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Gaussian mixtures are commonly used for modeling heavy-tailed error distributions in robust linear regression. Combining the likelihood of a multivariate robust linear regression model with a standard improper prior distribution yields an analytically intractable posterior distribution that can be sampled using a data augmentation algorithm. When the response matrix has missing entries, there are unique challenges to the application and analysis of the convergence properties of the algorithm. Conditions for geometric ergodicity are provided when the incomplete data have a “monotone” structure. In the absence of a monotone structure, an intermediate imputation step is necessary for implementing the algorithm. In this case, we provide sufficient conditions for the algorithm to be Harris ergodic. Finally, we show that, when there is a monotone structure and intermediate imputation is unnecessary, intermediate imputation slows the convergence of the underlying Monte Carlo Markov chain, while post hoc imputation does not. An R package for the data augmentation algorithm is provided. 

Quantum materials (QMs) with strong correlation and nontrivial topology are indispensable to next-generation information and computing technologies. Exploitation of topological band structure is an ideal starting point to realize correlated topological QMs. Here, we report that strain-induced symmetry modification in correlated oxide SrNbO 3 thin films creates an emerging topological band structure. Dirac electrons in strained SrNbO 3 films reveal ultrahigh mobility (μ max ≈ 100,000 cm 2 /Vs), exceptionally small effective mass ( m * ~ 0.04 m e ), and nonzero Berry phase. Strained SrNbO 3 films reach the extreme quantum limit, exhibiting a sign of fractional occupation of Landau levels and giant mass enhancement. Our results suggest that symmetry-modified SrNbO 3 is a rare example of correlated oxide Dirac semimetals, in which strong correlation of Dirac electrons leads to the realization of a novel correlated topological QM. 

Multi-task learning has been widely adopted in many computer vision tasks to improve overall computation efficiency or boost the performance of individual tasks, under the assumption that those tasks are correlated and complementary to each other. However, the relationships between the tasks are complicated in practice, especially when the number of involved tasks scales up. When two tasks are of weak relevance, they may compete or even distract each other during joint training of shared parameters, and as a consequence undermine the learning of all the tasks. This will raise destructive interference which decreases learning efficiency of shared parameters and lead to low quality loss local optimum w.r.t. shared parameters. To address the this problem, we propose a general modulation module, which can be inserted into any convolutional neural network architecture, to encourage the coupling and feature sharing of relevant tasks while disentangling the learning of irrelevant tasks with minor parameters addition. Equipped with this module, gradient directions from different tasks can be enforced to be consistent for those shared parameters, which benefits multi-task joint training. The module is end-to-end learnable without ad-hoc design for specific tasks, and can naturally handle many tasks at the same time. We apply our approach on two retrieval tasks, face retrieval on the CelebA dataset [1] and product retrieval on the UT-Zappos50K dataset [2, 3], and demonstrate its advantage over other multi-task learning methods in both accuracy and storage efficiency.