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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)
=
p>
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=
h3>
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=
h3>
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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