Inherently interpretable position-aware convolutional motif kernel networks for biological sequencing data

Abstract

Artificial neural networks show promising performance in detecting correlations within data that are associated with specific outcomes. However, the black-box nature of such models can hinder the knowledge advancement in research fields by obscuring the decision process and preventing scientist to fully conceptualize predicted outcomes. Furthermore, domain experts like healthcare providers need explainable predictions to assess whether a predicted outcome can be trusted in high stakes scenarios and to help them integrating a model into their own routine. Therefore, interpretable models play a crucial role for the incorporation of machine learning into high stakes scenarios like healthcare. In this paper we introduce Convolutional Motif Kernel Networks, a neural network architecture that involves learning a feature representation within a subspace of the reproducing kernel Hilbert space of the position-aware motif kernel function. The resulting model enables to directly interpret and evaluate prediction outcomes by providing a biologically and medically meaningful explanation without the need for additional post-hoc analysis. We show that our model is able to robustly learn on small datasets and reaches state-of-the-art performance on relevant healthcare prediction tasks. Our proposed method can be utilized on DNA and protein sequences. Furthermore, we show that the proposed method learns biologically meaningful concepts directly from data using an end-to-end learning scheme.

Figure 1

Schematic overview of an CMKN model. Each motif-position pair of the input is projected onto the subspace of the RKHS by the kernel layer. Afterwards, the projected input is classified using one or several linear fully-connected layers.

Figure 2

Evaluation of the interpretation capabilities of CMKN using synthetic data. (a) The matrix shows the embedded motifs (left column) and the motifs learned by CMKN (right column). The first row shows the motif at position 20 which was only embedded into negative sequences. The second row shows the motif at position 80 which was only embedded into positive sequences. (b) Positional feature importance of CMKN on the synthetic data. Each bar shows the derivation from the mean positional feature importance for the corresponding sequence position. Red bars indicate importance for the positive class and blue bars indicate importance for the negative class.

Figure 3

(a) (Global Interpretation): CMKNs can be used for data mining on biological sequences. The ten most important positions learned by the model, together with the top two contributing amino acids, are displayed. The height of the bar plot at each position indicates the normalized feature importance of that position, i.e., the mean position feature importance was subtracted from the feature importance of the specific position. Higher bars indicate more important positions. The importance of each sequence position was calculated as described in “Interpreting a CMKN model” section and peaks were identified using a sliding window approach with a window length of 11. Afterwards, the model’s learned motifs associated with the ten highest peaks were calculated (see “Interpreting a CMKN model” section) and the two amino acids with the highest contribution to these motifs were selected. Positions displayed in red (blue) are associated with the resistant (susceptible) class. (b) (Local Interpretation): We created an exemplary visualization of CMKN’s explanation capabilities. Prediction results of the nelfinavir (NFV) model for three randomly chosen input sequences are visualized by showing the learned top ten positions together with the amino acid occurring at the respective position in the input. For each position, the motif functions of the learned motifs are evaluated to identify the one with the highest ${\ell }_2$-norm on the input (see “Interpreting a CMKN model” section). If the corresponding motif is a learned resistance (susceptibility) associated motif, the position-amino-acid pair is highlighted in red (blue). The height of the bars above each position corresponds to the ${\ell }_2$-norm of the corresponding susceptible (blue) and resistant (red) motif functions (scaled between 0 and 1). For each isolate, the true and predicted label is displayed.