Causal effect identification considers whether an interventional probability distribution can be uniquely determined from a passively observed distribution in a given causal structure.

The variability of what "similar" means in this context, which transformations are allowed, and whether data points themselves or their feature representations

In particular, torsional diffusion does not address the longstanding difficulty that existing cheminformatics methods have with macrocycles--rings with 12 or more atoms that have found several applications in drug discovery [Driggers et al., 2008].

Moreover, when adopting our method to various tasks including part segmentation and standard 2D image classification, our method achieves competitive performance.

However, the leap in performance often comes at the cost of large-scale labeled data.

Estimating the probabilities of connections between vertices in a random network using an observed adjacency matrix is an important task for network data analysis. Many existing estimation methods are based on certain assumptions on network structure, which limit their applicability in practice. Without making strong assumptions, we develop an iterative connecting probability estimation method based on neighborhood averaging. Starting at a random initial point or an existing estimate, our method iteratively updates the pairwise vertex distances, the sets of similar vertices, and connecting probabilities to improve the precision of the estimate. We propose a two-stage neighborhood selection procedure to achieve the trade-off between smoothness of the estimate and the ability to discover local structure. The tuning parameters can be selected by cross-validation. We establish desirable theoretical properties for our method, and further justify its superior performance by comparing with existing methods in simulation and real data analysis.

To incorporate 3D information completely and efficiently, we propose a novel message passing scheme that operates within 1-hop neighborhood.