales and the US, while deserving further study, might plausibly be related to their much different patterns of settlement and group formation.... In PAGE 55: ... The first part of the table presents data from the Census of 1880 (females ages 0-9 years), and the second part presents data from the Census of 1920 (females ages 40-49 years). Considering figures for individual years helps to show measurement variance about the long-term trends discussed in Section II A (text and Table4 ) and Section III B (text and Table 7). Comparing averages of individual years to figures based on a decade grouping indicates effects of aggregation across years.... ..."
Table 4. Running time on a set of 25 alignments randomly selected from the catalytic site data set. The Jensen-Shannon divergence takes several orders of magnitude less time than Rate4Site and provides competitive performance. All information theoretic methods have similar running times.
2007
"... In PAGE 5: ... However, JSD and the other information-theoretic methods have a significant advantage over R4S when considering run time. Table4 gives (processor) running time statistics for several methods on a benchmark set of 25 ran- domly chosen alignments from the CSA data set. R4S took over 2.... In PAGE 7: ... Our evaluation demonstrates that methods such as JSD and RE that incorporate a background amino acid distribution are prefera- ble to SE (Figure 1). R4S also provides similar improvement over SE, but is quite slow in comparison to the information theoretic methods ( Table4 ). The speed of JSD would allow researchers to modify alignments and re-predict functional sites on the fly.... ..."
Table 1: This table summarizes the results known about learning monomials and k- DNF formulas under various models of noise. Note that the upper bounds correspond to polynomial-time algorithms that can tolerate the given noise rate, and the lower bounds correspond to information-theoretic proofs that no algorithm can tolerate the given noise rate.
1995
"... In PAGE 6: ... In this case he shows that a large amount of noise can be handled where the irrelevant attributes are a ected by arbitrary adversarial noise and the relevant attributes are a ected by random noise independently of one another. In Table1 we summarize the results (from previous work and this paper) about PAC learning monomials and k-DNF formulas from the noise oracles discussed in the Section 3.... ..."
Cited by 30
Table 1. Information-theoretic analysis of grouping cues. (a) shows the results for individual features. (b) shows the results when pairs of intra- and inter- region cues are combined. The first column is the amount of information these features contain about the class label. The second column is the amount of residual information these features retain when conditioned on the model output. The marginal entropy of the class label is BDBMBC ( bits ).
2003
"... In PAGE 4: ... The distributions are normalized and the marginal entropy of CW is BDBMBC ( bits ). The first column of Table1 (a) shows the results for individ- ual features. We also combine each pair of inter- and intra- features together to evaluate the overall power of contour, texture, and brightness cues.... In PAGE 4: ... We also combine each pair of inter- and intra- features together to evaluate the overall power of contour, texture, and brightness cues. These results are listed in the first column of Table1 (b). From this analysis of mutual information we find that the presence of boundary contours is the most informative grouping cue.... In PAGE 5: ...The residual information is measured by the mutual information of CW and BY conditioned on BZ. The results have been listed in the second columns of Table1 . We observe that there is little residual information left in the features, which indi- cates that the linear classifier fits the data well.... ..."
Cited by 35
Table 3. Results of general and exception rule mining.
2000
"... In PAGE 15: ... In particular, they find the exception rules e specially helpful in understanding some of the special subpopulation that exhibits trends which are contrary to the main population. Table3 gives a summary of the number of general and exception rules discovered . In the year 1993 , the decision tree did not produce any significant rules , and hence there is no general rule and exception .... ..."
Cited by 4
Table 1: Properties of movies in chosen target set. Ratings is total number of ratings (popularity), mean is average rating (likability), and entropy is the standard information-theoretic entropy of the ratings distribution. Recall that ratings are pro- vided on a 5-point scale.
"... In PAGE 5: ... In terms of ratings properties, this selection of items represents a wide range of pop- ularity (number of ratings), entropy (a measure of the variance of ratings), and likability (mean rating). Table1 displays the proper- ties of items in the target set. 3.... ..."
Table 1: Properties of movies in chosen target set. Ratings is total number of ratings (popularity), mean is average rating (likability), and entropy is the standard information-theoretic entropy of the ratings distribution. Recall that ratings are pro- vided on a 5-point scale.
"... In PAGE 5: ... In terms of ratings properties, this selection of items represents a wide range of pop- ularity (number of ratings), entropy (a measure of the variance of ratings), and likability (mean rating). Table1 displays the proper- ties of items in the target set. 3.... ..."
Table 4). Thus, in classical information-theoretic terms, K can be
2000
Cited by 8
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