We develop a simple and unified framework for nonlinear variable importance estimation that incorporates uncertainty in the prediction function and is compatible with a wide range of machine learning models (e.g., tree ensembles, kernel methods, neural networks, etc). In particular, for a learned nonlinear model $f(\mathbf{x})$, we consider quantifying the importance of an input variable $\mathbf{x}^j$ using the integrated partial derivative $\Psi_j = \Vert \frac{\partial}{\partial \mathbf{x}^j} f(\mathbf{x})\Vert^2_{P_\mathcal{X}}$. We then (1) provide a principled approach for quantifying uncertainty in variable importance by deriving its posterior distribution, and (2) show that the approach is generalizable even to non-differentiable models such as tree ensembles. Rigorous Bayesian nonparametric theorems are derived to guarantee the posterior consistency and asymptotic uncertainty of the proposed approach. Extensive simulations and experiments on healthcare benchmark datasets confirm that the proposed algorithm outperforms existing classical and recent variable selection methods.

Cancer stem cells (CSCs) actively reprogram their tumor microenvironment (TME) to sustain a supportive niche, which may have a dramatic impact on prognosis and immunotherapy. However, our knowledge of the landscape of the gastric cancer stem-like cell (GCSC) microenvironment needs to be further improved. A multi-step process of machine learning approaches was performed to develop and validate the prognostic and predictive potential of the GCSC-related score (GCScore). The high GCScore subgroup was not only associated with stem cell characteristics, but also with a potential immune escape mechanism. Furthermore, we experimentally demonstrated the upregulated infiltration of CD206+ tumor-associated macrophages (TAMs) in the invasive margin region, which in turn maintained the stem cell properties of tumor cells. Finally, we proposed that the GCScore showed a robust capacity for prediction for immunotherapy, and investigated potential therapeutic targets and compounds for patients with a high GCScore. The results indicate that the proposed GCScore can be a promising predictor of prognosis and responses to immunotherapy, which provides new strategies for the precision treatment of GCSCs.