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 ∈ Rp×n 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: Ensembling is a well-known technique in neural machine translation (NMT) to improve system performance. Instead of a single neural net, multiple neural nets with the same topology are trained separately, and the decoder generates predictions by averaging over the individual models. Ensembling often improves the quality of the generated translations drastically. However, it is not suitable for production systems because it is cumbersome and slow. This work aims to reduce the runtime to be on par with a single system without compromising the translation quality. First, we show that the ensemble can be unfolded into a single large neural network which imitates the output of the ensemble system. We show that unfolding can already improve the runtime in practice since more work can be done on the GPU. We proceed by describing a set of techniques to shrink the unfolded network by reducing the dimensionality of layers. On JapaneseEnglish we report that the resulting network has the size and decoding speed of a single NMT network but performs on the level of a 3-ensemble system.

Output: Unfolding and Shrinking Neural Machine Translation Ensembles


Input: Consider Input: We explore beyond existing work on learning from demonstration by asking the question: “Can robots learn to teach?”, that is, can a robot autonomously learn an instructional policy from expert demonstration and use it to instruct or collaborate with humans in executing complex tasks in uncertain environments? In this paper we pursue a solution to this problem by leveraging the idea that humans often implicitly decompose a higher level task into several subgoals whose execution brings the task closer to completion. We propose Dirichlet process based non-parametric Inverse Reinforcement Learning (DPMIRL) approach for reward based unsupervised clustering of task space into subgoals. This approach is shown to capture the latent subgoals that a human teacher would have utilized to train a novice. The notion of “action primitive” is introduced as the means to communicate instruction policy to humans in the least complicated manner, and as a computationally efficient tool to segment demonstration data. We evaluate our approach through experiments on hydraulic actuated scaled model of an excavator and evaluate and compare different teaching strategies utilized by the robot.


Output: Can Co-robots Learn to Teach?