475
14 Quantitative Structure-Property Relationship Analysis …
Finally, the presence of information useful for molecular design is expected from
QSAR models corresponding to the third level of purposes. Fragmentary descriptors are usually used in such models. In this case, the analysis of the degree and direction of influence of such descriptors on activity can give immediate information
for the optimization of known structures and the design of novel substances with
desired properties.
However, one should be aware that, first of all, any selected model must be
predictive and only after that interpretable and informative, and so forth. It is a necessary condition of its subsequent usage that mechanistic-based or interpretabilityoriented models, which are not predictive, are not acceptable and senseless.
RF is an effective nonparametric statistical technique for large databases analysis
[52]. The main features of RF are listed below: (1) it is possible to analyze compounds with different mechanism of action within one dataset; (2) there is no need
to pre-select descriptors; (3) the method has its own reliable procedure for the estimation of model quality and its internal predictive ability; (4) models obtained are
tolerant to “noise” in source experimental data.
RF model construction is based on an original algorithm [53]. RF is an ensemble of single decision trees built by a classification and regression trees algorithm
(CART) [54]. Decision trees are the ensemble of hierarchically structured rules. Every rule is a logical construction that can be represented as “if … then …” criterion.
An RF algorithm recursively tries to find common criteria for objects from the same
class, using some randomly selected descriptors.
Each tree grows according to the following algorithm: (1) Bootstrap sample
which will be a training set for current tree is produced from the whole training
set of N compounds. About one-third of the compounds which aren’t in the current
training set are placed in out-of-bag (OOB) set. It is used to get a running unbiased
estimate of the model error and variable importance; (2) The best split among the
m randomly selected descriptors taken from the whole set of M ones in each node
is chosen. The value of m is the only tuning parameter for which RF models are
sensitive; (3) Each tree is grown to the largest possible extent. There is no pruning.
RF possesses its own reliable statistical characteristics, which could be used for
validation and model selection. Determination coefficients for training set (R
2
) and
out-of bag set (R
2
ооb
) are two main characteristics of the model. The major criterion
for estimation of internal predictive ability of the RF models and model selection is
the value of R
2
ооb
[55, 56].
Determination of optimal values of T (trees count) and m (descriptors count) are
the traditional starting points for every RF investigation. The following procedure
is recommended for determination of an optimal T value: starting from a small constant number of descriptors, increase the number of trees stepwise until R
2
ооb
does
not change significantly. Once an optimal T value has been identified, build models
with the optimal number of trees by increasing the variable number in a stepwise
manner. The final model is determined by the highest value of OOB set prediction.
In this study, T and m values equal to 100 and 200, respectively, were found as optimal and were chosen for subsequent models.
14 Quantitative Structure-Property Relationship Analysis …
Finally, the presence of information useful for molecular design is expected from
QSAR models corresponding to the third level of purposes. Fragmentary descriptors are usually used in such models. In this case, the analysis of the degree and direction of influence of such descriptors on activity can give immediate information
for the optimization of known structures and the design of novel substances with
desired properties.
However, one should be aware that, first of all, any selected model must be
predictive and only after that interpretable and informative, and so forth. It is a necessary condition of its subsequent usage that mechanistic-based or interpretabilityoriented models, which are not predictive, are not acceptable and senseless.
RF is an effective nonparametric statistical technique for large databases analysis
[52]. The main features of RF are listed below: (1) it is possible to analyze compounds with different mechanism of action within one dataset; (2) there is no need
to pre-select descriptors; (3) the method has its own reliable procedure for the estimation of model quality and its internal predictive ability; (4) models obtained are
tolerant to “noise” in source experimental data.
RF model construction is based on an original algorithm [53]. RF is an ensemble of single decision trees built by a classification and regression trees algorithm
(CART) [54]. Decision trees are the ensemble of hierarchically structured rules. Every rule is a logical construction that can be represented as “if … then …” criterion.
An RF algorithm recursively tries to find common criteria for objects from the same
class, using some randomly selected descriptors.
Each tree grows according to the following algorithm: (1) Bootstrap sample
which will be a training set for current tree is produced from the whole training
set of N compounds. About one-third of the compounds which aren’t in the current
training set are placed in out-of-bag (OOB) set. It is used to get a running unbiased
estimate of the model error and variable importance; (2) The best split among the
m randomly selected descriptors taken from the whole set of M ones in each node
is chosen. The value of m is the only tuning parameter for which RF models are
sensitive; (3) Each tree is grown to the largest possible extent. There is no pruning.
RF possesses its own reliable statistical characteristics, which could be used for
validation and model selection. Determination coefficients for training set (R
2
) and
out-of bag set (R
2
ооb
) are two main characteristics of the model. The major criterion
for estimation of internal predictive ability of the RF models and model selection is
the value of R
2
ооb
[55, 56].
Determination of optimal values of T (trees count) and m (descriptors count) are
the traditional starting points for every RF investigation. The following procedure
is recommended for determination of an optimal T value: starting from a small constant number of descriptors, increase the number of trees stepwise until R
2
ооb
does
not change significantly. Once an optimal T value has been identified, build models
with the optimal number of trees by increasing the variable number in a stepwise
manner. The final model is determined by the highest value of OOB set prediction.
In this study, T and m values equal to 100 and 200, respectively, were found as optimal and were chosen for subsequent models.