To reduce annotation costs, it is common in crowdsourcing to collect only a few noisy labels from different crowd workers for each instance. However, the limited noisy labels restrict the performance of label integration algorithms in inferring the unknown true label for the instance. Recent works have shown that leveraging neighbor instances can help alleviate this problem. Yet, these works all assume that each instance has the same neighborhood size, which defies common sense. To address this gap, we propose a novel label integration algorithm called K-free nearest neighbor (KFNN). In KFNN, the neighborhood size of each instance is automatically determined based on its attributes and noisy labels.

The success of graph neural networks (GNNs) largely relies on the process of aggregating information from neighbors defined by the input graph structures. Notably, message passing based GNNs, e.g., graph convolutional networks, leverage the immediate neighbors of each node during the aggregation process, and recently, graph diffusion convolution (GDC) is proposed to expand the propagation neighborhood by leveraging generalized graph diffusion. However, the neighborhood size in GDC is manually tuned for each graph by conducting grid search over the validation set, making its generalization practically limited. To address this issue, we propose the adaptive diffusion convolution (ADC) strategy to automatically learn the optimal neighborhood size from the data. Furthermore, we break the conventional assumption that all GNN layers and feature channels (dimensions) should use the same neighborhood for propagation. We design strategies to enable ADC to learn a dedicated propagation neighborhood for each GNN layer and each feature channel, making the GNN architecture fully coupled with graph structures---the unique property that differs GNNs from traditional neural networks. By directly plugging ADC into existing GNNs, we observe consistent and significant outperformance over both GDC and their vanilla versions across various datasets, demonstrating the improved model capacity brought by automatically learning unique neighborhood size per layer and per channel in GNNs.

Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden changes, or "jumps" in the output variable. The "jump GP" (JGP) was developed for modeling data from such processes, combining local GPs and latent "level" variables under a joint inferential framework. But joint modeling can be fraught with difficulty. We aim to simplify by suggesting a more modular setup, eschewing joint inference but retaining the main JGP themes: (a) learning optimal neighborhood sizes that locally respect manifolds of discontinuity; and (b) a new cluster-based (latent) feature to capture regions of distinct output levels on both sides of the manifold. We show that each of (a) and (b) separately leads to dramatic improvements when modeling processes with jumps. In tandem (but without requiring joint inference) that benefit is compounded, as illustrated on real and synthetic benchmark examples from the recent literature.

We introduce Deep Jump Gaussian Processes (DJGP), a novel method for surrogate modeling of high-dimensional piecewise continuous functions. DJGP overcomes the limitations of conventional Jump Gaussian Processes in high-dimensional input spaces by adding a locally linear projection layer to Jump Gaussian Processes. This projection uses region-specific matrices to capture local subspace structures, naturally complementing the localized nature of JGP, a variant of local Gaussian Processes. To control model complexity, we place a Gaussian Process prior on the projection matrices, allowing them to evolve smoothly across the input space. The projected inputs are then modeled with a JGP to capture piecewise continuous relationships with the response. This yields a distinctive two-layer deep learning of GP/JGP. We further develop a scalable variational inference algorithm to jointly learn the projection matrices and JGP hyperparameters. Experiments on synthetic and benchmark datasets demonstrate that DJGP delivers superior predictive accuracy and more reliable uncertainty quantification compared to existing approaches.