[[["เข้าใจง่าย","easyToUnderstand","thumb-up"],["แก้ปัญหาของฉันได้","solvedMyProblem","thumb-up"],["อื่นๆ","otherUp","thumb-up"]],[["ไม่มีข้อมูลที่ฉันต้องการ","missingTheInformationINeed","thumb-down"],["ซับซ้อนเกินไป/มีหลายขั้นตอนมากเกินไป","tooComplicatedTooManySteps","thumb-down"],["ล้าสมัย","outOfDate","thumb-down"],["ปัญหาเกี่ยวกับการแปล","translationIssue","thumb-down"],["ตัวอย่าง/ปัญหาเกี่ยวกับโค้ด","samplesCodeIssue","thumb-down"],["อื่นๆ","otherDown","thumb-down"]],["อัปเดตล่าสุด 2025-05-22 UTC"],[],[],null,["# Thresholds and the confusion matrix\n\nLet's say you have a logistic regression model for spam-email detection that\npredicts a value between 0 and 1, representing the probability that a given\nemail is spam. A prediction of 0.50 signifies a 50% likelihood that the email is\nspam, a prediction of 0.75 signifies a 75% likelihood that the email is spam,\nand so on.\n\nYou'd like to deploy this model in an email application to filter spam into\na separate mail folder. But to do so, you need to convert the model's raw\nnumerical output (e.g., `0.75`) into one of two categories: \"spam\" or \"not\nspam.\"\n\nTo make this conversion, you choose a threshold probability, called a\n[**classification threshold**](/machine-learning/glossary#classification-threshold).\nExamples with a probability above the threshold value are then assigned\nto the [**positive class**](/machine-learning/glossary#positive_class),\nthe class you are testing for (here, `spam`). Examples with a lower\nprobability are assigned to the [**negative class**](/machine-learning/glossary#negative_class),\nthe alternative class (here, `not spam`). \n\n**Click here for more details on the classification threshold**\n\nYou may be wondering: what happens if the predicted score is equal to\nthe classification threshold (for instance, a score of 0.5 where\nthe classification threshold is also 0.5)? Handling for this case\ndepends on the particular implementation chosen for the classification\nmodel. The [Keras](https://keras.io/)\nlibrary predicts the negative class if the score and threshold\nare equal, but other tools/frameworks may handle this case\ndifferently.\n\nSuppose the model scores one email as 0.99, predicting\nthat email has a 99% chance of being spam, and another email as\n0.51, predicting it has a 51% chance of being spam. If you set the\nclassification threshold to 0.5, the model will classify both emails as\nspam. If you set the threshold to 0.95, only the email scoring 0.99 will\nbe classified as spam.\n\nWhile 0.5 might seem like an intuitive threshold, it's not a good idea if the\ncost of one type of wrong classification is greater than the other, or if the\nclasses are imbalanced. If only 0.01% of emails are spam, or if misfiling\nlegitimate emails is worse than letting spam into the inbox,\nlabeling anything the model considers at least 50% likely to be spam\nas spam produces undesirable results.\n\nConfusion matrix\n----------------\n\nThe probability score is not reality, or\n[**ground truth**](/machine-learning/glossary#ground_truth).\nThere are four possible outcomes for each output from a binary classifier.\nFor the spam classifier example, if you lay out the ground truth as columns\nand the model's prediction as rows, the following table, called a\n[**confusion matrix**](/machine-learning/glossary#confusion_matrix), is the\nresult:\n\n| | Actual positive | Actual negative |\n| Predicted positive | **True positive (TP)**: A spam email correctly classified as a spam email. These are the spam messages automatically sent to the spam folder. | **False positive (FP)**: A not-spam email misclassified as spam. These are the legitimate emails that wind up in the spam folder. |\n| Predicted negative | **False negative (FN)**: A spam email misclassified as not-spam. These are spam emails that aren't caught by the spam filter and make their way into the inbox. | **True negative (TN)**: A not-spam email correctly classified as not-spam. These are the legitimate emails that are sent directly to the inbox. |\n|--------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------------------------------------------|\n\nNotice that the total in each row gives all predicted positives (TP + FP) and\nall predicted negatives (FN + TN), regardless of validity. The total in each\ncolumn, meanwhile, gives all real positives (TP + FN) and all real negatives\n(FP + TN) regardless of model classification.\n\nWhen the total of actual positives is not close to the total of actual\nnegatives, the dataset is\n[**imbalanced**](/machine-learning/glossary#class_imbalanced_data_set). An instance\nof an imbalanced dataset might be a set of thousands of photos of clouds, where\nthe rare cloud type you are interested in, say, volutus clouds, only appears\na few times.\n\nEffect of threshold on true and false positives and negatives\n-------------------------------------------------------------\n\nDifferent thresholds usually result in different numbers of true and false\npositives and true and false negatives. The following video explains why this is\nthe case. \n\nTry changing the threshold yourself.\n\nThis widget includes three toy datasets:\n\n- **Separated**, where positive examples and negative examples are generally well differentiated, with most positive examples having higher scores than negative examples.\n- **Unseparated**, where many positive examples have lower scores than negative examples, and many negative examples have higher scores than positive examples.\n- **Imbalanced**, containing only a few examples of the positive class.\n\n### Check your understanding\n\n1. Imagine a phishing or malware classification model where phishing and malware websites are in the class labeled **1** (true) and harmless websites are in the class labeled **0** (false). This model mistakenly classifies a legitimate website as malware. What is this called? \nA false positive \nA negative example (legitimate site) has been wrongly classified as a positive example (malware site). \nA true positive \nA true positive would be a malware site correctly classified as malware. \nA false negative \nA false negative would be a malware site incorrectly classified as a legitimate site. \nA true negative \nA true negative would be a legitimate site correctly classified as a legitimate site. \n2. In general, what happens to the number of false positives when the classification threshold increases? What about true positives? Experiment with the slider above. \nBoth true and false positives decrease. \nAs the threshold increases, the model will likely predict fewer positives overall, both true and false. A spam classifier with a threshold of .9999 will only label an email as spam if it considers the classification to be at least 99.99% likely, which means it is highly unlikely to mislabel a legitimate email, but also likely to miss actual spam email. \nBoth true and false positives increase. \nUsing the slider above, try setting the threshold to 0.1, then dragging it to 0.9. What happens to the number of false positives and true positives? \nTrue positives increase. False positives decrease. \nUsing the slider above, try setting the threshold to 0.1, then dragging it to 0.9. What happens to the number of false positives and true positives? \n3. In general, what happens to the number of false negatives when the classification threshold increases? What about true negatives? Experiment with the slider above. \nBoth true and false negatives increase. \nAs the threshold increases, the model will likely predict more negatives overall, both true and false. At a very high threshold, almost all emails, both spam and not-spam, will be classified as not-spam. \nBoth true and false negatives decrease. \nUsing the slider above, try setting the threshold to 0.1, then dragging it to 0.9. What happens to the number of false negatives and true negatives? \nTrue negatives increase. False negatives decrease. \nUsing the slider above, try setting the threshold to 0.1, then dragging it to 0.9. What happens to the number of false negatives and true negatives?\n| **Key terms:**\n|\n| - [Binary classification](/machine-learning/glossary#binary-classification)\n| - [Class-imbalanced dataset](/machine-learning/glossary#class_imbalanced_data_set)\n| - [Classification threshold](/machine-learning/glossary#classification-threshold)\n| - [Confusion matrix](/machine-learning/glossary#confusion_matrix)\n| - [Ground truth](/machine-learning/glossary#ground_truth)\n| - [Negative class](/machine-learning/glossary#negative_class)\n- [Positive class](/machine-learning/glossary#positive_class) \n[Help Center](https://support.google.com/machinelearningeducation)"]]
