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Regression on manifolds, and, more broadly, statistics on manifolds, has garnered significant importance in recent years due to the vast number of applications for this type of data. Circular data is a classic example, but so is data in the space of covariance matrices, data on the Grassmannian manifold obtained as a result of principal component analysis, among many others. In this work we investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space. This extends the concepts delineated in [Lei and Wasserman, 2014] to this novel context. Aligning with traditional principles in conformal inference, these prediction sets are distribution-free, indicating that no specific assumptions are imposed on the joint distribution of $(X, Y)$, and they maintain a non-parametric character. We prove the asymptotic almost sure convergence of the empirical version of these regions on the manifold to their population counterparts. The efficiency of this method is shown through a comprehensive simulation study and an analysis involving real-world data.

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We present Decomposer, a semi-supervised reconstruction model that decomposes distorted image sequences into their fundamental building blocks - the original image and the applied augmentations, i.e., shadow, light, and occlusions. To solve this problem, we use the SIDAR dataset that provides a large number of distorted image sequences: each sequence contains images with shadows, lighting, and occlusions applied to an undistorted version. Each distortion changes the original signal in different ways, e.g., additive or multiplicative noise. We propose a transformer-based model to explicitly learn this decomposition. The sequential model uses 3D Swin-Transformers for spatio-temporal encoding and 3D U-Nets as prediction heads for individual parts of the decomposition. We demonstrate that by separately pre-training our model on weakly supervised pseudo labels, we can steer our model to optimize for our ambiguous problem definition and learn to differentiate between the different image distortions.

Temporal information extraction (TIE) has attracted a great deal of interest over the last two decades, leading to the development of a significant number of datasets. Despite its benefits, having access to a large volume of corpora makes it difficult when it comes to benchmark TIE systems. On the one hand, different datasets have different annotation schemes, thus hindering the comparison between competitors across different corpora. On the other hand, the fact that each corpus is commonly disseminated in a different format requires a considerable engineering effort for a researcher/practitioner to develop parsers for all of them. This constraint forces researchers to select a limited amount of datasets to evaluate their systems which consequently limits the comparability of the systems. Yet another obstacle that hinders the comparability of the TIE systems is the evaluation metric employed. While most research works adopt traditional metrics such as precision, recall, and $F_1$, a few others prefer temporal awareness -- a metric tailored to be more comprehensive on the evaluation of temporal systems. Although the reason for the absence of temporal awareness in the evaluation of most systems is not clear, one of the factors that certainly weights this decision is the necessity to implement the temporal closure algorithm in order to compute temporal awareness, which is not straightforward to implement neither is currently easily available. All in all, these problems have limited the fair comparison between approaches and consequently, the development of temporal extraction systems. To mitigate these problems, we have developed tieval, a Python library that provides a concise interface for importing different corpora and facilitates system evaluation. In this paper, we present the first public release of tieval and highlight its most relevant features.

With the advancement of IoT technology, many electronic devices are interconnected through networks, communicating with each other and performing specific roles. However, as numerous devices join networks, the threat of cyberattacks also escalates. Preventing and detecting cyber threats are crucial, and one method of preventing such threats involves using attack graphs. Attack graphs are widely used to assess security threats within networks. However, a drawback emerges as the network scales, as generating attack graphs becomes time-consuming. To overcome this limitation, artificial intelligence models can be employed. By utilizing AI models, attack graphs can be created within a short period, approximating optimal outcomes. AI models designed for attack graph generation consist of encoders and decoders, trained using reinforcement learning algorithms. After training the AI models, we confirmed the model's learning effectiveness by observing changes in loss and reward values. Additionally, we compared attack graphs generated by the AI model with those created through conventional methods.

We generalise the popular cops and robbers game to multi-layer graphs, where each cop and the robber are restricted to a single layer (or set of edges). We show that initial intuition about the best way to allocate cops to layers is not always correct, and prove that the multi-layer cop number is neither bounded from above nor below by any increasing function of the cop numbers of the individual layers. We determine that it is NP-hard to decide if $k$ cops are sufficient to catch the robber, even if every cop layer is a tree and a set of isolated vertices. However, we give a polynomial time algorithm to determine if $k$ cops can win when the robber layer is a tree. Additionally, we investigate a question of worst-case divisions of a simple graph into layers: given a simple graph $G$, what is the maximum number of cops required to catch a robber over all multi-layer graphs where each edge of $G$ is in at least one layer and all layers are connected? For cliques, suitably dense random graphs, and graphs of bounded treewidth, we determine this parameter up to multiplicative constants. Lastly we consider a multi-layer variant of Meyniel's conjecture, and show the existence of an infinite family of graphs whose multi-layer cop number is bounded from below by a constant times $n / \log n$, where $n$ is the number of vertices in the graph.

Interest-free promotions are a prevalent strategy employed by credit card lenders to attract new customers, yet the research exploring their effects on both consumers and lenders remains relatively sparse. The process of selecting an optimal promotion strategy is intricate, involving the determination of an interest-free period duration and promotion-availability window, all within the context of competing offers, fluctuating market dynamics, and complex consumer behaviour. In this paper, we introduce an agent-based model that facilitates the exploration of various credit card promotions under diverse market scenarios. Our approach, distinct from previous agent-based models, concentrates on optimising promotion strategies and is calibrated using benchmarks from the UK credit card market from 2019 to 2020, with agent properties derived from historical distributions of the UK population from roughly the same period. We validate our model against stylised facts and time-series data, thereby demonstrating the value of this technique for investigating pricing strategies and understanding credit card customer behaviour. Our experiments reveal that, in the absence of competitor promotions, lender profit is maximised by an interest-free duration of approximately 12 months while market share is maximised by offering the longest duration possible. When competitors do not offer promotions, extended promotion availability windows yield maximum profit for lenders while also maximising market share. In the context of concurrent interest-free promotions, we identify that the optimal lender strategy entails offering a more competitive interest-free period and a rapid response to competing promotional offers. Notably, a delay of three months in responding to a rival promotion corresponds to a 2.4% relative decline in income.

Model averaging has received much attention in the past two decades, which integrates available information by averaging over potential models. Although various model averaging methods have been developed, there are few literatures on the theoretical properties of model averaging from the perspective of stability, and the majority of these methods constrain model weights to a simplex. The aim of this paper is to introduce stability from statistical learning theory into model averaging. Thus, we define the stability, asymptotic empirical risk minimizer, generalization, and consistency of model averaging and study the relationship among them. Our results indicate that stability can ensure that model averaging has good generalization performance and consistency under reasonable conditions, where consistency means model averaging estimator can asymptotically minimize the mean squared prediction error. We also propose a L2-penalty model averaging method without limiting model weights and prove that it has stability and consistency. In order to reduce the impact of tuning parameter selection, we use 10-fold cross-validation to select a candidate set of tuning parameters and perform a weighted average of the estimators of model weights based on estimation errors. The Monte Carlo simulation and an illustrative application demonstrate the usefulness of the proposed method.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.

The core of information retrieval (IR) is to identify relevant information from large-scale resources and return it as a ranked list to respond to user's information need. Recently, the resurgence of deep learning has greatly advanced this field and leads to a hot topic named NeuIR (i.e., neural information retrieval), especially the paradigm of pre-training methods (PTMs). Owing to sophisticated pre-training objectives and huge model size, pre-trained models can learn universal language representations from massive textual data, which are beneficial to the ranking task of IR. Since there have been a large number of works dedicating to the application of PTMs in IR, we believe it is the right time to summarize the current status, learn from existing methods, and gain some insights for future development. In this survey, we present an overview of PTMs applied in different components of IR system, including the retrieval component, the re-ranking component, and other components. In addition, we also introduce PTMs specifically designed for IR, and summarize available datasets as well as benchmark leaderboards. Moreover, we discuss some open challenges and envision some promising directions, with the hope of inspiring more works on these topics for future research.

Object detectors usually achieve promising results with the supervision of complete instance annotations. However, their performance is far from satisfactory with sparse instance annotations. Most existing methods for sparsely annotated object detection either re-weight the loss of hard negative samples or convert the unlabeled instances into ignored regions to reduce the interference of false negatives. We argue that these strategies are insufficient since they can at most alleviate the negative effect caused by missing annotations. In this paper, we propose a simple but effective mechanism, called Co-mining, for sparsely annotated object detection. In our Co-mining, two branches of a Siamese network predict the pseudo-label sets for each other. To enhance multi-view learning and better mine unlabeled instances, the original image and corresponding augmented image are used as the inputs of two branches of the Siamese network, respectively. Co-mining can serve as a general training mechanism applied to most of modern object detectors. Experiments are performed on MS COCO dataset with three different sparsely annotated settings using two typical frameworks: anchor-based detector RetinaNet and anchor-free detector FCOS. Experimental results show that our Co-mining with RetinaNet achieves 1.4%~2.1% improvements compared with different baselines and surpasses existing methods under the same sparsely annotated setting.

Search in social networks such as Facebook poses different challenges than in classical web search: besides the query text, it is important to take into account the searcher's context to provide relevant results. Their social graph is an integral part of this context and is a unique aspect of Facebook search. While embedding-based retrieval (EBR) has been applied in eb search engines for years, Facebook search was still mainly based on a Boolean matching model. In this paper, we discuss the techniques for applying EBR to a Facebook Search system. We introduce the unified embedding framework developed to model semantic embeddings for personalized search, and the system to serve embedding-based retrieval in a typical search system based on an inverted index. We discuss various tricks and experiences on end-to-end optimization of the whole system, including ANN parameter tuning and full-stack optimization. Finally, we present our progress on two selected advanced topics about modeling. We evaluated EBR on verticals for Facebook Search with significant metrics gains observed in online A/B experiments. We believe this paper will provide useful insights and experiences to help people on developing embedding-based retrieval systems in search engines.

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