Rough Concept Analysis 
The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak with the theory of Formal Concept Analysis pioneered by Rudolf Wille. The central notion in this paper of a rough formal concept combines in a natural fashion the notion of a rough set with the notion of a formal concept: ‘rough set + formal concept = rough formal concept’. A follow-up paper will provide a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis and Entity-Relationship database modeling. …
Adviser Problem
Humans have an unparalleled visual intelligence and can overcome visual ambiguities that machines currently cannot. Recent works have shown that incorporating guidance from humans during inference for real-world, challenging tasks like viewpoint-estimation and fine-grained classification, can help overcome difficult cases in which the computer-alone would have otherwise failed. These hybrid intelligence approaches are hence gaining traction. However, deciding what question to ask the human in the loop at inference time remains an unknown for these problems. We address this question by formulating it as what we call the Adviser Problem: can we learn a mapping from the input to a specific question to ask the human in the loop so as to maximize the expected positive impact to the overall task? We formulate a solution to the adviser problem using a deep network and apply it to the viewpoint estimation problem where the question asks for the location of a specific keypoint in the input image. We show that by using the keypoint guidance from the Adviser Network and the human, the model is able to outperform the previous hybrid-intelligence state-of-the-art by 3.27%, and outperform the computer-only state-of-the-art by 10.44% absolute. …
Adaptive Huber Regression
Big data are often contaminated by outliers and heavy-tailed errors, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our framework is able to handle heavy-tailed data with bounded $(1 ! + ! \delta)$-th moment for any $\delta!>!0$. We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when $\delta !\geq! 1$, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime $0 !<! \delta !<! 1$ and the transition is smooth and optimal. Moreover, a nonasymptotic Bahadur representation for finite-sample inference is derived when the variance is finite. Numerical experiments lend further support to our obtained theory. …
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