The hold-out cross validation approximation to the generalization error was computed by training on 70% of the data, namely 399 samples and testing on the remaining 170. The recall, the ratio of true positives to actual positives, as a measure of the lack of false negatives, and the precision, the ratio of true positives to labeled positives, as a measure of the lack of false positives were also computed on the above data sampling. It is clear from the above tables that GDA produces higher precision than logistic regression and SVM, whereas logistic regression produces highest recall. In this problem in particular, the higher recall may be more valuable, since a false negative could be more dangerous to the care of a patient, who then may not be treated, whereas with a false positive, the patient would most likely undergo more testing before treatment.
Furthermore, we also note that in all cases, the hold-out CV error decreases as the number of features increase,
which is indicative of a high bias problem. This error for GDA is generally lower, which can be explained by
GDA’s property to use data more e"ciently, since it can learn more quickly on smaller datasets.
The hold-out cross validation approximation to the generalization error was computed by training on 70% of the data, namely 399 samples and testing on the remaining 170. The recall, the ratio of true positives to actual positives, as a measure of the lack of false negatives, and the precision, the ratio of true positives to labeled positives, as a measure of the lack of false positives were also computed on the above data sampling. It is clear from the above tables that GDA produces higher precision than logistic regression and SVM, whereas logistic regression produces highest recall. In this problem in particular, the higher recall may be more valuable, since a false negative could be more dangerous to the care of a patient, who then may not be treated, whereas with a false positive, the patient would most likely undergo more testing before treatment.Furthermore, we also note that in all cases, the hold-out CV error decreases as the number of features increase,which is indicative of a high bias problem. This error for GDA is generally lower, which can be explained byGDA’s property to use data more e"ciently, since it can learn more quickly on smaller datasets.
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