data mining
play

Data Mining Hypothesis Evaluation Hamid Beigy Sharif University of - PowerPoint PPT Presentation

Nov 18, 2023 •554 likes •1.94k views

Data Mining Hypothesis Evaluation Hamid Beigy Sharif University of Technology Fall 1396 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 1 / 31 Table of contents Introduction 1 Some performance measures of classifiers

  1. Measuring performance of a classifier Measuring performance of a hypothesis is partitioning data to 1 Training set Validation set different from training set. Test set different from training and validation sets. Problems with this approach 2 Training and validation sets may be small and may contain exceptional instances such as noise, which may mislead us. The learning algorithm may depend on other random factors affecting the accuracy such as initial weights of a neural network trained with BP. We must train/test several times and average the results. Important points 3 Performance of a hypothesis estimated using training set conditioned on the used data set and cant used to compare algorithms in domain independent ways. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 5 / 31

  2. Measuring performance of a classifier Measuring performance of a hypothesis is partitioning data to 1 Training set Validation set different from training set. Test set different from training and validation sets. Problems with this approach 2 Training and validation sets may be small and may contain exceptional instances such as noise, which may mislead us. The learning algorithm may depend on other random factors affecting the accuracy such as initial weights of a neural network trained with BP. We must train/test several times and average the results. Important points 3 Performance of a hypothesis estimated using training set conditioned on the used data set and cant used to compare algorithms in domain independent ways. Validation set is used for model selection, comparing two algorithms, and decide to stop learning. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 5 / 31

  3. Measuring performance of a classifier Measuring performance of a hypothesis is partitioning data to 1 Training set Validation set different from training set. Test set different from training and validation sets. Problems with this approach 2 Training and validation sets may be small and may contain exceptional instances such as noise, which may mislead us. The learning algorithm may depend on other random factors affecting the accuracy such as initial weights of a neural network trained with BP. We must train/test several times and average the results. Important points 3 Performance of a hypothesis estimated using training set conditioned on the used data set and cant used to compare algorithms in domain independent ways. Validation set is used for model selection, comparing two algorithms, and decide to stop learning. In order to report the expected performance, we should use a separate test set unused during learning. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 5 / 31

  4. Error of a classifier Definition (Sample error) The sample error (denoted E E ( h )) of hypothesis h with respect to target concept c and data sample S of size N is. E E ( h ) = 1 � I [ c ( x ) � = h ( x )] N x ∈ S Definition (True error) The true error (denoted E ( h )) of hypothesis h with respect to target concept c and distribution D is the probability that h will misclassify an instance drawn at random according to distribution D . E ( h ) = P x ∼D [ c ( x ) � = h ( x )] Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 6 / 31

  5. Notions of errors True error is 1 Instance space X c h Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 7 / 31

  6. Notions of errors True error is 1 Instance space X c h Our concern 2 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 7 / 31

  7. Notions of errors True error is 1 Instance space X c h Our concern 2 How we can estimate the true error ( E ( h )) of hypothesis using its sample error ( E E ( h )) ? Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 7 / 31

  8. Notions of errors True error is 1 Instance space X c h Our concern 2 How we can estimate the true error ( E ( h )) of hypothesis using its sample error ( E E ( h )) ? Can we bound true error of h given sample error of h ? Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 7 / 31

  9. Outline Introduction 1 Some performance measures of classifiers 2 Evaluating the performance of a classifier 3 Estimating true error 4 Confidence intervals 5 Paired t Test 6 ROC Curves 7 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 8 / 31

  10. Some performance measures of classifiers Error rate The error rate is the fraction of incorrect predictions for 1 the classifier over the testing set, defined as E E ( h ) = 1 � I [ c ( x ) � = h ( x )] N x ∈ S Error rate is an estimate of the probability of misclassification. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 8 / 31

  11. Some performance measures of classifiers Error rate The error rate is the fraction of incorrect predictions for 1 the classifier over the testing set, defined as E E ( h ) = 1 � I [ c ( x ) � = h ( x )] N x ∈ S Error rate is an estimate of the probability of misclassification. Accuracy The accuracy of a classifier is the fraction of correct 2 predictions over the testing set: Accuracy ( h ) = 1 � I [ c ( x ) = h ( x )] = 1 − E E ( h ) N x ∈ S Accuracy gives an estimate of the probability of a correct prediction. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 8 / 31

  12. Some performance measures of classifiers What you can say about the accuracy of 90% or the error of 10% ? 1 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 9 / 31

  13. Some performance measures of classifiers What you can say about the accuracy of 90% or the error of 10% ? 1 For example, if 3 − 4% of examples are from negative class, clearly 2 accuracy of 90% is not acceptable. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 9 / 31

  14. Some performance measures of classifiers What you can say about the accuracy of 90% or the error of 10% ? 1 For example, if 3 − 4% of examples are from negative class, clearly 2 accuracy of 90% is not acceptable. Confusion matrix 3 Actual label (+) ( − ) Predicted label TP FP (+) FN TN ( − ) Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 9 / 31

  15. Some performance measures of classifiers What you can say about the accuracy of 90% or the error of 10% ? 1 For example, if 3 − 4% of examples are from negative class, clearly 2 accuracy of 90% is not acceptable. Confusion matrix 3 Actual label (+) ( − ) Predicted label TP FP (+) FN TN ( − ) Given C classes, a confusion matrix is a table of C × C . 4 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 9 / 31

  16. Some performance measures of classifiers Precision (Positive predictive value) Precision is proportion of 1 predicted positives which are actual positive and defined as TP Precision ( h ) = TP + FP Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 10 / 31

  17. Some performance measures of classifiers Precision (Positive predictive value) Precision is proportion of 1 predicted positives which are actual positive and defined as TP Precision ( h ) = TP + FP Recall (Sensitivity) Recall is proportion of actual positives which are 2 predicted positive and defined as TP Recall ( h ) = TP + FN Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 10 / 31

  18. Some performance measures of classifiers Precision (Positive predictive value) Precision is proportion of 1 predicted positives which are actual positive and defined as TP Precision ( h ) = TP + FP Recall (Sensitivity) Recall is proportion of actual positives which are 2 predicted positive and defined as TP Recall ( h ) = TP + FN Specificity Specificity is proportion of actual negative which are 3 predicted negative and defined as TN Specificity ( h ) = TN + FP Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 10 / 31

  19. Some performance measures of classifiers Balanced classification rate (BCR) Balanced classification rate 1 provides an average of recall (sensitivity) and specificity, it gives a more precise picture of classifier effectiveness. Balanced classification rate defined as BCR ( h ) = 1 2 [ Specificity ( h ) + Recall ( h )] Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 11 / 31

  20. Some performance measures of classifiers Balanced classification rate (BCR) Balanced classification rate 1 provides an average of recall (sensitivity) and specificity, it gives a more precise picture of classifier effectiveness. Balanced classification rate defined as BCR ( h ) = 1 2 [ Specificity ( h ) + Recall ( h )] F-measure F-measure is harmonic mean between precision and recall 2 and defined as F − Measure ( h ) = 2 × Persicion ( h ) × Recall ( h ) Persicion ( h ) + Recall ( h ) Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 11 / 31

  21. Outline Introduction 1 Some performance measures of classifiers 2 Evaluating the performance of a classifier 3 Estimating true error 4 Confidence intervals 5 Paired t Test 6 ROC Curves 7 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 12 / 31

  22. Evaluating the performance of a classifier Hold-out method 1 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 12 / 31

  23. Evaluating the performance of a classifier Hold-out method 1 Random Sub-sampling 2 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 12 / 31

  24. Evaluating the performance of a classifier Hold-out method 1 Random Sub-sampling 2 Cross validation method 3 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 12 / 31

  25. Evaluating the performance of a classifier Hold-out method 1 Random Sub-sampling 2 Cross validation method 3 Leave-one-out method 4 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 12 / 31

  26. Evaluating the performance of a classifier Hold-out method 1 Random Sub-sampling 2 Cross validation method 3 Leave-one-out method 4 5 × 2 Cross validation method 5 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 12 / 31

  27. Evaluating the performance of a classifier Hold-out method 1 Random Sub-sampling 2 Cross validation method 3 Leave-one-out method 4 5 × 2 Cross validation method 5 Bootstrapping method 6 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 12 / 31

  28. Hold-out method Hold-out Hold-out partitions the given data into two independent 1 sets : training and test sets. Total number of examples Training Set Test Set Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 13 / 31

  29. Hold-out method Hold-out Hold-out partitions the given data into two independent 1 sets : training and test sets. Total number of examples Training Set Test Set Typically two-thirds of the data are allocated to the training set and the remaining one-third is allocated to the test set. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 13 / 31

  30. Hold-out method Hold-out Hold-out partitions the given data into two independent 1 sets : training and test sets. Total number of examples Training Set Test Set Typically two-thirds of the data are allocated to the training set and the remaining one-third is allocated to the test set. The training set is used to drive the model. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 13 / 31

  31. Hold-out method Hold-out Hold-out partitions the given data into two independent 1 sets : training and test sets. Total number of examples Training Set Test Set Typically two-thirds of the data are allocated to the training set and the remaining one-third is allocated to the test set. The training set is used to drive the model. The test set is used to estimate the accuracy of the model. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 13 / 31

  32. Random sub-sampling method Random sub-sampling Random sub-sampling is a variation of the 1 hold-out method in which hold-out is repeated k times. Total number of examples Test example Experiment 1 Experiment 2 Experiment 3 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 14 / 31

  33. Random sub-sampling method Random sub-sampling Random sub-sampling is a variation of the 1 hold-out method in which hold-out is repeated k times. Total number of examples Test example Experiment 1 Experiment 2 Experiment 3 The estimated error rate is the average of the error rates for classifiers derived for the independently and randomly generated test partitions. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 14 / 31

  34. Random sub-sampling method Random sub-sampling Random sub-sampling is a variation of the 1 hold-out method in which hold-out is repeated k times. Total number of examples Test example Experiment 1 Experiment 2 Experiment 3 The estimated error rate is the average of the error rates for classifiers derived for the independently and randomly generated test partitions. Random subsampling can produce better error estimates than a single train-and-test partition. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 14 / 31

  35. Cross validation method K -fold cross validation The initial data are randomly partitioned into 1 K mutually exclusive subsets or folds, S 1 , S 2 , . . . , S K , each of approximately equal size. . Total number of examples Experiment 1 Experiment 2 Experiment 3 Test examples Experiment 4 K-Fold Cross validation is similar to Random Subsampling Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 15 / 31

  36. Cross validation method K -fold cross validation The initial data are randomly partitioned into 1 K mutually exclusive subsets or folds, S 1 , S 2 , . . . , S K , each of approximately equal size. . Total number of examples Experiment 1 Experiment 2 Experiment 3 Test examples Experiment 4 K-Fold Cross validation is similar to Random Subsampling Training and testing is performed K times. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 15 / 31

  37. Cross validation method K -fold cross validation The initial data are randomly partitioned into 1 K mutually exclusive subsets or folds, S 1 , S 2 , . . . , S K , each of approximately equal size. . Total number of examples Experiment 1 Experiment 2 Experiment 3 Test examples Experiment 4 K-Fold Cross validation is similar to Random Subsampling Training and testing is performed K times. In iteration k , partition S k is used for test and the remaining partitions collectively used for training. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 15 / 31

  38. Cross validation method K -fold cross validation The initial data are randomly partitioned into 1 K mutually exclusive subsets or folds, S 1 , S 2 , . . . , S K , each of approximately equal size. . Total number of examples Experiment 1 Experiment 2 Experiment 3 Test examples Experiment 4 K-Fold Cross validation is similar to Random Subsampling Training and testing is performed K times. In iteration k , partition S k is used for test and the remaining partitions collectively used for training. The accuracy is the percentage of the total number of correctly classified test examples. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 15 / 31

  39. Cross validation method K -fold cross validation The initial data are randomly partitioned into 1 K mutually exclusive subsets or folds, S 1 , S 2 , . . . , S K , each of approximately equal size. . Total number of examples Experiment 1 Experiment 2 Experiment 3 Test examples Experiment 4 K-Fold Cross validation is similar to Random Subsampling Training and testing is performed K times. In iteration k , partition S k is used for test and the remaining partitions collectively used for training. The accuracy is the percentage of the total number of correctly classified test examples. The advantage of K -fold cross validation is that all the examples in the dataset are eventually used for both training and testing. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 15 / 31

  40. Cross validation method K -fold cross validation The initial data are randomly partitioned into 1 K mutually exclusive subsets or folds, S 1 , S 2 , . . . , S K , each of approximately equal size. . Total number of examples Experiment 1 Experiment 2 Experiment 3 Test examples Experiment 4 K-Fold Cross validation is similar to Random Subsampling Training and testing is performed K times. In iteration k , partition S k is used for test and the remaining partitions collectively used for training. The accuracy is the percentage of the total number of correctly classified test examples. The advantage of K -fold cross validation is that all the examples in the dataset are eventually used for both training and testing. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 15 / 31

  41. Leave-one-out method Leave-one-out Leave-one-out is a special case of K -fold cross 1 validation where K is set to number of examples in dataset. Total number of examples Experiment 1 Experiment 2 Experiment 3 Single test example Experiment N As usual, the true error is estimated as the average error rat Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 16 / 31

  42. Leave-one-out method Leave-one-out Leave-one-out is a special case of K -fold cross 1 validation where K is set to number of examples in dataset. Total number of examples Experiment 1 Experiment 2 Experiment 3 Single test example Experiment N As usual, the true error is estimated as the average error rat For a dataset with N examples, perform N experiments. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 16 / 31

  43. Leave-one-out method Leave-one-out Leave-one-out is a special case of K -fold cross 1 validation where K is set to number of examples in dataset. Total number of examples Experiment 1 Experiment 2 Experiment 3 Single test example Experiment N As usual, the true error is estimated as the average error rat For a dataset with N examples, perform N experiments. For each experiment use N − 1 examples for training and the remaining example for testing Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 16 / 31

  44. 5 × 2 Cross validation method (1 1) (1 1) (1) 1 2 1 1 (1 2) (1 2) (2) 1 5 × 2 Cross validation method repeates 1 (2 1) (2 1) (1) 2 2 five times 2-fold cross validation 2 2 (2 2) (2 2) (2) method. 2 (3 1) (3 1) (1) 3 2 3 3 (3 2) (3 2) (2) 3 (4 1) (4 1) (1) 4 2 4 4 (4 2) (4 2) (2) 4 (5 1) (5 1) (1) 5 2 5 5 (5 2) (5 2) (2) 5 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 17 / 31

  45. 5 × 2 Cross validation method (1 1) (1 1) (1) 1 2 1 1 (1 2) (1 2) (2) 1 5 × 2 Cross validation method repeates 1 (2 1) (2 1) (1) 2 2 five times 2-fold cross validation 2 2 (2 2) (2 2) (2) method. 2 Training and testing is performed 10 2 (3 1) (3 1) (1) 3 2 times. 3 3 (3 2) (3 2) (2) 3 (4 1) (4 1) (1) 4 2 4 4 (4 2) (4 2) (2) 4 (5 1) (5 1) (1) 5 2 5 5 (5 2) (5 2) (2) 5 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 17 / 31

  46. 5 × 2 Cross validation method (1 1) (1 1) (1) 1 2 1 1 (1 2) (1 2) (2) 1 5 × 2 Cross validation method repeates 1 (2 1) (2 1) (1) 2 2 five times 2-fold cross validation 2 2 (2 2) (2 2) (2) method. 2 Training and testing is performed 10 2 (3 1) (3 1) (1) 3 2 times. 3 3 (3 2) (3 2) (2) 3 The estimated error rate is the average 3 of the error rates for classifiers derived (4 1) (4 1) (1) 4 2 for the independently and randomly 4 4 (4 2) (4 2) (2) generated test partitions. 4 (5 1) (5 1) (1) 5 2 5 5 (5 2) (5 2) (2) 5 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 17 / 31

  47. Bootstrapping method Bootstrapping The bootstrap uses sampling with replacement to 1 form the training set. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 18 / 31

  48. Bootstrapping method Bootstrapping The bootstrap uses sampling with replacement to 1 form the training set. Sample a dataset of N instances N times with replacement to form a new dataset of N instances. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 18 / 31

  49. Bootstrapping method Bootstrapping The bootstrap uses sampling with replacement to 1 form the training set. Sample a dataset of N instances N times with replacement to form a new dataset of N instances. Use this data as the training set. An instance may occur more than once in the training set. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 18 / 31

  50. Bootstrapping method Bootstrapping The bootstrap uses sampling with replacement to 1 form the training set. Sample a dataset of N instances N times with replacement to form a new dataset of N instances. Use this data as the training set. An instance may occur more than once in the training set. Use the instances from the original dataset that dont occur in the new training set for testing. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 18 / 31

  51. Bootstrapping method Bootstrapping The bootstrap uses sampling with replacement to 1 form the training set. Sample a dataset of N instances N times with replacement to form a new dataset of N instances. Use this data as the training set. An instance may occur more than once in the training set. Use the instances from the original dataset that dont occur in the new training set for testing. This method traines classifieron just on 63% of the instances. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 18 / 31

  52. Outline Introduction 1 Some performance measures of classifiers 2 Evaluating the performance of a classifier 3 Estimating true error 4 Confidence intervals 5 Paired t Test 6 ROC Curves 7 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  53. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  54. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  55. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  56. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hypothesis h misclassifies 12 of the 40 examples in S . What is E ( h )? 2 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  57. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hypothesis h misclassifies 12 of the 40 examples in S . What is E ( h )? 2 We use the following experiment 3 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  58. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hypothesis h misclassifies 12 of the 40 examples in S . What is E ( h )? 2 We use the following experiment 3 Choose sample S of size N according to distribution D . Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  59. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hypothesis h misclassifies 12 of the 40 examples in S . What is E ( h )? 2 We use the following experiment 3 Choose sample S of size N according to distribution D . Measure E E ( h ) Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  60. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hypothesis h misclassifies 12 of the 40 examples in S . What is E ( h )? 2 We use the following experiment 3 Choose sample S of size N according to distribution D . Measure E E ( h ) E E ( h ) is a random variable (i.e., result of an experiment). Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  61. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hypothesis h misclassifies 12 of the 40 examples in S . What is E ( h )? 2 We use the following experiment 3 Choose sample S of size N according to distribution D . Measure E E ( h ) E E ( h ) is a random variable (i.e., result of an experiment). E E ( h ) is an unbiased estimator for E ( h ). Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  62. Estimating true error How well does E E ( h ) estimate E ( h )? 1 Bias in the estimate If training / test set is small, then the accuracy of the resulting hypothesis is a poor estimator of its accuracy over future examples. bias = E [ E E ( h )] − E ( h ) . For unbiased estimate, h and S must be chosen independently. Variance in the estimate Even with unbiased S , E E ( h ) may still vary from E ( h ). The smaller test set results in a greater expected variance. Hypothesis h misclassifies 12 of the 40 examples in S . What is E ( h )? 2 We use the following experiment 3 Choose sample S of size N according to distribution D . Measure E E ( h ) E E ( h ) is a random variable (i.e., result of an experiment). E E ( h ) is an unbiased estimator for E ( h ). Given observed E E ( h ), what can we conclude about E ( h )? 4 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 19 / 31

  63. Distribution of error E E ( h ) is a random variable with binomial distribution, for the 1 experiment with different randomly drawn S of size N , the probability of observing r misclassified examples is N ! r !( N − r )! E ( h ) r [1 − E ( h )] N − r P ( r ) = Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 20 / 31

  64. Distribution of error E E ( h ) is a random variable with binomial distribution, for the 1 experiment with different randomly drawn S of size N , the probability of observing r misclassified examples is N ! r !( N − r )! E ( h ) r [1 − E ( h )] N − r P ( r ) = For example for N = 40 and E ( h ) = p = 0 . 2, 2 0 . 2 0 . 1 0 . 1 0 . 0 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 20 / 31 0 10 20 30 40

  65. Distribution of error For binomial distribution, we have 1 E ( r ) = Np Var ( r ) = Np (1 − p ) We have shown that the random variable E E ( h ) obeys a Binomial distribution. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 21 / 31

  66. Distribution of error For binomial distribution, we have 1 E ( r ) = Np Var ( r ) = Np (1 − p ) We have shown that the random variable E E ( h ) obeys a Binomial distribution. Let p be the probability that the result of trial is a success. 2 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 21 / 31

  67. Distribution of error For binomial distribution, we have 1 E ( r ) = Np Var ( r ) = Np (1 − p ) We have shown that the random variable E E ( h ) obeys a Binomial distribution. Let p be the probability that the result of trial is a success. 2 The E E ( h ) and E ( h ) are 3 E E ( h ) = r N E ( h ) = p where Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 21 / 31

  68. Distribution of error For binomial distribution, we have 1 E ( r ) = Np Var ( r ) = Np (1 − p ) We have shown that the random variable E E ( h ) obeys a Binomial distribution. Let p be the probability that the result of trial is a success. 2 The E E ( h ) and E ( h ) are 3 E E ( h ) = r N E ( h ) = p where N is the number of instances in the sample S , Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 21 / 31

  69. Distribution of error For binomial distribution, we have 1 E ( r ) = Np Var ( r ) = Np (1 − p ) We have shown that the random variable E E ( h ) obeys a Binomial distribution. Let p be the probability that the result of trial is a success. 2 The E E ( h ) and E ( h ) are 3 E E ( h ) = r N E ( h ) = p where N is the number of instances in the sample S , r is the number of instances from S misclassified by h , and Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 21 / 31

  70. Distribution of error For binomial distribution, we have 1 E ( r ) = Np Var ( r ) = Np (1 − p ) We have shown that the random variable E E ( h ) obeys a Binomial distribution. Let p be the probability that the result of trial is a success. 2 The E E ( h ) and E ( h ) are 3 E E ( h ) = r N E ( h ) = p where N is the number of instances in the sample S , r is the number of instances from S misclassified by h , and p is the probability of misclassifying a single instance drawn from D . Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 21 / 31

  71. Distribution of error It can be shown that E E ( h ) is unbiased estimator for E ( h ). 1 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 22 / 31

  72. Distribution of error It can be shown that E E ( h ) is unbiased estimator for E ( h ). 1 Since r is Binomially distributed, its variance is Np (1 − p ). 2 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 22 / 31

  73. Distribution of error It can be shown that E E ( h ) is unbiased estimator for E ( h ). 1 Since r is Binomially distributed, its variance is Np (1 − p ). 2 Unfortunately p is unknown, but we can substitute our estimate r N for 3 p . Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 22 / 31

  74. Distribution of error It can be shown that E E ( h ) is unbiased estimator for E ( h ). 1 Since r is Binomially distributed, its variance is Np (1 − p ). 2 Unfortunately p is unknown, but we can substitute our estimate r N for 3 p . In general, given r errors in a sample of N independently drawn test 4 examples, the standard deviation for E E ( h ) is given by � p (1 − p ) Var [ E E ( h )] = N � E E ( h )(1 − E E ( h )) ≃ N Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 22 / 31

  75. Outline Introduction 1 Some performance measures of classifiers 2 Evaluating the performance of a classifier 3 Estimating true error 4 Confidence intervals 5 Paired t Test 6 ROC Curves 7 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 23 / 31

  76. Confidence intervals One common way to describe the uncertainty associated with an 1 estimate is to give an interval within which the true value is expected to fall, along with the probability with which it is expected to fall into this interval. Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 23 / 31

  77. Confidence intervals One common way to describe the uncertainty associated with an 1 estimate is to give an interval within which the true value is expected to fall, along with the probability with which it is expected to fall into this interval. How can we derive confidence intervals for E E ( h )? 2 Hamid Beigy (Sharif University of Technology) Data Mining Fall 1396 23 / 31

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

DATA MINING LECTURE 2 What is data? The data mining pipeline What is Data Mining? Data

DATA MINING LECTURE 2 What is data? The data mining pipeline What is Data Mining? Data

DATA MINING LECTURE 2 What is data? The data mining pipeline What is Data Mining? Data mining is the use of efficient techniques for the analysis of very large collections of data and the extraction of useful and possibly unexpected

2.4k views • 94 slides
Web Mining Web Mining Web Mining Web Mining Web mining is the use of data mining techniques

Web Mining Web Mining Web Mining Web Mining Web mining is the use of data mining techniques

What is Web Mining? Wh t i W b Mi i What is Web Mining? Wh t i W b Mi i ? ? Web Mining Web Mining Web Mining Web Mining Web mining is the use of data mining techniques to automat cally d scover and extract nformat on automatically

774 views • 20 slides
Web Mining Web Mining Web mining is the use of data mining techniques to automatically

Web Mining Web Mining Web mining is the use of data mining techniques to automatically

What is Web Mining? What is Web Mining? Web Mining Web Mining Web mining is the use of data mining techniques to automatically discover and extract information from Web documents/services (Etzioni, 1996, CACM 39(11)) Web mining aims to

566 views • 22 slides
DATA MINING LECTURE 1 Introduction What is data mining? After years of data mining there is

DATA MINING LECTURE 1 Introduction What is data mining? After years of data mining there is

DATA MINING LECTURE 1 Introduction What is data mining? After years of data mining there is still no unique answer to this question. A tentative definition: Data mining is the use of efficient techniques for the analysis of very large

1.28k views • 62 slides
THE DATA MINING PIPELINE What is data? The data mining pipeline: collection, preprocessing,

THE DATA MINING PIPELINE What is data? The data mining pipeline: collection, preprocessing,

DATA MINING THE DATA MINING PIPELINE What is data? The data mining pipeline: collection, preprocessing, mining, and post-processing Sampling, feature extraction and normalization Exploratory analysis of data basic statistics What is data

2.11k views • 139 slides
Introduction What is data mining? to Data Mining: On what kind of data? Data Mining

Introduction What is data mining? to Data Mining: On what kind of data? Data Mining

Introduction Motivation: Why data mining? Introduction What is data mining? to Data Mining: On what kind of data? Data Mining Data mining functionalities Major issues in data mining 2 Motivation: Necessity is

438 views • 14 slides
LECTURE 1: INTRODUCTION TO DATA MINING Dr. Dhaval Patel CSE, IIT-Roorkee What is data mining?

LECTURE 1: INTRODUCTION TO DATA MINING Dr. Dhaval Patel CSE, IIT-Roorkee What is data mining?

LECTURE 1: INTRODUCTION TO DATA MINING Dr. Dhaval Patel CSE, IIT-Roorkee What is data mining? Data mining is also called knowledge discovery and data mining (KDD) Data mining is extraction of useful patterns from data sources , e.g.,

1.29k views • 50 slides
Data Mining: A Powerful Data Mining: A Powerful Tool for Data Cleaning Tool for Data Cleaning

Data Mining: A Powerful Data Mining: A Powerful Tool for Data Cleaning Tool for Data Cleaning

Data Mining: A Powerful Data Mining: A Powerful Tool for Data Cleaning Tool for Data Cleaning Jiawei Han Department of Computer Science University of Illinois at Urbana-Champaign Nov. 4, 2003 1 Data mining for data quality assurance

721 views • 40 slides
Modeling Data the different views on Data Mining Views on Data Mining Fitting the data

Modeling Data the different views on Data Mining Views on Data Mining Fitting the data

Modeling Data the different views on Data Mining Views on Data Mining Fitting the data Density Estimation Learning being able to perform a task more accurately than before Prediction use the data to predict future data

517 views • 29 slides
Data Mining: Concepts and Techniques Web Mining Li Xiong Slides credits: Jiawei Han and

Data Mining: Concepts and Techniques Web Mining Li Xiong Slides credits: Jiawei Han and

Data Mining: Concepts and Techniques Web Mining Li Xiong Slides credits: Jiawei Han and Micheline Kamber; Anand Rajaraman, Jeffrey D. Ullman Olfa Nasraoui Bing Liu 4/9/2008 1 Web Mining Web mining vs. data mining Structure (or lack

997 views • 60 slides
Introduction to Web Mining What is Web Mining? Discovering useful information from the

Introduction to Web Mining What is Web Mining? Discovering useful information from the

CS 345A Data Mining Lecture 1 Introduction to Web Mining What is Web Mining? Discovering useful information from the World-Wide Web and its usage patterns Web Mining v. Data Mining Structure (or lack of it) Textual information and

744 views • 31 slides
Contents Text Mining Concept Tasks Twitter Data Analysis with R Twitter Extracting Tweets

Contents Text Mining Concept Tasks Twitter Data Analysis with R Twitter Extracting Tweets

Text Mining with R Yanchang Zhao http://www.RDataMining.com R and Data Mining Course Beijing University of Posts and Telecommunications, Beijing, China July 2019 Chapter 10: Text Mining, in R and Data Mining: Examples and Case Studies

904 views • 64 slides
Introduction to Data Mining Methods and Tools by Michael Hahsler Agenda What is Data Mining?

Introduction to Data Mining Methods and Tools by Michael Hahsler Agenda What is Data Mining?

Introduction to Data Mining Methods and Tools by Michael Hahsler Agenda What is Data Mining? Data Mining T asks Relationship to Statistics, Optimization, Machine Learning and AI T ools Data Legal, Privacy and Security

1.02k views • 69 slides
Week 5 Video 2 Relationship Mining Causal Mining Causal Data Mining These slides developed in

Week 5 Video 2 Relationship Mining Causal Mining Causal Data Mining These slides developed in

Week 5 Video 2 Relationship Mining Causal Mining Causal Data Mining These slides developed in partnership with Stephen Fancsali, Carnegie Learning, Inc. Causal Data Mining Distinct from prediction or correlation mining The goal is not

490 views • 33 slides
Course Content Principles of Knowledge Introduction to Data Mining Discovery in Data

Course Content Principles of Knowledge Introduction to Data Mining Discovery in Data

Course Content Principles of Knowledge Introduction to Data Mining Discovery in Data Data warehousing and OLAP Data cleaning Fall 2004 Data mining operations Chapter 9: Web Mining Data summarization

582 views • 30 slides
Da Data Min a Minin ing What at i is it? Ch. 1 I-DM- 1 IRDM 15/16 What is Data Mining?

Da Data Min a Minin ing What at i is it? Ch. 1 I-DM- 1 IRDM 15/16 What is Data Mining?

Da Data Min a Minin ing What at i is it? Ch. 1 I-DM- 1 IRDM 15/16 What is Data Mining? Data mining is the process of extracting hidden patterns from data. An Unethical Econometric practice of massaging and manipulating the

475 views • 24 slides
From AI K to AI D : Acquiring Social Media Intelligence via `Big Data Huan Liu Arizona State

From AI K to AI D : Acquiring Social Media Intelligence via `Big Data Huan Liu Arizona State

From AI K to AI D : Acquiring Social Media Intelligence via `Big Data Huan Liu Arizona State University SBP-BRiMS2017, DC AI, Social Media Intelligence, Big Data 1 Data Mining and Machine Learning Lab Thanks to Former & Current PhD

819 views • 53 slides
1 Introduction We consider a scenario where two parties having private databases wish to

1 Introduction We consider a scenario where two parties having private databases wish to

Privacy Preserving Data Mining Benny Pinkas Yehuda Lindell Department of Computer Science STAR Lab, Intertrust Technologies Weizmann Institute of Science 4750 Patrick Henry Drive Rehovot, Israel . Santa Clara CA 95054.

756 views • 26 slides
Data Mining with Weka Department of Computer Science University of Waikato New Zealand

Data Mining with Weka Department of Computer Science University of Waikato New Zealand

Data Mining with Weka Department of Computer Science University of Waikato New Zealand weka.waikato.ac.nz What is the course about? Data Mining Using data to make predictions Weka Open source software tool Developed at The

544 views • 5 slides
Co nc e pt a nd Applic a tio ns o f Da ta Mining We e k 1 Topics Topics Introduction

Co nc e pt a nd Applic a tio ns o f Da ta Mining We e k 1 Topics Topics Introduction

Co nc e pt a nd Applic a tio ns o f Da ta Mining We e k 1 Topics Topics Introduction Introduction Syllabus Data Mining Concepts Team Organization Introduction Session Introduction Session Your name and major The

858 views • 50 slides
An Overview of CS512 @Spring 2020 JIAWEI HAN COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT

An Overview of CS512 @Spring 2020 JIAWEI HAN COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT

An Overview of CS512 @Spring 2020 JIAWEI HAN COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN JANUARY 21, 2020 1 2 Data and Information Systems (DAIS) Course Structures at CS/UIUC Three main streams: Database, data mining

464 views • 12 slides
Data Mining meets Football (soccer) Ulf Brefeld Knowledge Mining & Assessment TU Darmstadt

Data Mining meets Football (soccer) Ulf Brefeld Knowledge Mining & Assessment TU Darmstadt

Data Mining meets Football (soccer) Ulf Brefeld Knowledge Mining & Assessment TU Darmstadt / DIPF brefeld@cs.tu-darmstadt.de Data Mining meets Football (soccer) Ulf Brefeld Machine Learning Group Leuphana University of Lneburg

1.25k views • 63 slides
Physics Analysis with Advanced Data Mining Techniques Hai-Jun Yang University of Michigan, Ann

Physics Analysis with Advanced Data Mining Techniques Hai-Jun Yang University of Michigan, Ann

Physics Analysis with Advanced Data Mining Techniques Hai-Jun Yang University of Michigan, Ann Arbor CCAST Workshop Beijing, November 6-10, 2006 Outline Why Advanced Techniques ? Artificial Neural Networks (ANN) Boosted Decision

986 views • 54 slides
Scalable and Memory-Efficient Clustering of Large-Scale Social Networks Joyce Jiyoung Whang, Xin

Scalable and Memory-Efficient Clustering of Large-Scale Social Networks Joyce Jiyoung Whang, Xin

Scalable and Memory-Efficient Clustering of Large-Scale Social Networks Joyce Jiyoung Whang, Xin Sui, Inderjit S. Dhillon Department of Computer Science The University of Texas at Austin IEEE International Conference on Data Mining (ICDM)

536 views • 37 slides

More recommend