instruction:
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.
question:
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.
answer:
Robust Regression via Hard Thresholding


question:
Recent research shows that deep neural networks (DNNs) can be used to extract deep speaker vectors (d-vectors) that preserve speaker characteristics and can be used in speaker verification. This new method has been tested on text-dependent speaker verification tasks, and improvement was reported when combined with the conventional i-vector method. This paper extends the d-vector approach to semi textindependent speaker verification tasks, i.e., the text of the speech is in a limited set of short phrases. We explore various settings of the DNN structure used for d-vector extraction, and present a phone-dependent training which employs the posterior features obtained from an ASR system. The experimental results show that it is possible to apply d-vectors on semi text-independent speaker recognition, and the phone-dependent training improves system performance.
answer:
Deep Speaker Vectors for Semi Text-independent Speaker Verification


question:
Recurrent neural networks scale poorly due to the intrinsic difficulty in parallelizing their state computations. For instance, the forward pass computation of ht is blocked until the entire computation of ht−1 finishes, which is a major bottleneck for parallel computing. In this work, we propose an alternative RNN implementation by deliberately simplifying the state computation and exposing more parallelism. The proposed recurrent unit operates as fast as a convolutional layer and 5-10x faster than cuDNN-optimized LSTM. We demonstrate the unit’s effectiveness across a wide range of applications including classification, question answering, language modeling, translation and speech recognition. We open source our implementation in PyTorch and CNTK1.
answer:

Training RNNs as Fast as CNNs