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.

Q: This article describes the systems jointly submitted by Institute for Infocomm (IR), the Laboratoire d’Informatique de l’Universit du Maine (LIUM), Nanyang Technology University (NTU) and the University of Eastern Finland (UEF) for 2015 NIST Language Recognition Evaluation (LRE). The submitted system is a fusion of nine sub-systems based on i-vectors [1] extracted from different types of features. Given the i-vectors, several classifiers are adopted for the language detection task including support vector machines (SVM) [2], multi-class logistic regression (MCLR), Probabilistic Linear Discriminant Analysis (PLDA) [3] and Deep Neural Networks (DNN).

A: Fantastic 4 system for NIST 2015 Language Recognition Evaluation
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Q: We consider relative error low rank approximation of tensors with respect to the Frobenius norm. Namely, given an order-q tensor A ∈ R ∏q i=1 ni , output a rank-k tensor B for which ‖A − B‖F ≤ (1 + ) OPT, where OPT = infrank-k A′ ‖A − A‖F . Despite much success on obtaining relative error low rank approximations for matrices, no such results were known for tensors. One structural issue is that there may be no rank-k tensor Ak achieving the above infinum. Another, computational issue, is that an efficient relative error low rank approximation algorithm for tensors would allow one to compute the rank of a tensor, which is NP-hard. We bypass these two issues via (1) bicriteria and (2) parameterized complexity solutions: 1. We give an algorithm which outputs a rank k′ = O((k/ )q−1) tensor B for which ‖A − B‖F ≤ (1+ ) OPT in nnz(A)+n ·poly(k/ ) time in the real RAM model, whenever either Ak exists or OPT > 0. Here nnz(A) denotes the number of non-zero entries in A. If both Ak does not exist and OPT = 0, then B instead satisfies ‖A − B‖F < γ, where γ is any positive, arbitrarily small function of n. 2. We give an algorithm for any δ > 0 which outputs a rank k tensor B for which ‖A−B‖F ≤ (1+ ) OPT and runs in (nnz(A)+n poly(k/ )+exp(k/ )) ·nδ time in the unit cost RAM model, whenever OPT > 2−O(n ) and there is a rank-k tensor B = ∑k i=1 ui ⊗ vi ⊗ wi for which ‖A − B‖F ≤ (1 + /2) OPT and ‖ui‖2, ‖vi‖2, ‖wi‖2 ≤ 2 δ). If OPT ≤ 2−Ω(nδ), then B instead satisfies ‖A−B‖F ≤ 2−Ω(n δ). Our first result is polynomial time, and in fact input sparsity time, in n, k, and 1/ , for any k ≥ 1 and any 0 < < 1, while our second result is fixed parameter tractable in k and 1/ . For outputting a rank-k tensor, or even a bicriteria solution with rank-Ck for a certain constant C > 1, we show a 2 1−o(1)) time lower bound under the Exponential Time Hypothesis. Our results are based on an “iterative existential argument”, and give the first relative error low rank approximations for tensors for a large number of error measures for which nothing was known. In particular, we give the first relative error approximation algorithms on tensors for: column row and tube subset selection, entrywise `p-low rank approximation for 1 ≤ p < 2, low rank approximation with respect to sum of Euclidean norms of faces or tubes, weighted low rank approximation, and low rank approximation in distributed and streaming models. We also obtain several new results for matrices, such as nnz(A)-time CUR decompositions, improving the previous nnz(A) log n-time CUR decompositions, which may be of independent interest. ∗Work done while visiting IBM Almaden, and supported in part by UTCS TAship (CS361 Spring 17 Introduction to Computer Security). †Supported in part by Simons Foundation, and NSF CCF-1617955. ar X iv :1 70 4. 08 24 6v 1 [ cs .D S] 2 6 A pr 2 01 7

A: Relative Error Tensor Low Rank Approximation
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Q: Syntax-Guided Synthesis (SyGuS) is the computational problem of finding an implementation f that meets both a semantic constraint given by a logical formula φ in a background theory T , and a syntactic constraint given by a grammar G, which specifies the allowed set of candidate implementations. Such a synthesis problem can be formally defined in SyGuS-IF, a language that is built on top of SMT-LIB. The Syntax-Guided Synthesis Competition (SyGuS-Comp) is an effort to facilitate, bring together and accelerate research and development of efficient solvers for SyGuS by providing a platform for evaluating different synthesis techniques on a comprehensive set of benchmarks. In this year’s competition we added a new track devoted to programming by examples. This track consisted of two categories, one using the theory of bit-vectors and one using the theory of strings. This paper presents and analyses the results of SyGuS-Comp’16.

A:
SyGuS-Comp 2016: Results and Analysis
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