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.

Ex 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.

Ex Output:
Robust Regression via Hard Thresholding


Ex Input:
We show that collaborative filtering can be viewed as a sequence prediction problem, and that given this interpretation, recurrent neural networks offer very competitive approach. In particular we study how the long short-term memory (LSTM) can be applied to collaborative filtering, and how it compares to standard nearest neighbors and matrix factorization methods on movie recommendation. We show that the LSTM is competitive in all aspects, and largely outperforms other methods in terms of item coverage and short term predictions.

Ex Output:
Collaborative Filtering with Recurrent Neural Networks


Ex Input:
The increasing diversity of languages used on the web introduces a new level of complexity to Information Retrieval (IR) systems. We can no longer assume that textual content is written in one language or even the same language family. In this paper, we demonstrate how to build massive multilingual annotators with minimal human expertise and intervention. We describe a system that builds Named Entity Recognition (NER) annotators for 40 major languages using Wikipedia and Freebase. Our approach does not require NER human annotated datasets or language specific resources like treebanks, parallel corpora, and orthographic rules. The novelty of approach lies therein using only language agnostic techniques, while achieving competitive performance. Our method learns distributed word representations (word embeddings) which encode semantic and syntactic features of words in each language. Then, we automatically generate datasets from Wikipedia link structure and Freebase attributes. Finally, we apply two preprocessing stages (oversampling and exact surface form matching) which do not require any linguistic expertise. Our evaluation is two fold: First, we demonstrate the system performance on human annotated datasets. Second, for languages where no gold-standard benchmarks are available, we propose a new method, distant evaluation, based on statistical machine translation.

Ex Output:

POLYGLOT-NER: Massive Multilingual Named Entity Recognition