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Forecasts crave a rating that reflects the forecast's quality in the context of what is possible in theory and what is reasonable to expect in practice. Granular forecasts in the regime of low count rates - as they often occur in retail, for which an intermittent demand of a handful might be observed per product, day, and location - are dominated by the inevitable statistical uncertainty of the Poisson distribution. This makes it hard to judge whether a certain metric value is dominated by Poisson noise or truly indicates a bad prediction model. To make things worse, every evaluation metric suffers from scaling: Its value is mostly defined by the predicted selling rate and the resulting rate-dependent Poisson noise, and only secondarily by the quality of the forecast. For any metric, comparing two groups of forecasted products often yields "the slow movers are performing worse than the fast movers" or vice versa - the na\"ive scaling trap. To distill the intrinsic quality of a forecast, we stratify predictions into buckets of approximately equal rate and evaluate metrics for each bucket separately. By comparing the achieved value per bucket to benchmarks, we obtain a scaling-aware rating of count forecasts. Our procedure avoids the na\"ive scaling trap, provides an immediate intuitive judgment of forecast quality, and allows to compare forecasts for different products or even industries.

One of the possible representations of three-valued instantaneous noise-based logic is proposed. The third value is an uncertain bit value, which can be useful in artificial intelligence applications. There is a forth value, too, that can represent a non-existing bit (vacuum-state) that is the same (1 numeric value) for all bits, however that is a squeezed state common for all bits. Some logic gates are explored. A ternary Universe has a significant advantage compared to the standard binary one: its amplitude is never zero during any clock period. All the known binary logic gates work for the binary bit values in the same way as earlier therefore the former binary algorithms can be run in the ternary system with no change and without the problems posed by zero values of the Universe.

The method of common lines is a well-established reconstruction technique in cryogenic electron microscopy (cryo-EM), which can be used to extract the relative orientations of an object given tomographic projection images from different directions. In this paper, we deal with an analogous problem in optical diffraction tomography. Based on the Fourier diffraction theorem, we show that rigid motions of the object, i.e., rotations and translations, can be determined by detecting common circles in the Fourier-transformed data. We introduce two methods to identify common circles. The first one is motivated by the common line approach for projection images and detects the relative orientation by parameterizing the common circles in the two images. The second one assumes a smooth motion over time and calculates the angular velocity of the rotational motion via an infinitesimal version of the common circle method. Interestingly, using the stereographic projection, both methods can be reformulated as common line methods, but these lines are, in contrast to those used in cryo-EM, not confined to pass through the origin and allow for a full reconstruction of the relative orientations. Numerical proof-of-the-concept examples demonstrate the performance of our reconstruction methods.

It is not difficult to think of applications that can be modelled as graph problems in which placing some facility or commodity at a vertex has some positive or negative effect on the values of all the vertices out to some distance, and we want to be able to calculate quickly the cumulative effect on any vertex's value at any time or the list of the most beneficial or most detrimential effects on a vertex. In this paper we show how, given an edge-weighted graph with constant-size separators, we can support the following operations on it in time polylogarithmic in the number of vertices and the number of facilities placed on the vertices, where distances between vertices are measured with respect to the edge weights: Add (v, f, w, d) places a facility of weight w and with effect radius d onto vertex v. Remove (v, f) removes a facility f previously placed on v using Add from v. Sum (v) or Sum (v, d) returns the total weight of all facilities affecting v or, with a distance parameter d, the total weight of all facilities whose effect region intersects the ``circle'' with radius d around v. Top (v, k) or Top (v, k, d) returns the k facilities of greatest weight that affect v or, with a distance parameter d, whose effect region intersects the ``circle'' with radius d around v. The weights of the facilities and the operation that Sum uses to ``sum'' them must form a semigroup. For Top queries, the weights must be drawn from a total order.

Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the attributes and/or structures of the graph. In recent years, graph neural networks (GNNs) have been studied extensively and have successfully performed difficult machine learning tasks in node classification, link prediction, and graph classification thanks to the highly expressive capability via message passing in effectively learning graph representations. To solve the graph anomaly detection problem, GNN-based methods leverage information about the graph attributes (or features) and/or structures to learn to score anomalies appropriately. In this survey, we review the recent advances made in detecting graph anomalies using GNN models. Specifically, we summarize GNN-based methods according to the graph type (i.e., static and dynamic), the anomaly type (i.e., node, edge, subgraph, and whole graph), and the network architecture (e.g., graph autoencoder, graph convolutional network). To the best of our knowledge, this survey is the first comprehensive review of graph anomaly detection methods based on GNNs.

Interpretability methods are developed to understand the working mechanisms of black-box models, which is crucial to their responsible deployment. Fulfilling this goal requires both that the explanations generated by these methods are correct and that people can easily and reliably understand them. While the former has been addressed in prior work, the latter is often overlooked, resulting in informal model understanding derived from a handful of local explanations. In this paper, we introduce explanation summary (ExSum), a mathematical framework for quantifying model understanding, and propose metrics for its quality assessment. On two domains, ExSum highlights various limitations in the current practice, helps develop accurate model understanding, and reveals easily overlooked properties of the model. We also connect understandability to other properties of explanations such as human alignment, robustness, and counterfactual minimality and plausibility.

Structural data well exists in Web applications, such as social networks in social media, citation networks in academic websites, and threads data in online forums. Due to the complex topology, it is difficult to process and make use of the rich information within such data. Graph Neural Networks (GNNs) have shown great advantages on learning representations for structural data. However, the non-transparency of the deep learning models makes it non-trivial to explain and interpret the predictions made by GNNs. Meanwhile, it is also a big challenge to evaluate the GNN explanations, since in many cases, the ground-truth explanations are unavailable. In this paper, we take insights of Counterfactual and Factual (CF^2) reasoning from causal inference theory, to solve both the learning and evaluation problems in explainable GNNs. For generating explanations, we propose a model-agnostic framework by formulating an optimization problem based on both of the two casual perspectives. This distinguishes CF^2 from previous explainable GNNs that only consider one of them. Another contribution of the work is the evaluation of GNN explanations. For quantitatively evaluating the generated explanations without the requirement of ground-truth, we design metrics based on Counterfactual and Factual reasoning to evaluate the necessity and sufficiency of the explanations. Experiments show that no matter ground-truth explanations are available or not, CF^2 generates better explanations than previous state-of-the-art methods on real-world datasets. Moreover, the statistic analysis justifies the correlation between the performance on ground-truth evaluation and our proposed metrics.

Commonsense causality reasoning (CCR) aims at identifying plausible causes and effects in natural language descriptions that are deemed reasonable by an average person. Although being of great academic and practical interest, this problem is still shadowed by the lack of a well-posed theoretical framework; existing work usually relies on deep language models wholeheartedly, and is potentially susceptible to confounding co-occurrences. Motivated by classical causal principles, we articulate the central question of CCR and draw parallels between human subjects in observational studies and natural languages to adopt CCR to the potential-outcomes framework, which is the first such attempt for commonsense tasks. We propose a novel framework, ROCK, to Reason O(A)bout Commonsense K(C)ausality, which utilizes temporal signals as incidental supervision, and balances confounding effects using temporal propensities that are analogous to propensity scores. The ROCK implementation is modular and zero-shot, and demonstrates good CCR capabilities on various datasets.

In many visual systems, visual tracking often bases on RGB image sequences, in which some targets are invalid in low-light conditions, and tracking performance is thus affected significantly. Introducing other modalities such as depth and infrared data is an effective way to handle imaging limitations of individual sources, but multi-modal imaging platforms usually require elaborate designs and cannot be applied in many real-world applications at present. Near-infrared (NIR) imaging becomes an essential part of many surveillance cameras, whose imaging is switchable between RGB and NIR based on the light intensity. These two modalities are heterogeneous with very different visual properties and thus bring big challenges for visual tracking. However, existing works have not studied this challenging problem. In this work, we address the cross-modal object tracking problem and contribute a new video dataset, including 654 cross-modal image sequences with over 481K frames in total, and the average video length is more than 735 frames. To promote the research and development of cross-modal object tracking, we propose a new algorithm, which learns the modality-aware target representation to mitigate the appearance gap between RGB and NIR modalities in the tracking process. It is plug-and-play and could thus be flexibly embedded into different tracking frameworks. Extensive experiments on the dataset are conducted, and we demonstrate the effectiveness of the proposed algorithm in two representative tracking frameworks against 17 state-of-the-art tracking methods. We will release the dataset for free academic usage, dataset download link and code will be released soon.

Video anomaly detection under weak labels is formulated as a typical multiple-instance learning problem in previous works. In this paper, we provide a new perspective, i.e., a supervised learning task under noisy labels. In such a viewpoint, as long as cleaning away label noise, we can directly apply fully supervised action classifiers to weakly supervised anomaly detection, and take maximum advantage of these well-developed classifiers. For this purpose, we devise a graph convolutional network to correct noisy labels. Based upon feature similarity and temporal consistency, our network propagates supervisory signals from high-confidence snippets to low-confidence ones. In this manner, the network is capable of providing cleaned supervision for action classifiers. During the test phase, we only need to obtain snippet-wise predictions from the action classifier without any extra post-processing. Extensive experiments on 3 datasets at different scales with 2 types of action classifiers demonstrate the efficacy of our method. Remarkably, we obtain the frame-level AUC score of 82.12% on UCF-Crime.