Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space.

Most work on estimating mixture models assumes an iid sampling scheme.

We introduce a practical approach for integrating uncertainty estimation into a class of state-of-the-art neural network methods used for individual-level causal estimates. We show that our methods enable us to deal gracefully with situations of "no-overlap", common in high-dimensional data, where standard applications of causal effect approaches fail.

Spectral clustering is popular among practitioners and theoreticians alike.

However, they often suffer from costly training and inference due to a tremendous amount of computations through neural networks.

We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals how the tensor dimensions (features) interact with each other. However, since the factors are a priori unknown, the corresponding optimization problems are inherently non-convex. The existing guaranteed algorithms which handle this non-convexity incur an irreducible error (bias), and only apply to cases where all factors have the same structure. To this end, we develop a provable algorithm for online structured tensor factorization, wherein one of the factors obeys some incoherence conditions, and the others are sparse. Specifically we show that, under some relatively mild conditions on initialization, rank, and sparsity, our algorithm recovers the factors exactly (up to scaling and permutation) at a linear rate. Complementary to our theoretical results, our synthetic and real-world data evaluations showcase superior performance compared to related techniques.