  Ensemble learning is a mainstay in modern data science practice. Conventional
ensemble algorithms assigns to base models a set of deterministic, constant
model weights that (1) do not fully account for variations in base model
accuracy across subgroups, nor (2) provide uncertainty estimates for the
ensemble prediction, which could result in mis-calibrated (i.e. precise but
biased) predictions that could in turn negatively impact the algorithm
performance in real-word applications. In this work, we present an adaptive,
probabilistic approach to ensemble learning using dependent tail-free process
as ensemble weight prior. Given input feature $\mathbf{x}$, our method
optimally combines base models based on their predictive accuracy in the
feature space $\mathbf{x} \in \mathcal{X}$, and provides interpretable
uncertainty estimates both in model selection and in ensemble prediction. To
encourage scalable and calibrated inference, we derive a structured variational
inference algorithm that jointly minimize KL objective and the model's
calibration score (i.e. Continuous Ranked Probability Score (CRPS)). We
illustrate the utility of our method on both a synthetic nonlinear function
regression task, and on the real-world application of spatio-temporal
integration of particle pollution prediction models in New England.
