In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: We study the problem of Robust Least Squares Regression (RLSR) where several response variables can be adversarially corrupted. More specifically, for a data matrix X Rpn and an underlying model w, the response vector is generated as y = XTw+b where b R is the corruption vector supported over at most C n coordinates. Existing exact recovery results for RLSR focus solely on L1-penalty based convex formulations and impose relatively strict model assumptions such as requiring the corruptions b to be selected independently of X. In this work, we study a simple hard-thresholding algorithm called Torrent which, under mild conditions on X, can recover w exactly even if b corrupts the response variables in an adversarial manner, i.e. both the support and entries of b are selected adversarially after observing X and w. Our results hold under deterministic assumptions which are satisfied if X is sampled from any sub-Gaussian distribution. Finally unlike existing results that apply only to a fixed w, generated independently of X, our results are universal and hold for any w R. Next, we propose gradient descent-based extensions of Torrent that can scale efficiently to large scale problems, such as high dimensional sparse recovery and prove similar recovery guarantees for these extensions. Empirically we find Torrent, and more so its extensions, offering significantly faster recovery than the state-of-the-art L1 solvers. For instance, even on moderate-sized datasets (with p = 50K) with around 40% corrupted responses, a variant of our proposed method called Torrent-HYB is more than 20 faster than the best L1 solver. "If among these errors are some which appear too large to be admissible, then those equations which produced these errors will be rejected, as coming from too faulty experiments, and the unknowns will be determined by means of the other equations, which will then give much smaller errors." A. M. Legendre, On the Method of Least Squares. 1805.

Output: Robust Regression via Hard Thresholding

Input: Consider Input: We envision a machine learning service provider facing a continuous stream of problems with the same input domain, but with output domains that may differ. Clients present the provider with problems implicitly, by labeling a few example inputs, and then ask the provider to train models which reasonably extend their labelings to novel inputs. The provider wants to avoid constraining its users to a set of common labels, so it does not assume any particular correspondence between labels for a new task and labels for previously encountered tasks. To perform well in this setting, the provider needs a representation of the input domain which, in expectation, permits effective models for new problems to be learned efficiently from a small number of examples. While this bears a resemblance to settings considered in previous work on multitask and lifelong learning, our non-assumption of inter-task label correspondence leads to a novel algorithm: Lifelong Learner of Discriminative Representations (LLDR), which explicitly minimizes a proxy for the intra-task small-sample generalization error. We examine the relative benefits of our approach on a diverse set of real-world datasets in three significant scenarios: representation learning, multitask learning and lifelong learning.

Output: Lifelong Learning of Discriminative Representations

Input: Consider Input: Twitter has become one of the main sources of news for many people. As real-world events and emergencies unfold, Twitter is abuzz with hundreds of thousands of stories about the events. Some of these stories are harmless, while others could potentially be lifesaving or sources of malicious rumors. Thus, it is critically important to be able to efficiently track stories that spread on Twitter during these events. In this paper, we present a novel semi-automatic tool that enables users to efficiently identify and track stories about real-world events on Twitter. We ran a user study with 25 participants, demonstrating that compared to more conventional methods, our tool can increase the speed and the accuracy with which users can track stories about real-
Output: A Semi-automatic Method for Efficient Detection of Stories on Social Media