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.
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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 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.

Answer: Robust Regression via Hard Thresholding

Question: We introduce an abductive method for a coherent integration of independent datasources. The idea is to compute a list of data-facts that should be inserted to the amalgamated database or retracted from it in order to restore its consistency. This method is implemented by an abductive solver, called Asystem, that applies SLDNFA-resolution on a meta-theory that relates different, possibly contradicting, input databases. We also give a pure model-theoretic analysis of the possible ways to 'recover' consistent data from an inconsistent database in terms of those models of the database that exhibit as minimal inconsistent information as reasonably possible. This allows us to characterize the 'recovered databases' in terms of the 'preferred' (i.e., most consistent) models of the theory. The outcome is an abductive-based application that is sound and complete with respect to a corresponding model-based, preferential semantics, and to the best of our knowledge is more expressive (thus more general) than any other implementation of coherent integration of databases.

Answer: Coherent Integration of Databases by Abductive Logic Programming

Question: Most recent work focused on affect from facial expressions, and not as much on body. This work focuses on body affect analysis. Affect does not occur in isolation. Humans usually couple affect with an action in natural interactions; for example, a person could be talking and smiling. Recognizing body affect in sequences requires efficient algorithms to capture both the micro movements that differentiate between happy and sad and the macro variations between different actions. We depart from traditional approaches for time-series data analytics by proposing a multi-task learning model that learns a shared representation that is well-suited for action-affect classification as well as generation. For this paper we choose Conditional Restricted Boltzmann Machines to be our building block. We propose a new model that enhances the CRBM model with a factored multi-task component to become Multi-Task Conditional Restricted Boltzmann Machines (MTCRBMs). We evaluate our approach on two publicly available datasets, the Body Affect dataset and the Tower Game dataset, and show superior classification performance improvement over the state-of-the-art, as well as the generative abilities of our model.

Answer:
Action-Affect Classification and Morphing using Multi-Task Representation Learning