Data assimilation algorithms combine information from observations and prior model information to obtain the most likely state of a dynamical system. The linearised weak-constraint four-dimensional variational assimilation problem can be reformulated as a saddle point problem, which admits more scope for preconditioners than the primal form. In this paper we design new terms which can be used within existing preconditioners, such as block diagonal and constraint-type preconditioners. Our novel preconditioning approaches: (i) incorporate model information, and (ii) are designed to target correlated observation error covariance matrices. To our knowledge (i) has not previously been considered for data assimilation problems. We develop new theory demonstrating the effectiveness of the new preconditioners within Krylov subspace methods. Linear and non-linear numerical experiments reveal that our new approach leads to faster convergence than existing state-of-the-art preconditioners for a broader range of problems than indicated by the theory alone. We present a range of numerical experiments performed in serial.
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In proof-theoretic semantics, meaning is based on inference. It may seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a `base' of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT , K4, and S4, with $\square$ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between $\square$ and a natural presentation of $\lozenge$. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases.
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from having them made separately for each problem via a machine learning model. This study reports lessons on such use of machine learning in symbolic computation, in particular on the importance of analysing datasets prior to machine learning and on the different machine learning paradigms that may be utilised. We present results for a particular case study, the selection of variable ordering for cylindrical algebraic decomposition, but expect that the lessons learned are applicable to other decisions in symbolic computation. We utilise an existing dataset of examples derived from applications which was found to be imbalanced with respect to the variable ordering decision. We introduce an augmentation technique for polynomial systems problems that allows us to balance and further augment the dataset, improving the machine learning results by 28\% and 38\% on average, respectively. We then demonstrate how the existing machine learning methodology used for the problem $-$ classification $-$ might be recast into the regression paradigm. While this does not have a radical change on the performance, it does widen the scope in which the methodology can be applied to make choices.
Receiver operating characteristic (ROC) analysis is widely used for evaluating diagnostic systems. Recent studies have shown that estimating an area under ROC curve (AUC) with standard cross-validation methods suffers from a large bias. The leave-pair-out (LPO) cross-validation has been shown to correct this bias. However, while LPO produces an almost unbiased estimate of AUC, it does not provide a ranking of the data needed for plotting and analyzing the ROC curve. In this study, we propose a new method called tournament leave-pair-out (TLPO) cross-validation. This method extends LPO by creating a tournament from pair comparisons to produce a ranking for the data. TLPO preserves the advantage of LPO for estimating AUC, while it also allows performing ROC analyses. We have shown using both synthetic and real world data that TLPO is as reliable as LPO for AUC estimation, and confirmed the bias in leave-one-out cross-validation on low-dimensional data. As a case study on ROC analysis, we also evaluate how reliably sensitivity and specificity can be estimated from TLPO ROC curves.
Due to the ability of modeling relationships between two different types of entities, bipartite graphs are naturally employed in many real-world applications. Community Search in bipartite graphs is a fundamental problem and has gained much attention. However, existing studies focus on measuring the structural cohesiveness between two sets of vertices, while either completely ignoring the edge attributes or only considering one-dimensional importance in forming communities. In this paper, we introduce a novel community model, named edge-attributed skyline community (ESC), which not only preserves the structural cohesiveness but unravels the inherent dominance brought about by multi-dimensional attributes on the edges of bipartite graphs. To search the ESCs, we develop an elegant peeling algorithm by iteratively deleting edges with the minimum attribute in each dimension. In addition, we also devise a more efficient expanding algorithm to further reduce the search space and speed up the filtering of unpromising vertices, where a upper bound is proposed and proven. Extensive experiments on real-world large-scale datasets demonstrate the efficiency, effectiveness, and scalability of the proposed ESC search algorithms. A case study was conducted to compare with existing community models, substantiating that our approach facilitates the precision and diversity of results.
Mobile app repositories have been largely used in scientific research as large-scale, highly adaptive crowdsourced information systems. These software platforms can potentially nourish multiple software and requirements engineering tasks based on user reviews and other natural language documents, including feedback analysis, recommender systems and topic modelling. Consequently, researchers often endeavour to overcome domain-specific challenges, including integration of heterogeneous data sources, large-scale data collection and adaptation of a publicly available data set for a given research scenario. In this paper, we present MApp-KG, a combination of software resources and data artefacts in the field of mobile app repositories to support extended knowledge generation tasks. Our contribution aims to provide a framework for automatically constructing a knowledge graph modelling a domain-specific catalogue of mobile apps. Complementarily, we distribute MApp-KG in a public triplestore and as a static data snapshot, which may be promptly employed for future research and reproduction of our findings.
Ultra-wideband (UWB) time-difference-of-arrival (TDOA)-based localization has emerged as a promising, low-cost, and scalable indoor localization solution, which is especially suited for multi-robot applications. However, there is a lack of public datasets to study and benchmark UWB TDOA positioning technology in cluttered indoor environments. We fill in this gap by presenting a comprehensive dataset using Decawave's DWM1000 UWB modules. To characterize the UWB TDOA measurement performance under various line-of-sight (LOS) and non-line-of-sight (NLOS) conditions, we collected signal-to-noise ratio (SNR), power difference values, and raw UWB TDOA measurements during the identification experiments. We also conducted a cumulative total of around 150 minutes of real-world flight experiments on a customized quadrotor platform to benchmark the UWB TDOA localization performance for mobile robots. The quadrotor was commanded to fly with an average speed of 0.45 m/s in both obstacle-free and cluttered environments using four different UWB anchor constellations. Raw sensor data including UWB TDOA, inertial measurement unit (IMU), optical flow, time-of-flight (ToF) laser altitude, and millimeter-accurate ground truth robot poses were collected during the flights. The dataset and development kit are available at //utiasdsl.github.io/util-uwb-dataset/.
Conventional entity typing approaches are based on independent classification paradigms, which make them difficult to recognize inter-dependent, long-tailed and fine-grained entity types. In this paper, we argue that the implicitly entailed extrinsic and intrinsic dependencies between labels can provide critical knowledge to tackle the above challenges. To this end, we propose \emph{Label Reasoning Network(LRN)}, which sequentially reasons fine-grained entity labels by discovering and exploiting label dependencies knowledge entailed in the data. Specifically, LRN utilizes an auto-regressive network to conduct deductive reasoning and a bipartite attribute graph to conduct inductive reasoning between labels, which can effectively model, learn and reason complex label dependencies in a sequence-to-set, end-to-end manner. Experiments show that LRN achieves the state-of-the-art performance on standard ultra fine-grained entity typing benchmarks, and can also resolve the long tail label problem effectively.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.
Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.
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