A common challenge faced in practical supervised learning, such as medical image processing and robotic interactions, is that there are plenty of tasks but each task cannot afford to collect enough labeled examples to be learned in isolation. However, by exploiting the similarities across those tasks, one can hope to overcome such data scarcity. Under a canonical scenario where each task is drawn from a mixture of $k$ linear regressions, we study a fundamental question: can abundant small-data tasks compensate for the lack of big-data tasks? Existing second moment based approaches of \cite{2020arXiv200208936K} show that such a trade-off is efficiently achievable, with the help of medium-sized tasks with $\Omega(k^{1/2})$ examples each. However, this algorithm is brittle in two important scenarios.

More specifically, suppose we deal with n linear regression data sets after which we are challenged with a final learning task of linear regression, but the parameters of these "tasks" are not completely unrelated. In particular, suppose there is a prior distribution (with at most k possible outcomes) from which parameters of linear regression (i.e., the linear function and noise's variance) are sampled. The general idea here is that by learning from "different" (yet related) tasks the learner aims to do better on the final task, and the paper's focus is on a theoretically natural setting.

The reviewers uniformly felt that this is an interesting paper and a good contribution to the community.

A common challenge faced in practical supervised learning, such as medical image processing and robotic interactions, is that there are plenty of tasks but each task cannot afford to collect enough labeled examples to be learned in isolation. However, by exploiting the similarities across those tasks, one can hope to overcome such data scarcity. Under a canonical scenario where each task is drawn from a mixture of k linear regressions, we study a fundamental question: can abundant small-data tasks compensate for the lack of big-data tasks? Existing second moment based approaches of \cite{2020arXiv200208936K} show that such a trade-off is efficiently achievable, with the help of medium-sized tasks with \Omega(k {1/2}) examples each. However, this algorithm is brittle in two important scenarios.

Manual annotation of bounding boxes for object detection in digital images is tedious, and time and resource consuming. In this paper, we propose a semi-automatic method for efficient bounding box annotation. The method trains the object detector iteratively on small batches of labeled images and learns to propose bounding boxes for the next batch, after which the human annotator only needs to correct possible errors. We propose an experimental setup for simulating the human actions and use it for comparing different iteration strategies, such as the order in which the data is presented to the annotator. We experiment on our method with three datasets and show that it can reduce the human annotation effort significantly, saving up to 75% of total manual annotation work.