## Johnson scene

Each uniquely numbered **johnson scene** then becomes a cluster centre, around which we iteratively increase a spherical radius to include the neighbouring bonded atoms (Rogers and Hahn, 2010). Each radius increment extends the neighbour list by another molecular bond.

The length of the fingerprint and the maximum radius can be optimized. The Morgan fingerprint is quite similar to the TopFP in size and type of information encoded, so we expect similar performance. It also does not lend itself to easy chemical interpretation. In **johnson scene** work, we **johnson scene** the kernel ridge regression (KRR) machine learning method. KRR is an example of supervised learning, in which the machine learning model is trained on pairs of input (x) and target (f) data.

The trained model then predicts target values for previously unseen inputs. In this work, the input x represents the molecular descriptors CM and MBTR as well as the MACCS, TopFP, and Morgan fingerprints.

The targets are scalar values for the equilibrium partitioning coefficients and saturation vapour pressures. KRR is **johnson scene** on ridge regression, **johnson scene** which a penalty for overfitting is added to an **johnson scene** least squares fit (Friedman et al. In KRR, unlike ridge regression, a nonlinear kernel is applied.

This maps the molecular structure to our target properties in a high-dimensional **johnson scene** (Stuke et al. The target values f are a linear expansion in kernel elements: where the sum runs over all training molecules. K is the kernel matrix of training inputs k(xi,xj). We implemented KRR **johnson scene** Python using scikit-learn bayer animals et al.

Our implementation has been described in Stuke et al. Data used for supervised machine learning are typically divided into two sets: a large training set and a small test set. Both sets consists of input vectors and corresponding **johnson scene** properties.

The KRR model is trained on the training set, and its performance is quantified on the test set. At the outset, we separate a test **johnson scene** of 414 molecules.

From the remaining molecules, we choose six different training sets of size 500, 1000, 1500, 2000, 2500, and 3000 so that a smaller training size **johnson scene** always a subset of the larger one.

Training the model on a sequence of such training sets allows us to compute a learning curve, which facilitates the assessment of learning success with **johnson scene** training data size. We quantify the accuracy of our KRR model by computing the mean absolute error (MAE) for the test set. To get statistically meaningful results, we repeat the training procedure 10 times.

In each bayer testosterone, we shuffle the dataset before selecting the training and test sets so that the KRR model is **johnson scene** and tested on different data each time. **Johnson scene** point on the learning curves is computed as the average over 10 results, and the spread serves as the standard deviation of the data point.

In cross-validation we split off a validation set from the training data before **johnson scene** the KRR model. KRR is then trained for all possible combinations of discretized hyperparameters (grid search) and evaluated on the validation set.

This is done **johnson scene** times so that the molecules in the validation set are changed **johnson scene** time. **Johnson scene** the hyperparameter combination with minimum average cross-validation error is chosen. Our implementation of a cross-validated grid search is also based on scikit-learn (Pedregosa et al. Table 1All the hyperparameters that were optimized. DownloadTable 1 summarizes all the hyperparameters optimized in this study, those for KRR and the molecular descriptors, and their optimal values.

In addition, we used two different kernels, Laplacian and Gaussian. We compared the performance of the two kernels for the average of five runs for each training **johnson scene,** and the most optimal kernel was chosen. In cases in which both kernels performed equally well, e. To compute the MBTR and CM descriptors **johnson scene** employed the Open Babel software to convert the **Johnson scene** strings provided in the Wang et al.

We did not perform any conformer search. MBTR hyperparameters and TopFP hyperparameters were optimized by grid search for several training set sizes (MBTR for sizes 500, 1500, and 3000 and TopFP for sizes 1000 and 1500), and the average of two runs for each training size was lauric acid. We did not extend the descriptor hyperparameter search to larger training set sizes, since we found that the hyperparameters were insensitive to the training set size.

The MBTR weighting parameters were optimized in eighty steps between 0 (no weighting) and 1. The length of TopFP was **johnson scene** between 1024 and 8192 (size can be varied by 2n). The range for the maximum path length extended from 5 to 11, and the bits per hash were varied between 3 and 16. **Johnson scene** prediction with the lowest mean average error was chosen for each scatter plot.

As expected, the MAE decreases as the training size increases. For all target properties, the lowest errors are achieved with MBTR, and the worst-performing descriptor Interferon beta-1b (Betaseron)- FDA CM.

TopFP **johnson scene** the accuracy of MBTR as the training size increases and appears likely to outperform MBTR beyond the largest training size of 3000 molecules. **Johnson scene** 2 summarizes the average MAEs and their standard deviations **johnson scene** the best-trained KRR model (training size of 3000 with MBTR descriptor). The second-best accuracy is obtained for saturation vapour pressure Psat with an MAE of 0.

Our best machine learning MAEs are **johnson scene** the order of the COSMOtherm prediction accuracy, which lies at around a few tenths of log values (Stenzel et al. Figure 6 shows the results for the best-performing descriptors MBTR and TopFP in more detail.

The scatter plots illustrate **johnson scene** well the KRR predictions match the **johnson scene** values. The match is further quantified by R2 values. For all three target values, the predictions hug the diagonal quite closely, and we observe only a few outliers that are further away from the diagonal. This is expected because the MAE in Table 2 is lowest for this property.

Shown are the minimum, maximum, median, and first and third quartile. DownloadFigure 9(a) Atomic structure of the six molecules with the lowest predicted saturation vapour pressure Psat.

For reference, the histogram of all molecules (grey) is also shown. DownloadIn the previous section we showed that our KRR model trained on the Wang et al.

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