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For the $h$-finite-element method ($h$-FEM) applied to the Helmholtz equation, the question of how quickly the meshwidth $h$ must decrease with the frequency $k$ to maintain accuracy as $k$ increases has been studied since the mid 80's. Nevertheless, there still do not exist in the literature any $k$-explicit bounds on the relative error of the FEM solution (the measure of the FEM error most often used in practical applications), apart from in one dimension. The main result of this paper is the sharp result that, for the lowest fixed-order conforming FEM (with polynomial degree, $p$, equal to one), the condition "$h^2 k^3$ sufficiently small" is sufficient for the relative error of the FEM solution in 2 or 3 dimensions to be controllably small (independent of $k$) for scattering of a plane wave by a nontrapping obstacle and/or a nontrapping inhomogeneous medium. We also prove relative-error bounds on the FEM solution for arbitrary fixed-order methods applied to scattering by a nontrapping obstacle, but these bounds are not sharp for $p\geq 2$. A key ingredient in our proofs is a result describing the oscillatory behaviour of the solution of the plane-wave scattering problem, which we prove using semiclassical defect measures.

In recent years, knowledge graph embedding becomes a pretty hot research topic of artificial intelligence and plays increasingly vital roles in various downstream applications, such as recommendation and question answering. However, existing methods for knowledge graph embedding can not make a proper trade-off between the model complexity and the model expressiveness, which makes them still far from satisfactory. To mitigate this problem, we propose a lightweight modeling framework that can achieve highly competitive relational expressiveness without increasing the model complexity. Our framework focuses on the design of scoring functions and highlights two critical characteristics: 1) facilitating sufficient feature interactions; 2) preserving both symmetry and antisymmetry properties of relations. It is noteworthy that owing to the general and elegant design of scoring functions, our framework can incorporate many famous existing methods as special cases. Moreover, extensive experiments on public benchmarks demonstrate the efficiency and effectiveness of our framework. Source codes and data can be found at \url{//github.com/Wentao-Xu/SEEK}.

Distributional semantics has had enormous empirical success in Computational Linguistics and Cognitive Science in modeling various semantic phenomena, such as semantic similarity, and distributional models are widely used in state-of-the-art Natural Language Processing systems. However, the theoretical status of distributional semantics within a broader theory of language and cognition is still unclear: What does distributional semantics model? Can it be, on its own, a fully adequate model of the meanings of linguistic expressions? The standard answer is that distributional semantics is not fully adequate in this regard, because it falls short on some of the central aspects of formal semantic approaches: truth conditions, entailment, reference, and certain aspects of compositionality. We argue that this standard answer rests on a misconception: These aspects do not belong in a theory of expression meaning, they are instead aspects of speaker meaning, i.e., communicative intentions in a particular context. In a slogan: words do not refer, speakers do. Clearing this up enables us to argue that distributional semantics on its own is an adequate model of expression meaning. Our proposal sheds light on the role of distributional semantics in a broader theory of language and cognition, its relationship to formal semantics, and its place in computational models.

We present a new clustering method in the form of a single clustering equation that is able to directly discover groupings in the data. The main proposition is that the first neighbor of each sample is all one needs to discover large chains and finding the groups in the data. In contrast to most existing clustering algorithms our method does not require any hyper-parameters, distance thresholds and/or the need to specify the number of clusters. The proposed algorithm belongs to the family of hierarchical agglomerative methods. The technique has a very low computational overhead, is easily scalable and applicable to large practical problems. Evaluation on well known datasets from different domains ranging between 1077 and 8.1 million samples shows substantial performance gains when compared to the existing clustering techniques.

This paper addresses the problem of stylized text generation in a multilingual setup. A version of a language model based on a long short-term memory (LSTM) artificial neural network with extended phonetic and semantic embeddings is used for stylized poetry generation. The quality of the resulting poems generated by the network is estimated through bilingual evaluation understudy (BLEU), a survey and a new cross-entropy based metric that is suggested for the problems of such type. The experiments show that the proposed model consistently outperforms random sample and vanilla-LSTM baselines, humans also tend to associate machine generated texts with the target author.

Multilingual topic models enable crosslingual tasks by extracting consistent topics from multilingual corpora. Most models require parallel or comparable training corpora, which limits their ability to generalize. In this paper, we first demystify the knowledge transfer mechanism behind multilingual topic models by defining an alternative but equivalent formulation. Based on this analysis, we then relax the assumption of training data required by most existing models, creating a model that only requires a dictionary for training. Experiments show that our new method effectively learns coherent multilingual topics from partially and fully incomparable corpora with limited amounts of dictionary resources.

Multilingual topic models enable document analysis across languages through coherent multilingual summaries of the data. However, there is no standard and effective metric to evaluate the quality of multilingual topics. We introduce a new intrinsic evaluation of multilingual topic models that correlates well with human judgments of multilingual topic coherence as well as performance in downstream applications. Importantly, we also study evaluation for low-resource languages. Because standard metrics fail to accurately measure topic quality when robust external resources are unavailable, we propose an adaptation model that improves the accuracy and reliability of these metrics in low-resource settings.

Tracking humans that are interacting with the other subjects or environment remains unsolved in visual tracking, because the visibility of the human of interests in videos is unknown and might vary over time. In particular, it is still difficult for state-of-the-art human trackers to recover complete human trajectories in crowded scenes with frequent human interactions. In this work, we consider the visibility status of a subject as a fluent variable, whose change is mostly attributed to the subject's interaction with the surrounding, e.g., crossing behind another object, entering a building, or getting into a vehicle, etc. We introduce a Causal And-Or Graph (C-AOG) to represent the causal-effect relations between an object's visibility fluent and its activities, and develop a probabilistic graph model to jointly reason the visibility fluent change (e.g., from visible to invisible) and track humans in videos. We formulate this joint task as an iterative search of a feasible causal graph structure that enables fast search algorithm, e.g., dynamic programming method. We apply the proposed method on challenging video sequences to evaluate its capabilities of estimating visibility fluent changes of subjects and tracking subjects of interests over time. Results with comparisons demonstrate that our method outperforms the alternative trackers and can recover complete trajectories of humans in complicated scenarios with frequent human interactions.

We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.

Context: Topic modeling finds human-readable structures in unstructured textual data. A widely used topic modeler is Latent Dirichlet allocation. When run on different datasets, LDA suffers from "order effects" i.e. different topics are generated if the order of training data is shuffled. Such order effects introduce a systematic error for any study. This error can relate to misleading results;specifically, inaccurate topic descriptions and a reduction in the efficacy of text mining classification results. Objective: To provide a method in which distributions generated by LDA are more stable and can be used for further analysis. Method: We use LDADE, a search-based software engineering tool that tunes LDA's parameters using DE (Differential Evolution). LDADE is evaluated on data from a programmer information exchange site (Stackoverflow), title and abstract text of thousands ofSoftware Engineering (SE) papers, and software defect reports from NASA. Results were collected across different implementations of LDA (Python+Scikit-Learn, Scala+Spark); across different platforms (Linux, Macintosh) and for different kinds of LDAs (VEM,or using Gibbs sampling). Results were scored via topic stability and text mining classification accuracy. Results: In all treatments: (i) standard LDA exhibits very large topic instability; (ii) LDADE's tunings dramatically reduce cluster instability; (iii) LDADE also leads to improved performances for supervised as well as unsupervised learning. Conclusion: Due to topic instability, using standard LDA with its "off-the-shelf" settings should now be depreciated. Also, in future, we should require SE papers that use LDA to test and (if needed) mitigate LDA topic instability. Finally, LDADE is a candidate technology for effectively and efficiently reducing that instability.