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.

The right to be forgotten calls for efficient machine unlearning techniques that make trained machine learning models forget a cohort of data.

We present an approach that eliminates this problem.

There has been a great empirical progress in robust training of neural networks against noisy labels.

It suggests that, for any m { k,...,n 1 } and z R, L A.2 Proofs for Lemma 2 and 3 for the case when K is unknown in 4 Lemma 2 . It suggests that, for any m { 0,...,n 1 } and z R, L For any m { 0,...,n 1 } and z R, we have L A.3 Additional tricks for methods proposed in 3. Finding optimal CP vector when z = in paraCP(n,k, ˆ T Additional pruning condition for parametric DP when K is fixed. In 3.3, we showed that Lemma 4. F orn [ N ], and k [ K ], let T Therefore, it fails to control the false positive rate. This is asymptotic test for multiple detected CPs. Fused Lasso (proposed by the same authors), is worse than BinSeg-SI. BinSeg-SI had been considered as a computationally efficient approximation of the problem in (7), where the authors additionally condition on extra information for computational tractability, e.g., the order that CPs are detected.

How would you go about checking if this proof is correct? One cumbersome way would be to directly refute the proof's claim, e.g., to demonstrate that actually