Message-ID: <333870697.205.1632427513151.JavaMail.bigchem@cpu> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_204_1904795722.1632427513150" ------=_Part_204_1904795722.1632427513150 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Statistical parameters

Statistical parameters

Here, we will briefly overview the statistical parameters used b= y OCHEM for evaluation of the predictive performance of QSAR models.

Regression models

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In the formulae below, denote predicted and real values of the predicted prope= rty for i-th compound in the set. are the means of thepredicted and real property= values; sigma (?) denotes the standard deviation.

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RMSE

RMSE stands for Root Mean Squared Error and is calculated according to t= he formula:

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The R2 and Q2 indicators can be a subject to confusion, since they often= mean different things in classical statistics and QSAR, depending on wheth= er they are calculated for the training set or for the cross-validated set.= All the formulae given here are calculated with respect to the selected va= lidation protocol (bagging, cross-validation or no validation)

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R2 (Pear= son correlation coefficient)

Q2 (Coeffic= ient of determination)

MAE

Classification models=

The most common case of classification models is binary classification, = where the instances belong to either positive (active) or negative (inactiv= e) class. Some statistical measures are applicable to binary classification= models only.

For binary classification models the accepted notion is to discriminate:=

TP =3D true positives  - number of instances of active cla= ss, that were correctly predicted by the model as actives

FP =3D false positives - number of instances of inactive class,= that were incorrectly predicted by the model as actives

TN =3D true negatives - number of instances of inactive class, = that were correctly predicted by the model as inactives

FN =3D false negatives - number of instances of active class, t= hat were incorrectly predicted by the model as inactives

Accuracy

"Accuracy" is merely the percentage of correctly classified sa= mples. For binary classification accuracy can be calculated as follows:

ACC =3D (TP + TN) / (TP + FP + TN + FN)

Class hit rate

Hit rate is a measure that is applicable to a single class in a classifi= cation model and denotes a ratio of instances of a specific class that were= correctly identified as belonging to this class.

For binary classification tasks class hit rate for positive class is cal= led sensitivity, and for negative class - specificity.

Precision

Precision in the context of classification models is a measure applicabl= e to a single class of a model and denotes a ratio between the instances co= rrectly identified as belonging to a particular class and a total number of= instances identified as belonging to this class.

For binary classification models precision for positive class is called = positive predictive value, and for negative class - negative p= redictive value.

Sensitivity

Sensitivity is a measure applicable to binary classifications and denote= s a ratio of positive instances that were correctly identified as such.

SENS =3D TP / (TP + FN)

Specificity

Specificity is a measure applicable to binary classifications and denote= s a ratio of negative instances that were correctly identified as such.

SPEC =3D TN / (TN + FP)

Positive p= redictive value

Positive predictive value is a binary classification measure and shows a= ratio of true positive to all instances that were classified as positive.<= /p>

PPV =3D TP / (TP + FP)

Negative p= redictive value

Negative predictive value is a binary classification measure and shows a= ratio of true positive to all instances that were classified as positive.<= /p>

NPV =3D TN / (TN + FN)

Balanced accuracy

Balanced accuracy is the averaged accuracy for each class, e.g. (positiv= e_class_accuracy + negative_class_accuracy) / 2.
This parameter is imp= ortant for imbalanced datasets, which have significantly different number o= f samples in different classes.
If a classifier has a similar performa= nce for both negative and positive classes, accuracy and balanced accuracy = are also similar.

BA =3D 0.5 * (TP / (TP + FN) + TN / (TN + FP)) =3D 0.5 * (SENS + SPE= C)

Matthews correlation coefficient (M= CC)

MCC takes into account true and fa= lse positives and negatives and is generally regarded as a balanced measure= which can be used even if the classes are of very different sizes. =

MCC =3D (TP*TN - FP FN)/ SQRT( (TP= +FP)(TP+FN)(TN+FP)(TN+FN) )

Area under the curv= e (AUC)

Receiver Operating Characteristic AUC= (ROC-AUC) is calculated on the plot of Sensitivity vs Specificity, which i= s shown for each classification model

Confusion matrix

Confusion matrix shows the number of samples from a particular class cla= ssified as another particular class.

Prediction int= ervals

The prediction intervals (68%, i.e. approximately ± one stan= dard deviation) for all statistical parameters are evaluated using bootstra= p procedure with n =3D 1000 samples.
Following model calculation we g= et predicted values zi for training (or test) samples with exper= imental values yi, i.e. {zi, yi} are pairs= of values with i =3D 1,..,N.
We randomly sample pairs {zi, yi} to form n =3D 1000 bootstrap sets of the same siz= e as the analyzed set. For each bootstrap set we calculate
statistica= l parameters and use their respective distributions to determine respective= confidence intervals.
Since the intervals are in general non-symmetri= c with respect to the values calculated for the analyzed sets, the average = values are reported.

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