We introduce the convolutional spectral kernel (CSK), a novel family of interpretable and non-stationary kernels derived from the convolution of two imaginary radial basis functions. We propose the input-frequency spectrogram as a novel tool to analyze nonparametric kernels as well as the kernels of deep Gaussian processes (DGPs). Observing through the lens of the spectrogram, we shed light on the interpretability of deep models, along with useful insights for effective inference. We also present scalable variational and stochastic Hamiltonian Monte Carlo inference to learn rich, yet interpretable frequency patterns from data using DGPs constructed via covariance functions. Empirically we show on simulated and real-world datasets that CSK extracts meaningful non-stationary periodicities.

Vacant taxi drivers' passenger seeking process in a road network generates additional vehicle miles traveled, adding congestion and pollution into the road network and the environment. This paper aims to employ a Markov Decision Process (MDP) to model idle e-hailing drivers' optimal sequential decisions in passenger-seeking. Transportation network companies (TNC) or e-hailing (e.g., Didi, Uber) drivers exhibit different behaviors from traditional taxi drivers because e-hailing drivers do not need to actually search for passengers. Instead, they reposition themselves so that the matching platform can match a passenger. Accordingly, we incorporate e-hailing drivers' new features into our MDP model. We then use 44,160 Didi drivers' 3-day trajectories to train the model. To validate the effectiveness of the model, a Monte Carlo simulation is conducted to simulate the performance of drivers under the guidance of the optimal policy, which is then compared with the performance of drivers following one baseline heuristic, namely, the local hotspot strategy. The results show that our model is able to achieve a 26% improvement over the local hotspot strategy in terms of the rate of return. The proposed MDP model captures the supply-demand ratio considering the fact that the number of drivers in this study is sufficiently large and thus the number of unmatched orders is assumed to be negligible. To better incorporate the competition among multiple drivers into the model, we have also devised and calibrated a dynamic adjustment strategy of the order matching probability.

It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to the set that baseline methods cannot solve, and proposes mixtures of stochastic vector fields as a model class that is capable of solving these essential problems. Dynamic vector field selection is of critical importance for our model, and our approach is to propagate component uncertainty over the integration interval with a technique based on forward filtering. We also formalise several loss functions that encourage desirable properties on the trajectory paths, and of particular interest are those that directly encourage fewer expected function evaluations. Experimentally, we demonstrate that our model class is capable of capturing the natural dynamics of human behaviour; a notoriously volatile application area.

Many real-world applications involve multivariate, geo-tagged time series data: at each location, multiple sensors record corresponding measurements. For example, air quality monitoring system records PM2.5, CO, etc. The resulting time-series data often has missing values due to device outages or communication errors. In order to impute the missing values, state-of-the-art methods are built on Recurrent Neural Networks (RNN), which process each time stamp sequentially, prohibiting the direct modeling of the relationship between distant time stamps. Recently, the self-attention mechanism has been proposed for sequence modeling tasks such as machine translation, significantly outperforming RNN because the relationship between each two time stamps can be modeled explicitly. In this paper, we are the first to adapt the self-attention mechanism for multivariate, geo-tagged time series data. In order to jointly capture the self-attention across multiple dimensions, including time, location and the sensor measurements, while maintain low computational complexity, we propose a novel approach called Cross-Dimensional Self-Attention (CDSA) to process each dimension sequentially, yet in an order-independent manner. Our extensive experiments on four real-world datasets, including three standard benchmarks and our newly collected NYC-traffic dataset, demonstrate that our approach outperforms the state-of-the-art imputation and forecasting methods. A detailed systematic analysis confirms the effectiveness of our design choices.

In this work we describe a new learning-based proof guidance -- ENIGMAWatch -- for saturation-style first-order theorem provers. ENIGMAWatch combines two guiding approaches for the given-clause selection implemented for the E ATP system: ProofWatch and ENIGMA. ProofWatch is motivated by the watchlist (hints) method and based on symbolic matching of multiple related proofs, while ENIGMA is based on statistical machine learning. The two methods are combined by using the evolving information about symbolic proof matching as an additional information that characterizes the saturation-style proof search for the statistical learning methods. The new system is experimentally evaluated on a large set of problems from the Mizar Library. We show that the added proof-matching information is considered important by the statistical machine learners, and that it leads to improvements in E's Performance over ProofWatch and ENIGMA.

Background. Most tutorial ontologies focus on illustrating one aspect of ontology development, notably language features and automated reasoners, but ignore ontology development factors, such as emergent modelling guidelines and ontological principles. Yet, novices replicate examples from the exercises they carry out. Not providing good examples holistically causes the propagation of sub-optimal ontology development, which may negatively affect the quality of a real domain ontology. Results. We identified 22 requirements that a good tutorial ontology should satisfy regarding subject domain, logics and reasoning, and engineering aspects. We developed a set of ontologies about African Wildlife to serve as tutorial ontologies. A majority of the requirements have been met with the set of African Wildlife Ontology tutorial ontologies, which are introduced in this paper. The African Wildlife Ontology is mature and has been used yearly in an ontology engineering course or tutorial since 2010 and is included in a recent ontology engineering textbook with relevant examples and exercises. Conclusion. The African Wildlife Ontology provides a wide range of options concerning examples and exercises for ontology engineering well beyond illustrating only language features and automated reasoning. It assists in demonstrating tasks about ontology quality, such as alignment to a foundational ontology and satisfying competency questions, versioning, and multilingual ontologies.

We propose a Bayesian optimization method over sets, to minimize a black-box function that can take a set as single input. Because set inputs are permutation-invariant and variable-length, traditional Gaussian process-based Bayesian optimization strategies which assume vector inputs can fall short. To address this, we develop a Bayesian optimization method with \emph{set kernel} that is used to build surrogate functions. This kernel accumulates similarity over set elements to enforce permutation-invariance and permit sets of variable size, but this comes at a greater computational cost. To reduce this burden, we propose a more efficient probabilistic approximation which we prove is still positive definite and is an unbiased estimator of the true set kernel. Finally, we present several numerical experiments which demonstrate that our method outperforms other methods in various applications.

Knowledge distillation is effective for producing small high-performance neural networks for classification, but these small networks are vulnerable to adversarial attacks. We first study how robustness transfers from robust teacher to student network during knowledge distillation. We find that a large amount of robustness may be inherited by the student even when distilled on only clean images. Second, we introduce Adversarially Robust Distillation (ARD) for distilling robustness onto small student networks. ARD is an analogue of adversarial training but for distillation. In addition to producing small models with high test accuracy like conventional distillation, ARD also passes the superior robustness of large networks onto the student. In our experiments, we find that ARD student models decisively outperform adversarially trained networks of identical architecture on robust accuracy. Finally, we adapt recent fast adversarial training methods to ARD for accelerated robust distillation.

Meta-learning has received a tremendous recent attention as a possible approach for mimicking human intelligence, i.e., acquiring new knowledge and skills with little or even no demonstration. Most of the existing meta-learning methods are proposed to tackle few-shot learning problems such as image and text, in rather Euclidean domain. However, there are very few works applying meta-learning to non-Euclidean domains, and the recently proposed graph neural networks (GNNs) models do not perform effectively on graph few-shot learning problems. Towards this, we propose a novel graph meta-learning framework -- Meta-GNN -- to tackle the few-shot node classification problem in graph meta-learning settings. It obtains the prior knowledge of classifiers by training on many similar few-shot learning tasks and then classifies the nodes from new classes with only few labeled samples. Additionally, Meta-GNN is a general model that can be straightforwardly incorporated into any existing state-of-the-art GNN. Our experiments conducted on three benchmark datasets demonstrate that our proposed approach not only improves the node classification performance by a large margin on few-shot learning problems in meta-learning paradigm, but also learns a more general and flexible model for task adaption.

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found effective. RNN based models usually assume a specific functional form for the time course of the intensity function of a point process (e.g., exponentially decreasing or increasing with the time since the most recent event). However, such an assumption can restrict the expressive power of the model. We herein propose a novel RNN based model in which the time course of the intensity function is represented in a general manner. In our approach, we first model the integral of the intensity function using a feedforward neural network and then obtain the intensity function as its derivative. This approach enables us to both obtain a flexible model of the intensity function and exactly evaluate the log-likelihood function, which contains the integral of the intensity function, without any numerical approximations. Our model achieves competitive or superior performances compared to the previous state-of-the-art methods for both synthetic and real datasets.