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    ,              .

          .            .

     ,             .

     ,           .

     ,             .

      ,      ,     .

      ,          .

Accuracy ()       ,     ,      .

Precision ()       ,          .

Recall ()       ,              .

F1-score (F-)       ,        .

ROC AUC       ,       .

Mean Squared Error (MSE)       ,         .

Root Mean Squared Error (RMSE)       ,      .

Mean Absolute Error (MAE)       ,          .

R-squared ( )       ,    ,     .

Silhouette coefficient ( )       ,     .

Calinski-Harabasz index ( -)       ,        .

Davies-Bouldin index ( -)       ,        .

AUROC (     )          ,          .

Mean Average Precision (mAP)        ,        .

Intersection over Union (IoU)        ,           .

Overfitting ()  ,              .

Underfitting ()  ,                 .

Cross-validation (-)                     .         ,     .

Hyperparameters ()     ,               .

Bias ()   ,   -          .

Variance ()   ,   -          .

Regularization ()  ,           .

Feature engineering ( )                  .




    





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,       ,    (accuracy),  (precision),  (recall), F- (F1-score)  ROC AUC.  (accuracy)    ,      .  (precision)         ,   (recall)         . F- (F1-score)       ,  ROC AUC      .

      ,     (MSE),    (RMSE),    (MAE),   (R-squared)  .

      ,     (silhouette coefficient),  - (Calinski-Harabasz index),  - (Davies-Bouldin index)  .

      ,     (precision),   (recall), F- (F1-score),       (AUROC)  .

          (mAP),   (IoU),  (precision),  (recall)  .

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     ,   Accuracy, Precision, Recall, F1-score, ROC AUC, Log Loss  Confusion Matrix ( ),     ,      .   :

 :         ,   ,        . ,   Accuracy, Precision, Recall, F1-score, ROC AUC  Confusion Matrix,            .

 :          -      . ,   Accuracy, Precision, Recall, F1-score, ROC AUC  Log Loss,           ,     .

 :            ,       . ,   Accuracy, Precision, Recall, F1-score, ROC AUC  Confusion Matrix,              .

 :   ,   -,     ,        . ,   Accuracy, Precision, Recall, F1-score  ROC AUC,         .

    :          ,      . ,   Accuracy, Precision, Recall, F1-score, ROC AUC  Confusion Matrix,            .

 :    ,      ,      ,     . ,   Accuracy, Precision, Recall, F1-score, ROC AUC  Confusion Matrix,              .

 :           ,      . ,   Accuracy, Precision, Recall, F1-score, ROC AUC  Confusion Matrix,            .

          ,    .   ,   Log Loss  Confusion Matrix,           .   ,        :








 Log Loss  Confusion Matrix      ,    ,         .  Log Loss            ,  Confusion Matrix        ,   .

 ,                 . ,    ,    ,      ,     ,    .




 Accuracy ()


 Accuracy ()              .             .

 Accuracy   :

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

:

TP (True Positives)      ;

TN (True Negatives)      ;

FP (False Positives)       ( );

FN (False Negatives)       ( ).

Accuracy      0  1 (  0%  100%).    Accuracy  1 ( 100%),     .

,  ,   Accuracy         ,         .      ,   Precision, Recall  F1-score,      .

  1:

    100 ,   90 ,  10 .     90    10  .   :

TP (True Positives) = 10 (   )

TN (True Negatives) = 90 (   )

FP (False Positives) = 0 (     )

FN (False Negatives) = 0 (     )

  Accuracy:

Accuracy = (TP + TN) / (TP + TN + FP + FN) = (10 + 90) / (10 + 90 + 0 + 0) = 100 / 100 = 1.0  100%

      100%.

  2:

           1000 ,     900  . , 500   ,   500  .     450     450   .   :

TP (True Positives) = 450 (    )

TN (True Negatives) = 450 (    )

FP (False Positives) = 50 (  ,   )

FN (False Negatives) = 50 (  ,   )

  Accuracy:

Accuracy = (TP + TN) / (TP + TN + FP + FN) = (450 + 450) / (450 + 450 + 50 + 50) = 900 / 1000 = 0.9  90%

      90%.




 Precision ()


 Precision ()         ,  ,      . Precision          ( ).

 Precision   :

Precision = TP / (TP + FP)

:

TP (True Positives)      ;

FP (False Positives)       ( ).

Precision      0  1 (  0%  100%).    Precision  1 ( 100%),      .

 ,   Precision     ,     (False Negatives).   ,         (,   ),    ,   Recall ()  F1-score,     ,   .

  1:    - ,      ,       .     10 -  15,        66.7%.

      Precision ()    1:

 ,      .      "".

    4 : True Positive (TP), False Positive (FP), True Negative (TN)  False Negative (FN).    :

TP:    -   (10 ).

FP:     -   (5 ).

TN:     -    (0 ).

FN:    -    (0 ).

    TP      (TP + FP):

Precision = TP / (TP + FP) = 10 / (10 + 5) = 0.667 = 66.7%

 ,       10  15 -,     66.7%.

  2:

              200 ,   150     50   .    120     40   . , 30         ,  10       .   Precision   "".

 ,      .      "".

    4 : True Positive (TP), False Positive (FP), True Negative (TN)  False Negative (FN).    :

TP:           (120 ).

FP:          (10 ).

TN:        (40 ).  TN     Precision,      .

FN:          (30 ).  FN      Precision.

    TP      (TP + FP): Precision = TP / (TP + FP) = 120 / (120 + 10) = 120 / 130 = 0.923 = 92.3%

 ,       120  130 ,       .     ""  92.3%.




 Recall ()


 Recall ()         ,  ,         . Recall          ( ).

 Recall   :

Recall = TP / (TP + FN)

:

TP (True Positives)      ;

FN (False Negatives)       ( ).

Recall      0  1 (  0%  100%).    Recall  1 ( 100%),         .

 ,   Recall     (False Positives).   ,       , ,    -,    ,   Precision ()  F1-score,     ,   .



  1:

  1:         ,      -.     80  100 -,      ""  80%.

      Recall ()    1:

 ,      .      "".

    4 : True Positive (TP), False Positive (FP), True Negative (TN)  False Negative (FN).    :

TP:    -   (80 ).

FP:     -   (20 ).

FN:    -    (20 ).

    TP      (TP + FN):

Recall = TP / (TP + FN) = 80 / (80 + 20) = 0.8 = 80%

 ,       80  100 -,     80%.

  2: ,      -,        .   ,                 "".

       200 ,      ""      .  ,     ,    :

 200  120         "" (TP).

 200  80         "" (FN).

   (recall)   "".

:

TP = 120 (,          "") FN = 80 (,          "")

Recall = TP / (TP + FN) = 120 / (120 + 80) = 0.6 = 60%

    ""  60%.  ,         60%  ,         .         ,        ,        "".




 F1-score (F-)


 F1-score (F-)         ,     Precision ()  Recall (). F1-score     Precision  Recall,      ,      . F1-score    ,               .

 F1-score   :

F1-score = 2 * (Precision * Recall) / (Precision + Recall)

:

Precision = TP / (TP + FP)  ;

Recall = TP / (TP + FN)  ;

TP (True Positives)      ;

FP (False Positives)       ( );

FN (False Negatives)       ( ).

F1-score      0  1 (  0%  100%).    F1-score  1 ( 100%),       ,    Precision  Recall.  F1-score  0,  ,        .

  1:   ,       ,       .     90%,    80%,  F1-score   84%.

      F1-score (F-)   1:

    ,   :

Precision = TP / (TP + FP) Recall = TP / (TP + FN)

  ,  = 0.9 ( 90%)   = 0.8 ( 80%).

 F1-score      :

F1-score = 2 * (Precision * Recall) / (Precision + Recall)

F1-score = 2 * (0.9 * 0.8) / (0.9 + 0.8) = 0.84 ( 84%)

 ,    F1-score  84%.

  F1-score  84%,    ,          (  ).                 .

  2:   ,      ,       .     85%,    90%,  F1-score   87.5%.

      F1-score (F-)   2:

    ,   :

Precision = TP / (TP + FP) Recall = TP / (TP + FN)

  ,  = 0.85 ( 85%)   = 0.9 ( 90%).

 F1-score      :

F1-score = 2 * (Precision * Recall) / (Precision + Recall)

F1-score = 2 * (0.85 * 0.9) / (0.85 + 0.9) = 0.875 ( 87.5%)

 ,    F1-score  87.5%.




 ROC AUC


 ROC AUC (Receiver Operating Characteristic  Area Under the Curve)      ,    ROC-. ROC-        (True Positive Rate, TPR)   (False Positive Rate, FPR)     .

True Positive Rate (TPR)  Recall ()   TP / (TP + FN);

False Positive Rate (FPR)   FP / (FP + TN).

ROC AUC   ,    ROC-.       0  1 (  0%  100%).    ROC AUC  1 ( 100%),       .  ROC AUC,  0.5, ,       ,  ,  0.5,   ,      .

   ROC AUC   ,       ,             .

  ,  ROC AUC         .       ,   Precision-Recall AUC,       .




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