Active Causal Learning for Decoding Chemical Complexities with Targeted Interventions

TL;DR

We address cross-dataset generalization in molecular design by embedding cause–effect reasoning into an active learning framework. The method reconstructs a global causal graph $\mathcal{G}_{\rho}$ from a minimal subset $\mathcal{D}_{AL}$ using a graph loss $\mathcal{L}$ based on adjacency spectral distances and LinGAM-based causal discovery. Applied to QM9 to design molecules with dipole moment above $3$ Debye, the approach combines causal feature selection, active sampling, and targeted interventions to identify design principles and generate near-neighbor candidates with desirable properties, achieving efficient reconstruction of structure–property relations and enabling targeted design beyond the training region. The framework enables real-time, autonomous exploration of chemical space by focusing on underlying structure–property causality and is applicable to broader molecular design tasks beyond the specific QM9 case. It thus offers a principled path toward interpretable, data-efficient molecular design and discovery.

Abstract

Predicting and enhancing inherent properties based on molecular structures is paramount to design tasks in medicine, materials science, and environmental management. Most of the current machine learning and deep learning approaches have become standard for predictions, but they face challenges when applied across different datasets due to reliance on correlations between molecular representation and target properties. These approaches typically depend on large datasets to capture the diversity within the chemical space, facilitating a more accurate approximation, interpolation, or extrapolation of the chemical behavior of molecules. In our research, we introduce an active learning approach that discerns underlying cause-effect relationships through strategic sampling with the use of a graph loss function. This method identifies the smallest subset of the dataset capable of encoding the most information representative of a much larger chemical space. The identified causal relations are then leveraged to conduct systematic interventions, optimizing the design task within a chemical space that the models have not encountered previously. While our implementation focused on the QM9 quantum-chemical dataset for a specific design task-finding molecules with a large dipole moment-our active causal learning approach, driven by intelligent sampling and interventions, holds potential for broader applications in molecular, materials design and discovery.

Figures (13)

• Figure 1: Overview of workflow: Illustration outlining the key steps of the active causal learning approach, which involves constructing a minimal dataset to encapsulate maximal information about molecular structures and properties. This is followed by the active learning of causal relations for the entire dataset, facilitating targeted molecular design.
• Figure 2: Causal discovery and property prediction in different regions of chemical space. (A) Feature distributions for different subsets. (B) Test $R^2$ and parity plots for a random forest model trained on $\mathcal{D}_1$, $\mathcal{D}_2$, $\mathcal{D}_3$ (left to right). Insets show the corresponding adjacency matrix of the nine downselected features, where green colors signify positive causal relations and pink/purple signify negative relations. Full causal graphs are given in the Appendix.
• Figure 3: Active learning to recover causal relations. (A) Average and one standard deviation of the graph distance (upper) between the global graph, $\mathcal{G}_\rho$ and the graph of the candidate data set $\mathcal{G}_{\rm AL}$ at each iteration of the active learning algorithm (red) and for randomly selected data (black). (B) Visualization of the adjacency matrices corresponding to $\mathcal{G}_{\rm AL}$ at different iterations and the global DAG $\mathcal{G}_\rho$. (C) The number of times each data subset was selected during the active learning procedure. (D) $R^2$ on test data throughout the active learning experiment. The dashed line corresponds to the value when all data is used. (E) Densities of the ECFPs for the entire dataset projected onto its first two principle components and samples from each data subset (scatter plots).
• Figure 4: (A) Overview of the method. The $\mathcal{D}_{\rm AL}$ and its associated causal structure is used to find molecular interventions that drive the dipole to the prescribed value. We then search a reference dataset for the molecules which are most similar to the intervened features, shown in the right panel. (B) Scatter plot of the structural similarity between each molecule in $\mathcal{D}_{\rm AL}$ and the reference dataset and the distance in feature space between the intervened molecules and reference molecules. (C) Dipole moments in the original (red) and intervened (blue) datasets. The dipole moments of the closest-to-intervened molecules are show in the pink histogram.
• Figure 5: The effect of the interventions in chemical space. The red heatmap is the density of molecules in $\mathcal{D}_{\rm AL}$ projected onto the first two principal components of their ECFPs. Black squares indicate individual molecules from $\mathcal{D}_{\rm AL}$. Green circles indicate the closest reference to the intervened molecules. Two example molecules from $\mathcal{D}_{\rm AL}$ and the closest reference molecules are shown on the right