Statistical distances, i.e., discrepancy measures between probability distributions, are ubiquitous in probability theory, statistics and machine learning. To combat the curse of dimensionality when estimating these distances from data, recent work has proposed smoothing out local irregularities in the measured distributions via convolution with a Gaussian kernel. Motivated by the scalability of the smooth framework to high dimensions, we conduct an in-depth study of the structural and statistical behavior of the Gaussian-smoothed $p$-Wasserstein distance $\mathsf{W}_p^{(\sigma)}$, for arbitrary $p\geq 1$. We start by showing that $\mathsf{W}_p^{(\sigma)}$ admits a metric structure that is topologically equivalent to classic $\mathsf{W}_p$ and is stable with respect to perturbations in $\sigma$. Moving to statistical questions, we explore the asymptotic properties of $\mathsf{W}_p^{(\sigma)}(\hat{\mu}_n,\mu)$, where $\hat{\mu}_n$ is the empirical distribution of $n$ i.i.d. samples from $\mu$. To that end, we prove that $\mathsf{W}_p^{(\sigma)}$ is controlled by a $p$th order smooth dual Sobolev norm $\mathsf{d}_p^{(\sigma)}$. Since $\mathsf{d}_p^{(\sigma)}(\hat{\mu}_n,\mu)$ coincides with the supremum of an empirical process indexed by Gaussian-smoothed Sobolev functions, it lends itself well to analysis via empirical process theory. We derive the limit distribution of $\sqrt{n}\mathsf{d}_p^{(\sigma)}(\hat{\mu}_n,\mu)$ in all dimensions $d$, when $\mu$ is sub-Gaussian. Through the aforementioned bound, this implies a parametric empirical convergence rate of $n^{-1/2}$ for $\mathsf{W}_p^{(\sigma)}$, contrasting the $n^{-1/d}$ rate for unsmoothed $\mathsf{W}_p$ when $d \geq 3$. As applications, we provide asymptotic guarantees for two-sample testing and minimum distance estimation. When $p=2$, we further show that $\mathsf{d}_2^{(\sigma)}$ can be expressed as a maximum mean discrepancy.

Learning node representation on dynamically-evolving, multi-relational graph data has gained great research interest. However, most of the existing models for temporal knowledge graph forecasting use Recurrent Neural Network (RNN) with discrete depth to capture temporal information, while time is a continuous variable. Inspired by Neural Ordinary Differential Equation (NODE), we extend the idea of continuum-depth models to time-evolving multi-relational graph data, and propose a novel Temporal Knowledge Graph Forecasting model with NODE. Our model captures temporal information through NODE and structural information through a Graph Neural Network (GNN). Thus, our graph ODE model achieves a continuous model in time and efficiently learns node representation for future prediction. We evaluate our model on six temporal knowledge graph datasets by performing link forecasting. Experiment results show the superiority of our model.

We present EventPlus, a temporal event understanding pipeline that integrates various state-of-the-art event understanding components including event trigger and type detection, event argument detection, event duration and temporal relation extraction. Event information, especially event temporal knowledge, is a type of common sense knowledge that helps people understand how stories evolve and provides predictive hints for future events. EventPlus as the first comprehensive temporal event understanding pipeline provides a convenient tool for users to quickly obtain annotations about events and their temporal information for any user-provided document. Furthermore, we show EventPlus can be easily adapted to other domains (e.g., biomedical domain). We make EventPlus publicly available to facilitate event-related information extraction and downstream applications.

Bayesian optimization is a popular method for optimizing expensive black-box functions. The objective functions of hard real world problems are oftentimes characterized by a fluctuated landscape of many local optima. Bayesian optimization risks in over-exploiting such traps, remaining with insufficient query budget for exploring the global landscape. We introduce Coordinate Backoff Bayesian optimization (CobBO) to alleviate those challenges. CobBO captures a smooth approximation of the global landscape by interpolating the values of queried points projected to randomly selected promising coordinate subspaces. Thus also a smaller query budget is required for the Gaussian process regressions applied over the lower dimensional subspaces. This approach can be viewed as a variant of coordinate ascent, tailored for Bayesian optimization, using a stopping rule for backing off from a certain subspace and switching to another coordinate subset. Additionally, adaptive trust regions are dynamically formed to expedite the convergence, and stagnant local optima are escaped by switching trust regions. Further smoothness and acceleration are achieved by filtering out clustered queried points. Through comprehensive evaluations over a wide spectrum of benchmarks, CobBO is shown to consistently find comparable or better solutions, with a reduced trial complexity compared to the state-of-the-art methods in both low and high dimensions.

The volume of "free" data on the internet has been key to the current success of deep learning. However, it also raises privacy concerns about the unauthorized exploitation of personal data for training commercial models. It is thus crucial to develop methods to prevent unauthorized data exploitation. This paper raises the question: can data be made unlearnable for deep learning models? We present a type of error-minimizing noise that can indeed make training examples unlearnable. Error-minimizing noise is intentionally generated to reduce the error of one or more of the training example(s) close to zero, which can trick the model into believing there is "nothing" to learn from these example(s). The noise is restricted to be imperceptible to human eyes, and thus does not affect normal data utility. We empirically verify the effectiveness of error-minimizing noise in both samplewise and class-wise forms. We also demonstrate its flexibility under extensive experimental settings and practicability in a case study of face recognition. Our work establishes an important first step towards making personal data unexploitable to deep learning models. In recent years, deep learning has had groundbreaking successes in several fields, such as computer vision (He et al., 2016) and natural language processing (Devlin et al., 2018). This is partly attributed to the availability of large-scale datasets crawled freely from the Internet such as ImageNet (Russakovsky et al., 2015) and ReCoRD (Zhang et al., 2018b). Whilst these datasets provide a playground for developing deep learning models, a concerning fact is that some datasets were collected without mutual consent (Prabhu & Birhane, 2020). Personal data has also been unconsciously collected from the Internet and used for training commercial models (Hill, 2020). This has raised public concerns about the "free" exploration of personal data for unauthorized or even illegal purposes.

General Motors (GM) is taking its business to new heights by unveiling a flying self-driving taxi under its Cadillac brand at the Consumer Electronics Show (CES). The American carmaker shared a concept video showcasing a single-seater electric vertical takeoff and landing (eVTOL) aircraft that tops speeds of 56mph. Not only is GM's future taking to the skies, but the video also showed it is heading down the road with a new luxury autonomous shuttle that seats two passengers. The concept vehicles were revealed during the firm's morning remarks at the tech conference that is being held virtually for the first time due to the lingering coronavirus pandemic. General Motors (GM) shared a concept video of two futuristic vehicles under the Cadillac brand.

Vision and language tasks such as Visual Relation Detection and Visual Question Answering benefit from semantic features that afford proper grounding of language. The 3D depth of objects depicted in 2D images is one such feature. However it is very difficult to obtain accurate depth information without learning the appropriate features, which are scene dependent. The state of the art in this area are complex Neural Network models trained on stereo image data to predict depth per pixel. Fortunately, in some tasks, its only the relative depth between objects that is required. In this paper the extent to which semantic features can predict course relative depth is investigated. The problem is casted as a classification one and geometrical features based on object bounding boxes, object labels and scene attributes are computed and used as inputs to pattern recognition models to predict relative depth. i.e behind, in-front and neutral. The results are compared to those obtained from averaging the output of the monodepth neural network model, which represents the state-of-the art. An overall increase of 14% in relative depth accuracy over relative depth computed from the monodepth model derived results is achieved.

This paper presents a computational evolutionary game model to study and understand fraud dynamics in the consumption tax system. Players are cooperators if they correctly declare their value added tax (VAT), and are defectors otherwise. Each player's payoff is influenced by the amount evaded and the subjective probability of being inspected by tax authorities. Since transactions between companies must be declared by both the buyer and seller, a strategy adopted by one influences the other's payoff. We study the model with a well-mixed population and different scale-free networks. Model parameters were calibrated using real-world data of VAT declarations by businesses registered in the Canary Islands region of Spain. We analyzed several scenarios of audit probabilities for high and low transactions and their prevalence in the population, as well as social rewards and penalties to find the most efficient policy to increase the proportion of cooperators. Two major insights were found. First, increasing the subjective audit probability for low transactions is more efficient than increasing this probability for high transactions. Second, favoring social rewards for cooperators or alternative penalties for defectors can be effective policies, but their success depends on the distribution of the audit probability for low and high transactions.

Video sentiment analysis as a decision-making process is inherently complex, involving the fusion of decisions from multiple modalities and the so-caused cognitive biases. Inspired by recent advances in quantum cognition, we show that the sentiment judgment from one modality could be incompatible with the judgment from another, i.e., the order matters and they cannot be jointly measured to produce a final decision. Thus the cognitive process exhibits "quantum-like" biases that cannot be captured by classical probability theories. Accordingly, we propose a fundamentally new, quantum cognitively motivated fusion strategy for predicting sentiment judgments. In particular, we formulate utterances as quantum superposition states of positive and negative sentiment judgments, and uni-modal classifiers as mutually incompatible observables, on a complex-valued Hilbert space with positive-operator valued measures. Experiments on two benchmarking datasets illustrate that our model significantly outperforms various existing decision level and a range of state-of-the-art content-level fusion approaches. The results also show that the concept of incompatibility allows effective handling of all combination patterns, including those extreme cases that are wrongly predicted by all uni-modal classifiers.

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for such 'likelihood-free' algorithms has been lacking. This has made it difficult to compare algorithms and identify their strengths and weaknesses. We set out to fill this gap: We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms including recent approaches employing neural networks and classical Approximate Bayesian Computation methods. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency. Neural network-based approaches generally exhibit better performance, but there is no uniformly best algorithm. We provide practical advice and highlight the potential of the benchmark to diagnose problems and improve algorithms. The results can be explored interactively on a companion website. All code is open source, making it possible to contribute further benchmark tasks and inference algorithms.