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Recommended search common evaluation indicators
20220423 15:27:00 【moletop】
. The evaluation index
Common indicators （ Classification and regression ）：

Accuracy rate ：Accuracy=(TP+TN)/(TP+FP+TN+FN)

Accuracy （ Check accuracy ）Precision=TP/(TP+FP), Recall rate （ Check all ）Recall=TP/(TP+FN)

F1 score（Fx fraction ,x Is the ratio of recall rate to accuracy rate ）
F1 score=2·Precision·Recall/(Precision+Recall)
Take it all into consideration , Recall rate Recall And accuracy Precision The harmonic average of , Only in the recall rate Recall And accuracy Precision When both are high ,F1 score Will be very high .

ROC and PR curve

ROC The curve can be used to evaluate the performance of a classifier under different thresholds . stay ROC In the curve , The abscissa of each point is (FPR), The ordinate is TPR, Depicts the classifier in True Positive and False Positive The balance between .

TPR=TP/(TP+FN), Represents the proportion of actual positive instances in all positive instances in the positive class predicted by the classifier .
FPR=FP/(FP+TN), Represents the proportion of actual negative instances in all negative instances in the positive class predicted by the classifier ,FPR The bigger it is , More negative classes in the predicted positive classes

AUC（Area Under Curve） by ROC The area under the curve , It represents a probability , The value of this area will not be greater than 1. Randomly select a positive sample and a negative sample ,AUC It represents the probability , The classifier will give a higher prediction value for the positive sample than the negative sample . The larger the area, the better , Greater than 0.5 It makes sense ,1 It's a perfect prediction , Less than 0.5 It means not even random prediction .

ROC The draw ：
 Suppose that a series of samples have been classified into positive classes Score value , Sort by size .
 From high to low , In turn “Score” Value as threshold threshold, When the test sample belongs to a positive sample, the probability is greater than or equal to this threshold when , We think it's a positive sample , Otherwise, it is a negative sample . for instance , For a sample , Its “Score” The value is 0.6, that “Score” A value greater than or equal to 0.6 All samples are considered positive samples , Other samples are considered negative .
 Choose one different... At a time threshold, Get a group of FPR and TPR, With FPR The values are abscissa and TPR The value is the ordinate , namely ROC A point on the curve .

4 There are two key points ：
spot (0,0)：FPR=TPR=0, It is predicted that all samples are negative samples ;
spot (1,1)：FPR=TPR=1, All samples are positive predictions ;
spot (0,1)：FPR=0, TPR=1, here FN＝0 And FP＝0, All samples are correctly classified ;
spot (1,0)：FPR=1,TPR=0, here TP＝0 And TN＝0, Worst classifier , Avoided all the right answers

When the distribution of positive and negative samples in the test set changes ,ROC The curve can stay the same
For example, the number of negative samples increases to the original 10 times ,TPR Unaffected ,FPR It's also proportionally increased , It won't change much . So the unbalanced sample problem is usually chosen as ROC As a standard of evaluation .


PR curve ：
 Drawing method and ROC equally , Take different thresholds , Calculate... For all samples p and r.
 F1 = 2 * P * R ／( P + R ). Balance point （BEP） yes P=R The value of time （ The slope is 1）


MAE( Mean absolute error ) and MSE（ Mean square error ）
 MSE Fast convergence , Sensitive to outliers . Because its punishment is square , So the of outliers loss It will be very big.
 MAE Compare with MSE, There is no function of the square term , The punishment for all training data is the same . Maybe because the gradient value is small , Make the model fall into local optimum
Search and recommend indicators ：

IOU( In target detection , In the field of image segmentation , Defined as the ratio of the intersection and union of the areas of two rectangular boxes ,IoU=A∩B/A∪B). If it overlaps completely , be IoU be equal to 1, It's the ideal situation . Generally in the detection task ,IoU Greater than or equal to 0.5 I think the recall , If set higher IoU threshold , The recall rate decreases , At the same time, the positioning box is more accurate .

AP and mAP
AP：average precision, After ranking the scores , from rank1 To rankn. Corresponding to each recall node Maximum accuracy , Then take the average to get AP.
Be careful ：AP The previous calculation invention method ： Make N It's all id, If from top1 To topN Count them all , The corresponding precision and recall, With recall Abscissa ,precision Vertical coordinates , The... Used in the detection is obtained precisionrecall curve , Although the overall trend and significance are related to precisionrecall The curves are the same , The calculation method is very different . In the classification pr It is to set different thresholds to determine the next value of all samples p and r, there AP After determining the threshold , from top1 To topN Count them all , Get current topx Of p and r.
MAP： Conduct N The average number of search results , Generally, all categories will be searched to calculate , Just like the calculation method of multi label image classification .
AP It measures the quality of the learned model in a category ,mAP It measures the quality of the model in all categories .

MRR(mean reciprocal rank) Average reciprocal ranking
 RR, Countdown ranking , It refers to the reciprocal of the ranking of the first relevant document in the search results .
 MRR The mean value of the reciprocal ranking of multiple queries , The formula is as follows ：rank_{i} It means the first one i Ranking of the first relevant document of a query .

NDCG（ It is also recommended to use ）

CG,Cumulative Gain） Cumulative benefits , k Express k A collection of documents ,rel It means the first one i The relevance of a document

DCG（Discounted Cumulative Gain） stay CG The location information is not taken into account in the calculation of , For example, the relevance of the retrieved three documents is （3,1,1） and （1,1,3）, according to CG The ranking is the same , But obviously the former is in a better order . So you need to be in CG On the basis of calculation, add the calculation of location information , Introduce discount factor . According to the increment of position , The corresponding decline in value .

IDCG（ideal DCG） Ideally , Sort according to the degree of correlation from large to small , And then calculate DCG When the maximum value can be obtained . among REL Indicates that documents are sorted according to their relevance from large to small , Take before k A collection of documents .

NDCG（Normalized DCG）
Because the length of the result document set that can be retrieved by each query is inconsistent ,k Different values will affect DCG Calculated results of . Therefore, you can't simply query different DCG The results were averaged , Need to normalize first .NDCG Is the use IDCG Normalize it , Represents the current DCG And ideally IDCG How different .
* Hit ratio The denominator is all the test sets , The molecule is before each user K The sum of the numbers belonging to the test set , This measure is the recall rate , The bigger the index, the better .

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