Predicting chemical ecotoxicity by learning latent space chemical representations

Abstract

In silico prediction of chemical ecotoxicity (HC₅₀) represents an important complement to improve in vivo and in vitro toxicological assessment of manufactured chemicals. Recent application of machine learning models to predict chemical HC₅₀ yields variable prediction performance that depends on effectively learning chemical representations from high-dimension data. To improve HC₅₀ prediction performance, we developed an autoencoder model by learning latent space chemical embeddings. This novel approach achieved state-of-the-art prediction performance of HC₅₀ with R² of 0.668 ± 0.003 and mean absolute error (MAE) of 0.572 ± 0.001, and outperformed other dimension reduction methods including principal component analysis (PCA) (R² = 0.601 ± 0.031 and MAE = 0.629 ± 0.005), kernel PCA (R² = 0.631 ± 0.008 and MAE = 0.625 ± 0.006), and uniform manifold approximation and projection dimensionality reduction (R² = 0.400 ± 0.008 and MAE = 0.801 ± 0.002). A simple linear layer with chemical embeddings learned from the autoencoder model performed better than random forest (R² = 0.663 ± 0.007 and MAE = 0.591 ± 0.008), fully connected neural network (R² = 0.614 ± 0.016 and MAE = 0.610 ± 0.008), least absolute shrinkage and selection operator (R² = 0.617 ± 0.037 and MAE = 0.619 ± 0.007), and ridge regression (R² = 0.638 ± 0.007 and MAE = 0.613 ± 0.005) using unlearned raw input features. Our results highlighted the usefulness of learning latent chemical representations, and our autoencoder model provides an alternative approach for robust HC₅₀ prediction.

1. Introduction

Evaluating chemical ecotoxicity (HC₅₀) is a valuable approach to identify potential hazardous effects of chemicals on ecosystems and is of great interest in academic and regulatory communities. The traditional gold standard for determining HC₅₀ uses in vivo animal models, but such approaches present challenges in the face of rapid increases in the number of chemicals manufactured each year and ethical concerns related to intentional exposure of animals to toxic chemicals (Xia et al., 2008). To circumvent these concerns, the US federal initiative proposed high-throughput in vitro chemical screening to efficiently identify hazardous compounds (Toxicology in the 21st Century, TOX21) (National Research Council, 2007). However, this approach requires laborintensive laboratory procedures that cannot keep pace with the manufacturing of new chemicals. In addition, current in vitro methods cannot capture complex effects such as endocrine effects and have limited ability to predict toxicity in in vivo systems through invitro to in vivo extrapolation models (Chang et al., 2015; Laue et al., 2020). Hence, selected chemicals must also go through in vivo animal testing to determine HC₅₀, highlighting the importance of chemical screening.

One approach to improve screening efficiency and minimize the number of chemicals needed for in vivo animal testing is using in silico models to predict chemical toxicity (e.g., effective concentration 50% [EC50] and lethal concentration 50% [LC₅₀]). Previous studies predicted chemical acute toxicity based on Abraham parameters and mode of action (MoA) for a diverse set of compounds using quantitative structure-activity relationship (QSAR) models (Barron et al., 2015; Boone and Di Toro, 2019a,b). Barron et al. (2015) used interspecies correlation estimation models to estimate EC/LC₅₀ values; Boone and Di Toro (2019a,b) utilized a target site model to predict chemical acute toxicity to aquatic organisms based on polyparameter linear free energy relationship. However, traditional QSAR models are usually linear; such models are not effective in capturing more complex, nonlinear relationships (Cherkasov et al., 2014; Gramatica, 2007; Hou et al., 2020b; Tropsha et al., 2003).

Recent developments in machine learning models can overcome the limitations of traditional predictive models for chemical ecotoxicity and reactivity prediction (Hou et al., 2020a; Hou et al., 2020b; Mansouri et al., 2021; Raza et al., 2019; Su and Rajan, 2021), which is increasingly valuable in the ever-expanding chemical database. Hou et al. (2020a) applied multiple machine learning models to predict HC₅₀ values for 2307 chemicals based on 14 chemical features. Hou et al. (2020b) further developed genetic algorithm optimized neural network models to predict HC⁵⁰ based on 691 calculated chemical features on a dataset of 1815 chemicals. Takata et al. (2020) classified chemicals into four Verhaar schema class categories from the ecological structure–activity relationship (ECOSAR) model and predicted chemical class with ensemble learning methods. Additionally, Raza et al. (2019) used fully connected neural network (FCNN) models to predict C-F energies in per- and poly-fluoroalkyl substances (PFAS). Yao et al. (2021) developed a variational autoencoder model for the design of nanoporous crystalline reticular materials, which is a generative model that outputs parameters of a pre-defined distribution in the latent space. These studies mostly focused on supervised learning tasks (e.g., classification or regression) and achieved better prediction accuracy than traditional QSAR methods. Additionally, unsupervised models such as t-distributed stochastic neighbor embedding (t-SNE) were used to explore patterns in a PFAS dataset based on chemical properties (Raza et al., 2019; Su and Rajan, 2021). Further developments in machine learning can offer a promising opportunity to develop new predictive models in this field.

In general, the success of machine learning and deep learning algorithms heavily depends on data representations (features) to which they are applied (Bengio et al., 2013; LeCun et al., 2015). Representation learning refers to learning data representations by extracting useful information from input features. Although machine learning models benefit from learning complicated relationships from enormous input features, redundant features may introduce noises and result in poor model performance – known as the curse of dimensionality (Bellman, 2015). Indeed, the curse of dimensionality is a significant challenge in developing machine learning models with high-dimension data, leading to increased errors with increasing number of features (Bellman, 2015).

The curse of dimensionality can be mitigated through dimensionality reduction, which reduces the number of features while maintaining useful information (Bengio et al., 2013). In general, dimensionality reduction methods fall into linear and nonlinear groups. Commonly used linear dimensionality reduction methods include factor analysis and principal component analysis (PCA). Linear methods, however, often do not work well for data with intrinsic nonlinear relationships because it is difficult to successfully embed nonlinear data in the latent space. Nonlinear relationships are instead addressed through nonlinear dimensionality reduction methods such as multidimensional scaling (MDS) (Mead, 1992), t-SNE (Van der Maaten and Hinton, 2008), and uniform manifold approximation and projection (UMAP) (McInnes et al., 2018). However, these nonlinear dimensionality reduction methods are designed to preserve a predefined pairwise distance or local/global structures rather than learning meaningful data representations and are mainly used for visualization purposes.

A novel alternative is to learn low-dimension latent space representations through autoencoders (Bengio et al., 2007; Vincent et al., 2008). Autoencoder is an unsupervised representation learning method that can perform nonlinear dimensionality reduction. Instead of aiming to preserve distances or local structures, it learns latent space embeddings. These embeddings contain representations of data that are more meaningful or comprehensive than predefined distances. An autoencoder consists of a pair of encoder and decoder that can be parameterized by neural networks (Fig. 1). The encoder reduces the high-dimension input features to lower-dimension embeddings, while the decoder reconstructs the input features from the lower-dimension embeddings. This process enables the reduction of dimension by compressing data and noises, while preserving essential information for feature reconstruction. The low-dimensional space embeddings are learned from data and retrieved by minimizing the reconstruction loss. Then, the learned latent space embeddings can be used for various downstream tasks, e.g., supervised classification or regression tasks and unsupervised clustering. Other machine learning models, such as FCNN, do not have this encoding-decoding process (Figure S1). Thus, an autoencoder model is trained through reconstruction loss, while FCNN is trained through prediction loss.

Fig. 1. Schematic of the autoencoder model.

Dark blue nodes are input features, green nodes are generated embeddings, and light blue nodes are output layers. HC₅₀ is predicted using one linear layer.

In this study, we developed an autoencoder model to learn chemical latent space representations and predict HC₅₀ from the in vivo USEtox database containing 1815 chemicals and their 691 chemical features. Our autoencoder model can perform nonlinear dimensionality reduction through the encoding-decoding process to account for the intrinsic nonlinearity in data and learn meaningful representation of chemical features, which is different from other linear and non-linear methods such as PCA, MDS and UMAP as well as other machine learning models using raw input features. Specifically, we aimed to utilize this model to learn low-dimension latent space representations of chemicals for dimensionality reduction and denoising to alleviate the curse of dimensionality and to improve the prediction accuracy of HC₅₀ by machine learning.

2. Materials and methods

2.1. Data

USEtox is a scientific consensus model for evaluating human and ecotoxicological effects of chemicals. USEtox produces a database of chemical hazard concentrations or chemical ecotoxicity (HC₅₀) from the geometric mean of EC₅₀ (effect concentration 50%, i.e., the concentration of a chemical when 50% of its maximal effect is observed) and LC₅₀ (lethal concentration 50%, i.e., the concentration of chemical at which 50% of a group died during observation period) (Fantke et al., 2017; Hou et al., 2020b; Rosenbaum et al., 2008). Hou et al. (2020b) calculated input features for 1815 chemicals from USEtox (11 physiochemical properties), U.S. Environmental Protection Agency Toxicity Estimation Software Tool (797 theoretical descriptors), and QikProp (51 physically and pharmaceutically significant properties), and assigned the classification of MoA of chemicals by Verhaar scheme using software ToxTree, resulting in 860 input variables. Hou et al. (2020b) further removed 169 highly uncertain and duplicate variables and obtained 691 final input features. The names and sources of the 691 input features were listed in the Supplementary Material B as a feature glossary. The abundant number of chemical features enables the model to learn chemical embeddings. We therefore followed the same inclusion criteria as Hou et al. (2020b) and collected the HC₅₀ value of 1815 chemicals and the corresponding 691 features. Dataset was provided in Supplementary Material B.

2.2. Autoencoder

Autoencoder is an unsupervised deep learning model that can be used to compress input data and learn low-dimension latent space embeddings. Our autoencoder model takes 691 features as input, produces the learned chemical embeddings, and predicts the HC₅₀ values. The model learns latent space representation of the input features by compressing them into low-dimensional space, and the learned latent space embeddings are then used to reconstruct the input features. This encoding-decoding process keeps essential information within the low-dimensional space while other less important information is compressed. Specifically, our autoencoder comprises two parts: an encoder that learns a lower dimension embedding of each chemical based on their 691 input features, and a decoder that reconstructs the input features (Fig. 1). For the selection of hidden units, number of layers and the activation function, we tested multiple architectures with different activation functions including ReLU, Sigmoid, and Tanh. The encoder gradually reduces the input dimensions, so we gradually reduced the number of neurons in each encoder layer. The architectures that were evaluated included 691-128-691, 691-256-128-256-691, 691-128-64-128-691, 691-512-256-128-256-512-691, 691-512-256-128-64-128-256-512-691, and 691-512-n-512-691 (the number of neurons, n = 2, 16, 32, 64, 128, or 256). Detailed prediction performances were summarized in Table S1 of Supplementary Material A. Based on the numerical results of these model architectures, the best-performing current architecture (i.e., 691-512-128-512-691) was selected. ReLU is a widely used activation function that is useful to solve the gradient vanishing problem of Sigmoid and Tanh functions (Agarap, 2018; Glorot et al., 2011; Yarotsky, 2017). Indeed, the ReLU activation function had the best performance (Table S1). In summary, our encoder consists of three fully connected layers, with an input layer of 691 neurons, a hidden layer of 512 neurons and an embedding layer of 128 neurons that is capable of reducing the feature dimension to 128. The decoder contains two fully connected layers with one hidden layer of 512 neurons and an output layer of 691 neurons. By forcing the encoder to reduce the dimensions of input features and to learn the embeddings of each sample, we used the learned embeddings to predict HC₅₀.

To validate the effectiveness of the learned embeddings, we input the learned embeddings into a simple linear layer for the prediction of HC₅₀ (Fig. 1). Although a more complex neural network with multiple hidden layers and nonlinear activations can be used, a simple linear layer for prediction can better reflect the representative power of learned chemical embeddings. Thus, our autoencoder consists of two processes, i.e., the encoding-decoding process that learns chemical embeddings, and the prediction process using learned embeddings to predict HC₅₀. These two processes were trained jointly. For the encoding-decoding (reconstruction) process, we utilized the reconstruction loss defined as $los{s}_{reconstruction}=\frac{1}{n}{\sum }_1^n(Featur{e}_{i,input}-Featur{e}_{i,reconstructed}{)}^2$, which measured the differences between the reconstructed and original features. For the prediction process, we introduced the prediction loss term quantified as $los{s}_{predicition}=\frac{1}{n}{\sum }_{i=1}^n(HC{50}_{i,predicted}-HC{50}_{i,measured}{)}^2$. The prediction loss measured the differences between the predicted HC₅₀ value and the measured HC₅₀ value. Hence the total loss was defined as $los{s}_{total}=los{s}_{reconstruction}+los{s}_{predicition}$. The autoencoder was trained using the Adam optimizer, with L2 regularization weight 0.0005. Evaluation of the trained model on the validation set was performed every 200 epochs and was only tested on the test set if the validation results were improved, which was used to avoid overfitting. We set a maximum of 1500 epochs for training (the optimal epochs were usually observed between 200 and 800 epochs), and a learning rate of 1E-3.

2.3. Chemical embedding visualization

To interpret and evaluate the quality of learned embeddings, we first visualized the learned latent space embeddings under their t-SNE coordinates (Van der Maaten and Hinton, 2008). T-SNE provides a tool to visualize high-dimensional data (Van der Maaten and Hinton, 2008). It embeds the local structure of the data and tends to extract clustered local groups of samples. This method converts similarities between data points to joint probabilities and tries to minimize the Kullback-Leibler divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data, and thus can be used to discover patterns in the data without knowing any HC₅₀ values in advance. In the t-SNE plot, chemicals with similar embeddings were near each other, and the HC₅₀ value of each chemical was colored with brighter color for greater HC₅₀ value and with darker color for lower HC₅₀ values (Fig. 2). We also colored the embeddings under the t-SNE coordinates with MoA since it is an important determinant of chemical toxicity (Barron et al., 2015; Boone and Di Toro, 2019a).

Fig. 2. Embedding size comparison of the autoencoder models.

Embedding layer size of a) 2; b) 16; c) 32; d) 64; e) 128; and f) 256 neurons.

2.4. Other dimension reduction methods and models

For comparison, we tested multiple popular dimensionality reduction methods including PCA, UMAP, kernel PCA, factor analysis, and MDS. We also applied several popular machine learning methods (LASSO, Ridge regression, RF and FCNN) using original 691 features and compared their performances with that of our autoencoder model.

2.4.1. Principle component analysis (PCA) and kernel PCA

PCA is a linear dimensionality reduction method that projects the input features onto a lower dimensional space with a set of orthogonal components and captures the majority of variance (Wold et al., 1987). Kernel PCA is an extension of PCA that achieves nonlinear dimensionality reduction through the use of kernels (Mika et al., 1998; Schölkopf et al., 1997). Here, we used radial basis function (RBF) kernel. We reduced the input feature dimensions to 128 using PCA and kernel PCA.

2.4.2. Uniform manifold approximation and projection (UMAP)

UMAP is a dimension reduction technique that can be used for visualization similar to t-SNE, but also for general nonlinear dimension reduction. UMAP constructs a high-dimensional graph representation of the data, and then optimizes a low-dimensional graph to be as structurally similar as possible. UMAP ensures that local structure is preserved in balance with global structure. McInnes et al. (2018) described the mathematics of UMAP. We reduced the input feature dimensions to 128 using UMAP.

2.4.3. Factor analysis

Factor analysis assumes that the observed variables are linear transformations of lower-dimensional latent factors with additional Gaussian noises. This method yields a maximum likelihood estimate of the loading matrix, through which latent variables can be transformed to the observed variables using singular value decomposition based approach (Barber, 2012; Kim and Mueller, 1978). We reduced the feature dimension to 128 using factor analysis.

2.4.4. Multidimensional scaling (MDS)

MDS achieves dimensionality reduction aimed to approximate the distances in the original high-dimensional space. General application of MDS is to analyze similarity or dissimilarity in data modeled as distances in a geometric space (Mead, 1992). We reduced the input features to 128 dimensions using MDS.

2.4.5. Least absolute shrinkage and selection operator (LASSO) and ridge regression

Mathematically, LASSO consists of a linear regression model with an added L1 regularization term. The objective function to minimize is:

$$\underset{w}{min}\mid \mid Xw-y\mid {\mid }_2^2+\alpha \mid \mid w\mid {\mid }_1$$

Similarly, ridge regression adds an L2 regularization term to the common ordinary least square objective function:

$$\underset{w}{min}\mid \mid Xw-y\mid {\mid }_2^2+\alpha \mid \mid w\mid {\mid }_2^2$$

Here, w are the weights of the linear regression model, and α controls the regularization strength.

2.4.6. Random forest (RF)

RF is an ensemble learning method that fits multiple decision trees on various subset of the dataset and averages results from each individual tree to improve the predictive accuracy and control over-fitting. RF previously performed best among six machine learning models and five traditional models for predicting HC₅₀ based on 14 chemical properties (Hou et al., 2020a). We built a RF model and carefully tuned hyperparameters including max features (suggested by scikit-learn package: ‘auto’, ‘sqrt’, ‘log2’) and number of trees (100, 200, 300, 500, 1000).

2.4.7. Fully connected neural network (FCNN)

FCNN consists of an input layer that takes the input features (i.e., chemicals,), multiple hidden layers, and finally an output layer that makes final predictions of HC₅₀. Nonlinear activation functions are usually used between hidden layers. Each layer contains multiple neurons, with each neuron calculated as:

$$y=f\left(b+{\sum }_{i=1}^n{w}_i{x}_i\right)$$

where f is the activation function, w_i is the weight, b is bias and x_i is the i – th input to this neuron. FCNN can learn complex non linear relationships between input features and predicted targets. Here, we developed an FCNN model with one hidden layer. ReLU activation was used between layers. Parameters in the model were updated through optimizing the loss function $los{s}_{predicition}=\frac{1}{n}{\sum }_{i=1}^n(HC{50}_{i,predicted}-HC{50}_{i,measured}{)}^2$. The Adam optimizer was used to update the weights through back propagation. For the FCNN model, we used one hidden layer with 512 hidden units and ReLU activation to compare with our HC₅₀ prediction using a linear layer without activation functions based on the learned embeddings from the autoencoder.

2.4.8. Ecological structure activity relationships (ECOSAR) predictive model evaluation

The ECOSAR software can be downloaded from the website of US EPA (USEPA, 2022). The software runs on Microsoft Windows systems. We input the CAS ID as batches to the ECOSAR model and extracted the calculated EC₅₀ values across different species. We then obtained HC₅₀ values by calculating the geometric mean of EC₅₀ across multiple species. All chemicals in our dataset that have predictions in ECOSAR were used (N = 1728) to evaluate the performance of ECOSAR model.

2.5. Applicability domain

The applicability domain of our trained model can be decided by calculating a distance $\mathrm{d}=\sqrt{{\sum }_{i=1}^n{\left({\text{property}}_{\text{i,j}}-\overline{{\text{property}}_{\mathrm{j}}}\right)}^2}$, where $\overline{propert{y}_j}=\frac{1}{n}{\sum }_{i=1}^{n}propert{y}_{i,j}$. Hence, d measures the distance between a new chemical and the center of the training dataset based on their physiochemical properties and theoretical molecular descriptors. This distance can be calculated when our model is applied to a new chemical to decide if it is in or outside of the application domain.

2.6. Hyperparameter tuning and model validation

We used five-fold cross-validation for hyperparameter tuning and model validation. Five-fold cross-validation enables the maximum efficiency in model selection and learning time (Hawkins et al., 2003; King et al., 2021). The dataset was randomly shuffled into five equivalent subsets. Each subset was used as an independent test set and taken out during the training process. Models were then trained using the remaining four subsets of data. To fine-tune the model and select the best parameter combinations, 12.5% of the training data (10% of the full dataset) were used as a validation subset; the remaining 87.5% of the training data (70% of full dataset) were used to train the model. The best parameter sets were retrieved by examining the performance of trained models on the validation set. The best combination of hyperparameters was then used to build the model that was tested on the held-out test subset. Each subset was therefore tested once. The final prediction results were averaged based on the performances on the five test sets. Finally, our model performance was evaluated by three criteria: R², mean absolute error (MAE), and root mean squared error (RMSE). R² is defined as $R^2(y,\widehat{y})=1-\frac{{\sum }_{i=1}^n{\left(y_i-\widehat{y}\right)}^2}{{\sum }_{i=1}^n{\left(y_i-\overline{\mathrm{y}}\right)}^2}$, where $\widehat{y}$ is the predicted HC₅₀ value of i-th sample, y_i is the corresponding true value, and $\overline{y}=\frac{1}{n}{\sum }_{i=1}^n{y}_i$. MAE is defined as $\text{MAE}(y,\widehat{y})=\frac{1}{n}{\sum }_{i=1}^n\mid y_i-{\widehat{y}}_{\mathrm{i}}\mid$ and RMSE is defined as $\text{RMSE}=\sqrt{\frac{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left(y_i-\widehat{y_i}\right)}^2}{n}}$. We also computed the standard deviation (±) of each model by repeating the above process five times.

The autoencoder and other models were implemented with PyTorch and scikit-learn. All data and python scripts are available at Github repository: https://github.com/YikeShen. Machine and model run time were listed in Supplementary Material A Table S2.

3. Results and discussion

3.1. Comparison of embedding sizes on HC₅₀ prediction

Autoencoder model can compress input feature dimensions without losing essential information. The embedding size must be optimized to avoid redundant features or losing essential information (Hinton and Salakhutdinov, 2006). Therefore, we compared different embedding sizes (i.e., 2, 16, 32, 64, 128, and 256) for optimal model selection. An embedding size of 128 achieved the best performance, with R² of 0.668 ± 0.003, MAE of 0.572 ± 0.001, and RMSE of 0.781 ± 0.005 (Fig. 2). Using a larger embedding size of 256 resulted in a slightly worse performance with R² of 0.667 ± 0.007, MAE of 0.571 ± 0.005, and RMSE of 0.778 ± 0.009 (Fig. 2). Yet, the performance also declined with decreasing embedding size from 128 to 2 (embedding size 64: R² = 0.657 ± 0.009, MAE = 0.576 ± 0.006, RMSE = 0.790 ± 0.013; embedding size 32: R² = 0.650 ± 0.007, MAE = 0.581 ± 0.009, and RMSE = 0.800 ± 0.008; embedding size 16: R² = 0.634 ± 0.006, MAE = 0.595 ± 0.007, and RMSE = 0.816 ± 0.008) (Fig. 2). At an embedding size of 2, the R² was 0.632 ± 0.007, with MAE of 0.599 ± 0.005 and RMSE of 0.820 ± 0.008 (Fig. 2). While smaller embedding sizes provided highly concentrated information of chemical features, additional features allowed the autoencoder model to achieve better performance. Therefore, we used an embedding size of 128 in this study.

3.2. Representation of chemicals in low-dimensional latent space

Our autoencoder model effectively learned useful chemical embeddings in low-dimensional latent space to predict HC₅₀. To examine the quality of the generated embeddings, we visualized the embeddings under their t-SNE coordinates colored by HC₅₀ values (Fig. 3a) and MoA (Fig. 3b). The embeddings themselves reflected the patterns of HC₅₀ values, with each point representing one of the chemicals in the dataset (Fig. 3a). Chemicals with similar embeddings should be near each other and thus share similar HC₅₀ values. There was a clear pattern of change from smaller HC₅₀ values (darker color) to larger HC₅₀ values (brighter color). The ability to reflect HC₅₀ values based on the learned chemical embeddings suggests that our autoencoder method is effective in learning low-dimension latent space representations of chemical HC₅₀. In Fig. 3b, chemicals acting by a specific mechanism (Class 4) were clustered in blue in the right region, corresponding to lower HC₅₀ values in Fig. 3a. On the other hand, inert chemicals (Class 1) had higher HC₅₀ values and were mostly clustered in green in the left region, separated from Class 4 chemicals. As expected, unclassifiable chemicals (Class 5) had a scattered distribution.

Fig. 3. Visualization of chemical embeddings in t-SNE coordinates.

a) t-SNE colored on HC₅₀ (brighter color represents greater HC₅₀ values); b) t-SNE colored on Mode of Action (Class 1 = inert chemicals, Class 2 = less inert chemicals, Class 3 = reactive chemicals, Class 4 = chemicals acting by a specific mechanism, and Class 5 = unclassifiable chemicals).

3.3. Autoencoder dimension reduction compared to PCA, kernel PCA, UMAP, factor analysis, and MDS

The effectiveness of the learned chemical embeddings from the autoencoder in terms of dimension reduction and denoising was demonstrated by predicting HC₅₀. For comparison, we predicted HC₅₀ values using a simple linear regression model in the autoencoder, factor analysis, PCA, kernel PCA, UMAP, and MDS (Fig. 4 and Figure S2). The average prediction accuracy of the autoencoder method had an R² of 0.668 ± 0.003. For other methods, the R² values were 0.601 ± 0.031 and 0.631 ± 0.008 for the 128 PCA and kernel PCA features, respectively, and 0.400 ± 0.008 for the 128 UMAP features (Fig. 4). In addition, the R² values for factor analysis and MDS were 0.577 ± 0.003 and 0.505 ± 0.007, respectively (Figure S2). The MAE of the autoencoder method was smaller (0.572 ± 0.001) than those of PCA (0.629 ± 0.005) and kernel PCA (0.625 ± 0.006) as well as that of UMAP (0.801 ± 0.002), factor analysis (0.680 ± 0.003), and MDS (0.731 ± 0.003). Similarly, the RMSE ranked as follows: autoencoder (0.781 ± 0.005), kernel PCA128 (0.827 ± 0.008), PCA128 (0.860 ± 0.036), factor analysis (0.886 ± 0.003), MDS (0.957 ± 0.006), and UMAP128 (1.055 ± 0.007). Thus, the autoencoder method performed better than other methods because it benefitted from learning the latent space representation of chemicals from the data. We further colored the results according to chemical types (i.e., acid, base, neutral, or amphoter) and calculated the MAE for each chemical type in the autoencoder model. The MAE was similar for neutral (green), base (orange), and acid (brown) compounds (i.e., 0.56, 0.57, and 0.59, respectively). However, the MAE (0.69) was slightly worse for amphoter (blue) compounds, probably due to more complex mechanisms of amphoters. Additionally, the autoencoder results were colored by MoA (Fig. 5), and the MAE was calculated for each MoA. The MAE was lower for Class 1 chemicals (0.41) and Class 2 chemicals (0.43). However, prediction was more challenging for more toxic chemicals, with larger MAE for Class 3 chemicals (0.60) and Class 4 chemicals (0.72). Finally, the MAE for Class 5 (unclassified chemicals) was 0.63 (Fig. 5).

Fig. 4. Comparison of different dimensionality reduction methods and machine learning models.

a) Autoencoder; b) PCA based on top 128 features; c) kernel PCA based on top 128 features; d) UMAP based on top 128 features; e) random forest (RF) model; f) fully connected neural network (FCNN) model; g) LASSO regression; h) ridge regression. Red lines are 1:1 plots (y = x) indicating predicted HC₅₀ values equal to measured HC₅₀ values. Green = neutral chemicals; orange = base chemicals; brown = acid chemicals; blue = amphoter chemicals.

Fig. 5. Autoencoder model results colored by Mode of Action.

(Class 1 = inert chemicals; Class 2 = less inert chemicals; Class 3 = reactive chemicals; Class 4 = chemicals acting by a specific mechanism; and Class 5 = unclassifiable chemicals).

3.4. Autoencoder compared with LASSO, ridge regression, random forest, and FCNN

Next, we compared our autoencoder model with other common machine learning models including LASSO, ridge regression, RF, and FCNN with the cross-validation procedure identical to that of the autoencoder method. The performance of RF (R² = 0.663 ± 0.007, MAE = 0.591 ± 0.008, and RMSE = 0.790 ± 0.009) was slightly poorer than that of the autoencoder model (R² = 0.668 ± 0.003, MAE = 0.572 ± 0.001, and RMSE = 0.781 ± 0.005) (Fig. 4). Although the R² value of the RF model was comparable to that of the autoencoder model, its MAE and RMSE were worse. Notably, the prediction of the autoencoder method was solely based on one simple linear layer in contrast with a RF model. The performance of the FCNN with one hidden layer (R² = 0.614 ± 0.016, MAE = 0.610 ± 0.008, and RMSE = 0.839 ± 0.016) was inferior to that of the autoencoder model. Our autoencoder model also outperformed popular linear models LASSO (R² = 0.617 ± 0.037, MAE = 0.619 ± 0.007, RMSE = 0.842 ± 0.039) and ridge regression (R² = 0.638 ± 0.007, MAE = 0.613 ± 0.005, RMSE = 0.819 ± 0.009) (Fig. 4). These results further highlighted the benefit of HC₅₀ prediction based on learning chemical embeddings rather than on raw chemical properties.

3.5. Autoencoder compared with other methods from the literature

Hou et al. (2020b) used genetic algorithm optimized neural network models to predict HC₅₀ and achieved an R² of 0.63 (Table 1). However, Hou et al. (2020b) randomly sampled test data instead of using cross-validation for the whole dataset to test every data point. Notably, fair comparison of different approaches should use the same dataset and validation methods. Our dataset matched that of Hou et al. (2020b), so we compared our results to theirs by matching validation procedures. Using the same validation procedures as Hou et al. (2020b), our autoencoder model yielded an R² of 0.67 (almost identical to that of the five-fold cross validation procedure) (Table 1). Thus, our approach was stable for different validation methods. Another study by Hou et al. (2020a) used a different input dataset with only 14 input features, precluding direct comparison of their results with the results of this study. We also directly predicted the HC₅₀ values using ECOSAR software (R² = 0.23), which had a much poorer performance than other tested models (Table1).

Table 1.

The coefficient of determination (R²) for the HC₅₀ prediction using other methods from the literature.

Method	Chemical numbers	Feature numbers	R2
ECOSAR	1728	NA	0.23
Random forest model (Hou et al., 2020a)	2307	14	0.63
*Genetic algorithm optimized neural network model (Hou et al., 2020b)	1815	691	0.63
*Autoencoder model with random sampling	1815	691	0.67

^*Results that can be compared. These results used the same dataset and validation method (random sampling).

3.6. Management implications

Effective use of machine learning approaches in management of chemical risks requires transparent and accessible communication of model development and results interpretation to stakeholders. Since machine learning methods are complex and not readily accessible to all stakeholders, such communication can be very challenging, but could be aided by flow diagrams, comparison with benchmark models (e.g., QSAR and other models), and selective use as screening tools. Additionally, with the ability to learn from complex high-dimensional data, the autoencoder approach may be useful to predict chronic and more subtle endpoints that drive management and market decisions. For example, the lowest observed effect concentration may be predicted for chemicals used in products to assist the Safer Choice Program in EPA Ecolabeling.

4. Conclusion

Overcoming challenges and limitations in in silico prediction of chemical ecotoxicity could provide valuable new approaches to identifying chemical hazards. This study developed an autoencoder model for predicting the HC₅₀ values. This autoencoder model can perform nonlinear dimensionality reduction and learn informative latent space chemical representations from input data, providing a unique way of processing redundant, high-dimension input data that is different from other methods such as PCA, MDS and UMAP. These learned chemical representations can achieve significant dimension reduction, supporting their use for more accurately predicting chemical ecotoxicity compared to methods directly using raw input features.

Abbreviations:

HC₅₀

hazardous concentration 50%

EC₅₀

effective concentration 50%

LC₅₀

lethal concentration 50%

MoA

mode of action

QSAR

quantitative structure-activity

PCA

principal component analysis

MDS

multidimensional scaling

UMAP

uniform manifold approximation and projection

t-SNE

t-distributed stochastic neighbor embedding

LASSO

least absolute shrinkage and selection operator

RF

random forest

FCNN

fully connected neural network

ECOSAR

ecological structure-activity relationship

MAE

mean absolute error

RMSE

root mean squared error