Receiver operating characteristic - Wikipedia. ROC curve of three predictors of peptide cleaving in the proteasome. In statistics, a receiver operating characteristic curve, i. ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. The true- positive rate is also known as sensitivity, recall or probability of detection[1] in machine learning. The false- positive rate is also known as the fall- out or probability of false alarm[1] and can be calculated as (1 − specificity). The ROC curve is thus the sensitivity as a function of fall- out. In general, if the probability distributions for both detection and false alarm are known, the ROC curve can be generated by plotting the cumulative distribution function (area under the probability distribution from −∞{\displaystyle - \infty } to the discrimination threshold) of the detection probability in the y- axis versus the cumulative distribution function of the false- alarm probability on the x- axis. ROC analysis provides tools to select possibly optimal models and to discard suboptimal ones independently from (and prior to specifying) the cost context or the class distribution. ROC analysis is related in a direct and natural way to cost/benefit analysis of diagnostic decision making. The ROC curve was first developed by electrical engineers and radar engineers during World War II for detecting enemy objects in battlefields and was soon introduced to psychology to account for perceptual detection of stimuli. ![]() The purpose of this page is to provide resources in the rapidly growing area computer simulation. This site provides a web-enhanced course on computer systems. Prof. Dr. Jorge Mateu. Catedrático de Universidad / Full Professor of Statistics Departamento de Matemáticas / Department of Mathematics Universitat Jaume I. ROC analysis since then has been used in medicine, radiology, biometrics, forecasting of natural hazards[2], meteorology[3], model performance assessment[4], and other areas for many decades and is increasingly used in machine learning and data mining research. The ROC is also known as a relative operating characteristic curve, because it is a comparison of two operating characteristics (TPR and FPR) as the criterion changes.[5]Basic concept[edit]A classification model (classifier or diagnosis) is a mapping of instances between certain classes/groups. The classifier or diagnosis result can be a real value (continuous output), in which case the classifier boundary between classes must be determined by a threshold value (for instance, to determine whether a person has hypertension based on a blood pressure measure).
Or it can be a discrete class label, indicating one of the classes. Let us consider a two- class prediction problem (binary classification), in which the outcomes are labeled either as positive (p) or negative (n). There are four possible outcomes from a binary classifier. If the outcome from a prediction is p and the actual value is also p, then it is called a true positive (TP); however if the actual value is n then it is said to be a false positive (FP). Conversely, a true negative (TN) has occurred when both the prediction outcome and the actual value are n, and false negative (FN) is when the prediction outcome is n while the actual value is p. To get an appropriate example in a real- world problem, consider a diagnostic test that seeks to determine whether a person has a certain disease. A false positive in this case occurs when the person tests positive, but does not actually have the disease. A false negative, on the other hand, occurs when the person tests negative, suggesting they are healthy, when they actually do have the disease. Let us define an experiment from P positive instances and N negative instances for some condition. The four outcomes can be formulated in a 2×2 contingency table or confusion matrix, as follows: True condition. Total population. Condition positive. Condition negative. Prevalence= Σ Condition positive/Σ Total population. Accuracy (ACC) = Σ True positive + Σ True negative/Σ Total population. Predictedcondition. Predicted conditionpositive. Tmpgenc Dvd Author V1 5 13 44 Keygen Free on this page. True positive. False positive,Type I error. Positive predictive value (PPV), Precision = Σ True positive/Σ Predicted condition positive. False discovery rate (FDR), probability of false alarm = Σ False positive/Σ Predicted condition positive. Predicted conditionnegative. False negative,Type II error. True negative. False omission rate (FOR) = Σ False negative/Σ Predicted condition negative. Negative predictive value (NPV) = Σ True negative/Σ Predicted condition negative. Click thumbnail for interactive chart. True positive rate (TPR), Recall, Sensitivity, probability of detection = Σ True positive/Σ Condition positive. False positive rate (FPR), Fall- out= Σ False positive/Σ Condition negative. Positive likelihood ratio(LR+)= TPR/FPRDiagnostic odds ratio (DOR) = LR+/LR−F1 score = 2/1/Recall + 1/Precision. False negative rate (FNR), Miss rate = Σ False negative/Σ Condition positive. True negative rate (TNR), Specificity (SPC) = Σ True negative/Σ Condition negative. Negative likelihood ratio(LR−)= FNR/TNRROC space[edit]. The ROC space and plots of the four prediction examples. The contingency table can derive several evaluation "metrics" (see infobox). To draw a ROC curve, only the true positive rate (TPR) and false positive rate (FPR) are needed (as functions of some classifier parameter). The TPR defines how many correct positive results occur among all positive samples available during the test. FPR, on the other hand, defines how many incorrect positive results occur among all negative samples available during the test. A ROC space is defined by FPR and TPR as x and y axes, respectively, which depicts relative trade- offs between true positive (benefits) and false positive (costs). Since TPR is equivalent to sensitivity and FPR is equal to 1 − specificity, the ROC graph is sometimes called the sensitivity vs (1 − specificity) plot. Each prediction result or instance of a confusion matrix represents one point in the ROC space. The best possible prediction method would yield a point in the upper left corner or coordinate (0,1) of the ROC space, representing 1. The (0,1) point is also called a perfect classification. A random guess would give a point along a diagonal line (the so- called line of no- discrimination) from the left bottom to the top right corners (regardless of the positive and negative base rates). An intuitive example of random guessing is a decision by flipping coins. As the size of the sample increases, a random classifier's ROC point migrates towards the diagonal line. In the case of a balanced coin, it will migrate to the point (0. The diagonal divides the ROC space. Points above the diagonal represent good classification results (better than random), points below the line represent poor results (worse than random). Note that the output of a consistently poor predictor could simply be inverted to obtain a good predictor. Let us look into four prediction results from 1. ABCC′TP=6. 3FN=3. FP=2. 8TN=7. 21. 00. TP=7. 7FN=2. 31. 00. FP=7. 7TN=2. 31. 00. TP=2. 4FN=7. 61. 00. FP=8. 8TN=1. 21. 00. TP=7. 6FN=2. 41. 00. FP=1. 2TN=8. 81. 00. TPR = 0. 6. 3TPR = 0. TPR = 0. 2. 4TPR = 0. FPR = 0. 2. 8FPR = 0. FPR = 0. 8. 8FPR = 0. PPV = 0. 6. 9PPV = 0. PPV = 0. 2. 1PPV = 0. F1 = 0. 6. 6F1 = 0. F1 = 0. 2. 2F1 = 0. ACC = 0. 6. 8ACC = 0. ACC = 0. 1. 8ACC = 0. there. Plots of the four results above in the ROC space are given in the figure. The result of method A clearly shows the best predictive power among A, B, and C. The result of B lies on the random guess line (the diagonal line), and it can be seen in the table that the accuracy of B is 5. However, when C is mirrored across the center point (0. C′ is even better than A. This mirrored method simply reverses the predictions of whatever method or test produced the C contingency table. Although the original C method has negative predictive power, simply reversing its decisions leads to a new predictive method C′ which has positive predictive power. When the C method predicts p or n, the C′ method would predict n or p, respectively. In this manner, the C′ test would perform the best. The closer a result from a contingency table is to the upper left corner, the better it predicts, but the distance from the random guess line in either direction is the best indicator of how much predictive power a method has. If the result is below the line (i. Curves in ROC space[edit]In binary classification, the class prediction for each instance is often made based on a continuous random variable.
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