Recent evidence indicates that microribonucleic acids (miRNAs) are crucial in modulating drug sensitivity by orchestrating the expression of genes involved in drug metabolism and its pharmacological effects. Existing predictive methods struggle to extract features related to miRNAs and drugs, often overlooking the significance of data noise and the limitations of using a single similarity measure. To address these limitations, we propose an interpretable robust principal component analysis framework (IRPCA). IRPCA enhances the robustness of the model by employing a nonconvex low-rank approximation, thereby offering greater flexibility. Interpretability is ensured by analyzing low-rank matrix decomposition, which clarifies how miRNAs interact with drugs. Gaussian interaction profile kernel (GIPK) similarities are introduced to compute integrated similarities between miRNAs and drugs, addressing the issue of the single similarity feature. IRPCA is subsequently utilized to extract pertinent features, and a fully connected neural network is employed to generate the ultimate prediction scores. To assess the efficacy of IRPCA, we implemented 5-fold cross-validation (CV), which outperformed other leading methods, achieving the highest area under the curve (AUC) value of 0.9653. Additionally, case studies provide additional evidence supporting the efficacy of IRPCA.