Thepresence of multiple structural states in the data represents a major bottleneck in existing processing pipelines, often requiring expert user supervision.

A common approach for solving BSPPs is by using first-order methods, where local gradient information is used to iteratively improve the solution in order to converge to an equilibrium asymptotically.

A common assumption in machine learning is that the training set and test set are drawn from the same distribution [25]. However, this assumption often does not hold in practice when models are deployed in the real world [3, 28]. One common type of distribution shift is label shift, where the conditional distribution p(x|y) is fixed but the label distribution p(y) changes over time.

We also collect official crash reports from the Tennessee DepartmentofTransportation TrafficManagement Centerandmanuallylabelall other potential anomalies inthe dataset.

Large-scale vision-language models such as CLIP (Radford et al., 2021) and ALIGN (Jia et al., 2021) are trained using a multimodal contrastive

We construct two types of testers, exhibiting tradeoffs between sample complexity and computational complexity. Finally, we provide a two-way reduction between testing a subclass of multivariate product distributions and testing univariate distributions,and thereby obtainupper and lower bounds for testingthis subclassof product distributions.