Previous articles in this series:
- Prediction of Small Molecule Lipophilicity: Part 1 – Data Exploration
- Prediction of Small Molecule Lipophilicity: Part 2 – TPOT (Tree-based Pipeline Optimization Tool) With Morgan (Circular) Fingerprints
- Prediction of Small Molecule Lipophilicity: Part 3 – Ensemble of Multilayer Perceptrons With Morgan (Circular) Fingerprints
- Prediction of Small Molecule Lipophilicity: Part 4 – Ensemble of 1D Convolutional Neural Networks With Morgan (Circular) Fingerprints
1. Introduction
Using Morgan (circular) fingerprints as input data, we create an ensemble of 2D convolutional neural networks (CNNs) with Keras, to predict lipophilicity values. See Prediction of Small Molecule Lipophilicity: Part 1 – Data Exploration for the link to the raw data as well as code for converting SMILES strings to fingerprints via RDKit.
2. Data Shaping
Morgan fingerprints are 1D Numpy arrays of length 2048 consisting of 1s and 0s, which are then reshaped to (height, width) = (32, 64), see: Prediction of Small Molecule Lipophilicity: Part 1 – Data Exploration. In the CNN we are using the channels first option with a single channel. First, we read in a Numpy array with all of the input data and the reshape it to (number of data points, 1, height, width), where 1 = number of channels (see the main code at the end of this article).
Next, we must ensure that the correct data shape is specified. We have
input_tensor = Input(shape=(1, height_size, width_size))
In the 2D convolutional and max pooling layers we specify data_format=’channels_first’ (see model construction code at the end of this article).
Additionally, we must be careful with the sizes of the convolutional kernels and pooling. We use a fixed kernel_size of (3, 3), pool_size of (2, 2), and stride of 2. The number of filters is set to an initial value (which is a hyperparameter) for the first convolutional block, then it is allowed to change but is constrained by a maximum value (also a hyperparameter), (see model construction code at the end of this article).
3. Neural Network Parameters
We use randomized parameter search for the parameters of the multilayer perceptrons.
import numpy as np
from sklearn.model_selection import ParameterSampler
def parameters_cnn(num_samples):
batch_size = [32, 64]
dropout = np.linspace(0.0, 0.5, num=11, endpoint=True)
activation = ['relu','elu']
cnn_filters_initial = [16, 32]
cnn_filters_maximum = [32, 64, 128]
cnn_blocks = [2, 3]
layer_1_nodes_num = [32, 64, 128, 256]
grid = {'batch_size':batch_size, 'dropout':dropout,
'filters_initial':cnn_filters_initial,
'filters_maximum':cnn_filters_maximum,
'blocks':cnn_blocks, 'activation':activation,
'layer_1_nodes_num':layer_1_nodes_num}
parameter_grid = list(ParameterSampler(grid, n_iter=num_samples))
return parameter_grid
To create an ensemble of neural networks, we set a cross validation error threshold and keep 10 models with cross validation errors below the threshold. These are the parameters of those models.
2D CNN Hyperparameters
| layer_1_nodes_num | filters_maximum | filters_initial | dropout | blocks | batch_size | activation | Model Name | Metric | Mean CV Error | Max CV Epochs |
|---|---|---|---|---|---|---|---|---|---|---|
| 128 | 128 | 32 | 0 | 2 | 32 | relu | cnn_2d_fingerprints_104 | mean_squared_error | 0.002777 | 19 |
| 64 | 64 | 32 | 0.05 | 2 | 32 | relu | cnn_2d_fingerprints_3 | mean_squared_error | 0.002942 | 37 |
| 128 | 32 | 32 | 0.05 | 2 | 64 | relu | cnn_2d_fingerprints_82 | mean_squared_error | 0.003037 | 27 |
| 64 | 32 | 16 | 0 | 2 | 64 | relu | cnn_2d_fingerprints_103 | mean_squared_error | 0.00311 | 20 |
| 128 | 32 | 32 | 0 | 2 | 64 | relu | cnn_2d_fingerprints_197 | mean_squared_error | 0.003126 | 16 |
| 32 | 64 | 32 | 0.05 | 2 | 32 | relu | cnn_2d_fingerprints_189 | mean_squared_error | 0.00315 | 33 |
| 256 | 64 | 16 | 0.05 | 2 | 64 | relu | cnn_2d_fingerprints_122 | mean_squared_error | 0.003217 | 26 |
| 256 | 128 | 32 | 0 | 3 | 32 | elu | cnn_2d_fingerprints_173 | mean_squared_error | 0.003224 | 9 |
| 64 | 128 | 32 | 0 | 3 | 32 | relu | cnn_2d_fingerprints_151 | mean_squared_error | 0.003237 | 10 |
| 128 | 64 | 32 | 0 | 3 | 64 | relu | cnn_2d_fingerprints_71 | mean_squared_error | 0.003279 | 14 |
4. Results
Results were produced using unseen data.
Lipophilicity Errors
| Mean Squared Error | Root Mean Squared Error | Median Absolute Error | Correlation Coefficient | R2 | |
|---|---|---|---|---|---|
| cnn_2d_fingerprints_104 | 0.794 | 0.8911 | 0.503 | 0.6974 | 0.4732 |
| cnn_2d_fingerprints_3 | 0.7759 | 0.8808 | 0.5386 | 0.7041 | 0.4852 |
| cnn_2d_fingerprints_82 | 0.7954 | 0.8919 | 0.536 | 0.7037 | 0.4722 |
| cnn_2d_fingerprints_103 | 0.7774 | 0.8817 | 0.5154 | 0.704 | 0.4842 |
| cnn_2d_fingerprints_197 | 0.8026 | 0.8959 | 0.4865 | 0.6946 | 0.4674 |
| cnn_2d_fingerprints_189 | 0.7679 | 0.8763 | 0.5539 | 0.7088 | 0.4905 |
| cnn_2d_fingerprints_122 | 0.816 | 0.9033 | 0.5338 | 0.6948 | 0.4586 |
| cnn_2d_fingerprints_173 | 0.9104 | 0.9541 | 0.6087 | 0.6602 | 0.3959 |
| cnn_2d_fingerprints_151 | 0.9268 | 0.9627 | 0.5469 | 0.6435 | 0.3851 |
| cnn_2d_fingerprints_71 | 0.9789 | 0.9894 | 0.6028 | 0.6218 | 0.3505 |
| Ensemble Median | 0.7115 | 0.8435 | 0.4828 | 0.7305 | 0.5279 |
Below is a comparison of our results to those of the Molecule Net benchmark from MoleculeNet: A Benchmark for Molecular Machine Learning (page 51).
Our Results Versus Benchmark Results
| Model | Root Mean Squared Error |
|---|---|
| Random Forest (RF) | 0.876 +/- 0.040 |
| Multitask (Multilayer Perceptron with multiple outputs) | 0.859 +/- 0.013 |
| XGBoost | 0.799 +/- 0.054 |
| Kernel Ridge Regression (KRR) | 0.899 +/- 0.043 |
| Graph Convolutional Network (GC) | 0.655 +/- 0.036 |
| Directed Acyclic Graph (DAG) | 0.835 +/- 0.039 |
| Weave | 0.715 +/- 0.035 |
| Message Passing Neural Network (MPNN) | 0.719 +/- 0.031 |
| TPOT Best | 0.767 |
| TPOT Ensemble | 0.787 |
| Multilayer Perceptron Ensemble | 0.823 |
| 1D CNN Fingerprints | 0.857 |
| 2D CNN Fingerprints | 0.844 |
R2 results in barchart form can be seen at the Molecule Net site (see section Physical Chemistry -> lipo).
The benchmark results were obtained by running multiple random permutations of the dataset, which we did not do, so the comparisons with our results are not exact.
5. Code
Model construction function:
from keras.layers import Dense, Input, Dropout
from keras.layers import Conv2D, MaxPooling2D, Flatten
from keras.models import Model
from keras.optimizers import Adam
def cnn_2d_model_construction(dict_params_cnn, num_output_nodes,
loss_type, metric, height_size, width_size):
format_of_data = 'channels_first'
conv_kernel_size = (3,3)
padding_type = 'valid'
poolsize = (2, 2)
strides_value = 2
input_tensor = Input(shape=(1, height_size, width_size))
# 1st block
x = Conv2D(filters=dict_params_cnn['filters_initial'],
kernel_size=conv_kernel_size,
activation=dict_params_cnn['activation'],
padding = padding_type,
data_format=format_of_data)(input_tensor)
x = Dropout(dict_params_cnn['dropout'])(x)
x = MaxPooling2D(pool_size=poolsize, strides=strides_value,
data_format=format_of_data)(x)
num_filters = 2*dict_params_cnn['filters_initial']
for iblock in range(dict_params_cnn['blocks'] - 1):
x = Conv2D(filters=num_filters,
kernel_size=conv_kernel_size,
activation=dict_params_cnn['activation'],
padding = padding_type,
data_format=format_of_data)(x)
x = Dropout(dict_params_cnn['dropout'])(x)
x = MaxPooling2D(pool_size=poolsize, strides=strides_value,
data_format=format_of_data)(x)
num_filters = min(2*num_filters, dict_params_cnn['filters_maximum'])
x = Flatten()(x)
x = Dropout(dict_params_cnn['dropout'])(x)
x = Dense(dict_params_cnn['layer_1_nodes_num'],
activation = dict_params_cnn['activation'])(x)
x = Dropout(dict_params_cnn['dropout'])(x)
# target E [-0.15, 0.45] so no need of activation function
output_tensor = Dense(num_output_nodes)(x)
model_cnn_f = Model(input_tensor, output_tensor)
# compile the model
opt = Adam(lr=0.00025) # default = 0.001
model_cnn_f.compile(optimizer=opt, loss=loss_type, metrics=[metric])
return model_cnn_f
Cross validation, thresholding, and saving good models function:
import numpy as np
from keras.callbacks import EarlyStopping, ReduceLROnPlateau
def nn_cv(x_calib, y_calib, cv_folds, metric,
nn_model, nn_model_copy, batchsize, num_epochs, stop_epochs, verbosity,
models_dir, model_name, threshold, learn_rate_epochs):
callbacks_list = [EarlyStopping(monitor='val_loss', patience=stop_epochs),
ReduceLROnPlateau(monitor='val_loss', factor=0.1, patience=learn_rate_epochs,
verbose=0, mode='auto', min_lr=1.0e-6)]
cv_num = int(x_calib.shape[0]/cv_folds)
list_cv_metrics = []
list_cv_epochs = []
for fold in range(cv_folds):
# get train/valid
x_train = np.vstack((x_calib[:cv_num*fold], x_calib[cv_num*(fold+1):]))
y_train = np.hstack((y_calib[:cv_num*fold], y_calib[cv_num*(fold+1):]))
x_valid = x_calib[cv_num*fold:cv_num*(fold+1)]
y_valid = y_calib[cv_num*fold:cv_num*(fold+1)]
# fit the model
h = nn_model.fit(x_train, y_train, epochs=num_epochs,
batch_size=batchsize, validation_data=(x_valid, y_valid),
callbacks=callbacks_list, verbose=verbosity)
# collect cv stats
list_cv_metrics.append(np.min(h.history['val_' + metric]))
epoch_best_early_stop = len(h.history['val_loss']) - stop_epochs
list_cv_epochs.append(epoch_best_early_stop)
dict_return = {}
mean_cv_error = np.mean(list_cv_metrics)
max_cv_epochs = np.max(list_cv_epochs)
print('mean_cv_error =',mean_cv_error,'\tthreshold =',threshold)
print('max_cv_epochs =',max_cv_epochs)
if mean_cv_error < threshold:
# fit the model (use copy) with all calib data
h_refit = nn_model_copy.fit(x_calib, y_calib, epochs=max_cv_epochs,
batch_size=batchsize, verbose=0)
nn_model_copy.save(models_dir + model_name + '.h5')
dict_return['Model Name'] = model_name
dict_return['Metric'] = metric
dict_return['Mean CV Error'] = mean_cv_error
dict_return['Max CV Epochs'] = max_cv_epochs
return dict_return
In the main code below, we note that we divided the lipophilicity values by 10 so that their range is [-0.15, 0.45] and thus no output activation function is used.
import pandas as pd
import numpy as np
import time
import os
from pathlib import Path
import sys
sys.path.append(YOUR DIRECTORY)
import neural_network_ensemble
if __name__ == '__main__':
calculation_type = 'calibration' # production calibration
nn_type = 'cnn_2d'
target_divisor = 10.0 # target E [-0.15, 0.45] so no need of activation function
base_directory = YOUR DIRECTORY
data_directory = base_directory + 'data/'
results_directory_stub = base_directory + nn_type + '_fingerprints/'
if not Path(results_directory_stub).is_dir():
os.mkdir(results_directory_stub)
results_directory = results_directory_stub + 'results_' + nn_type + '_fingerprints/'
if not Path(results_directory).is_dir():
os.mkdir(results_directory)
models_directory = results_directory_stub + 'models_' + nn_type + '_fingerprints/'
if not Path(models_directory).is_dir():
os.mkdir(models_directory)
# limits and params
metric_type = 'mean_squared_error'
type_of_loss = metric_type
verbose = 0
epochs = 200
checkpoint_epochs_stop = 15
learning_rate_epochs = 10
cross_valid_folds = 3
size_of_parameter_list = 1000
error_threshold = 0.008
max_time_minutes = 6*60
number_of_models = 10
if calculation_type == 'calibration':
print('\n\n*** starting calibration at',pd.Timestamp.now())
start_time_calibration = time.time()
# get data
ycalib = np.load(data_directory + 'y_calib.npy')/target_divisor
xcalib = np.load(data_directory + 'x_calib_fingerprints_2d.npy')
try:
number_of_outputs = ycalib.shape[1]
except:
number_of_outputs = 1 # ycalib.shape[1]
# reshape data
num_pts = xcalib.shape[0]
height = xcalib[0].shape[0]
width = xcalib[0].shape[1]
# height*width = length_of_fingerprint_vector = 2048
xcalib = xcalib.reshape(num_pts, 1, height, width)
# set up parameters (stochastic)
list_param_dict = parameters_cnn(size_of_parameter_list)
list_dict_results = []
counter = 0
# loop over parameters
for dictionary_parameter in list_param_dict:
modelname = nn_type + '_fingerprints_' + str(counter)
counter = counter + 1
print('\n\n*** starting at',pd.Timestamp.now())
start_time_loop = time.time()
model_nn = cnn_2d_model_construction(dictionary_parameter,
number_of_outputs,
type_of_loss, metric_type,
height, width)
print(dictionary_parameter)
dict_results = nn_cv(xcalib, ycalib,
cross_valid_folds, metric_type,
model_nn, model_nn,
dictionary_parameter['batch_size'], epochs,
checkpoint_epochs_stop, verbose,
models_directory, modelname, error_threshold,
learning_rate_epochs)
elapsed_time_minutes = (time.time() - start_time_loop)/60
print('*** elapsed time =',elapsed_time_minutes,' mins\tcounter =',counter-1)
# add epochs and modelname to param dict and save it
if len(dict_results) > 0:
dictionary_parameter.update(dict_results)
list_dict_results.append(dictionary_parameter)
# check elapsed time for early stopping
elapsed_time_minutes = (time.time() - start_time_calibration)/60
if elapsed_time_minutes > max_time_minutes:
break
print('\n\n*** ending calibation at',pd.Timestamp.now())
print('elapsed time =',(time.time()-start_time_calibration)/60,' min')
# collect results in a df, then save
df_param_results = pd.DataFrame(data=list_dict_results)
df_param_results.to_pickle(models_directory + 'df_parameter_results.pkl')
df_param_results.to_csv(models_directory + 'df_parameter_results.csv')
list_dict_results.clear()
elif calculation_type == 'production':
# get data
yprod = np.load(data_directory + 'y_prod.npy') # UNALTERED (SEE CREATE_ENSEMBLE)
xprod = np.load(data_directory + 'x_prod_fingerprints_2d.npy')
# reshape
num_pts = xprod.shape[0]
height = xprod[0].shape[0]
width = xprod[0].shape[1]
# height*width = length_of_fingerprint_vector = 2048
xprod = xprod.reshape(num_pts, 1, height, width)
df_results = pd.read_pickle(models_directory + 'df_parameter_results.pkl')
neural_network_ensemble.create_ensemble('regression',
'Mean CV Error', 'Keras',
df_results, number_of_models, models_directory,
results_directory, xprod, yprod, target_divisor)
else:
raise NameError
For the production (unseen data) code, we sort the cross validation results then read in the 10 best models. The final result is the median lipophilicity prediction of these models. See Prediction of Small Molecule Lipophilicity: Part 3 – Ensemble of Multilayer Perceptrons With Morgan (Circular) Fingerprints
