A structure-preserving kernel ridge regression method is presented that allows the recovery of potentially high-dimensional and nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form solution that yields excellent numerical performances that surpass other techniques proposed in the literature in this setup. From the methodological point of view, the paper extends kernel regression methods to problems in which loss functions involving linear functions of gradients are required and, in particular, a differential reproducing property and a Representer Theorem are proved in this context. The relation between the structure-preserving kernel estimator and the Gaussian posterior mean estimator is analyzed. A full error analysis is conducted that provides convergence rates using fixed and adaptive regularization parameters. The good performance of the proposed estimator is illustrated with various numerical experiments.
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Recently, tensor low-rank representation (TLRR) has become a popular tool for tensor data recovery and clustering, due to its empirical success and theoretical guarantees. However, existing TLRR methods consider Gaussian or gross sparse noise, inevitably leading to performance degradation when the tensor data are contaminated by outliers or sample-specific corruptions. This paper develops an outlier-robust tensor low-rank representation (OR-TLRR) method that provides outlier detection and tensor data clustering simultaneously based on the t-SVD framework. For tensor observations with arbitrary outlier corruptions, OR-TLRR has provable performance guarantee for exactly recovering the row space of clean data and detecting outliers under mild conditions. Moreover, an extension of OR-TLRR is proposed to handle the case when parts of the data are missing. Finally, extensive experimental results on synthetic and real data demonstrate the effectiveness of the proposed algorithms. We release our code at //github.com/twugithub/2024-AISTATS-ORTLRR.
Modeling non-stationary data is a challenging problem in the field of continual learning, and data distribution shifts may result in negative consequences on the performance of a machine learning model. Classic learning tools are often vulnerable to perturbations of the input covariates, and are sensitive to outliers and noise, and some tools are based on rigid algebraic assumptions. Distribution shifts are frequently occurring due to changes in raw materials for production, seasonality, a different user base, or even adversarial attacks. Therefore, there is a need for more effective distribution shift detection techniques. In this work, we propose a continual learning framework for monitoring and detecting distribution changes. We explore the problem in a latent space generated by a bio-inspired self-organizing clustering and statistical aspects of the latent space. In particular, we investigate the projections made by two topology-preserving maps: the Self-Organizing Map and the Scale Invariant Map. Our method can be applied in both a supervised and an unsupervised context. We construct the assessment of changes in the data distribution as a comparison of Gaussian signals, making the proposed method fast and robust. We compare it to other unsupervised techniques, specifically Principal Component Analysis (PCA) and Kernel-PCA. Our comparison involves conducting experiments using sequences of images (based on MNIST and injected shifts with adversarial samples), chemical sensor measurements, and the environmental variable related to ozone levels. The empirical study reveals the potential of the proposed approach.
Pooling is a crucial operation in computer vision, yet the unique structure of skeletons hinders the application of existing pooling strategies to skeleton graph modelling. In this paper, we propose an Improved Graph Pooling Network, referred to as IGPN. The main innovations include: Our method incorporates a region-awareness pooling strategy based on structural partitioning. The correlation matrix of the original feature is used to adaptively adjust the weight of information in different regions of the newly generated features, resulting in more flexible and effective processing. To prevent the irreversible loss of discriminative information, we propose a cross fusion module and an information supplement module to provide block-level and input-level information respectively. As a plug-and-play structure, the proposed operation can be seamlessly combined with existing GCN-based models. We conducted extensive evaluations on several challenging benchmarks, and the experimental results indicate the effectiveness of our proposed solutions. For example, in the cross-subject evaluation of the NTU-RGB+D 60 dataset, IGPN achieves a significant improvement in accuracy compared to the baseline while reducing Flops by nearly 70%; a heavier version has also been introduced to further boost accuracy.
Near-field propagation, particularly that enabled by reconfigurable intelligent surfaces (RIS), has emerged as a promising research topic in recent years. However, a comprehensive literature review on RIS-based near-field technologies is still lacking. This article aims to fill this gap by providing a brief overview of near-field concepts and a systematic survey of the state-of-the-art RIS-based near-field technologies. The focus is on three key aspects: the construction of ubiquitous near-field wireless propagation environments using RIS, the enabling of new near-field paradigms for 6G networks through RIS, and the challenges faced by RIS-based near-field technologies. This technical review intends to facilitate the development and innovation of RIS-based near-field technologies.
Despite the recent progress in deep learning, most approaches still go for a silo-like solution, focusing on learning each task in isolation: training a separate neural network for each individual task. Many real-world problems, however, call for a multi-modal approach and, therefore, for multi-tasking models. Multi-task learning (MTL) aims to leverage useful information across tasks to improve the generalization capability of a model. This thesis is concerned with multi-task learning in the context of computer vision. First, we review existing approaches for MTL. Next, we propose several methods that tackle important aspects of multi-task learning. The proposed methods are evaluated on various benchmarks. The results show several advances in the state-of-the-art of multi-task learning. Finally, we discuss several possibilities for future work.
Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.
Domain shift is a fundamental problem in visual recognition which typically arises when the source and target data follow different distributions. The existing domain adaptation approaches which tackle this problem work in the closed-set setting with the assumption that the source and the target data share exactly the same classes of objects. In this paper, we tackle a more realistic problem of open-set domain shift where the target data contains additional classes that are not present in the source data. More specifically, we introduce an end-to-end Progressive Graph Learning (PGL) framework where a graph neural network with episodic training is integrated to suppress underlying conditional shift and adversarial learning is adopted to close the gap between the source and target distributions. Compared to the existing open-set adaptation approaches, our approach guarantees to achieve a tighter upper bound of the target error. Extensive experiments on three standard open-set benchmarks evidence that our approach significantly outperforms the state-of-the-arts in open-set domain adaptation.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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