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We investigate two efficient time discretizations for the post-processing technique of discontinuous Galerkin (DG) methods to solve hyperbolic conservation laws. The post-processing technique, which is applied at the final time of the DG method, can enhance the accuracy of the original DG solution (spatial superconvergence). One main difficulty of the post-processing technique is that the spatial superconvergence after post-processing needs to be matched with proper temporary accuracy. If the semi-discretized system (ODE system after spatial discretization) is under-resolved in time, then the space superconvergence will be concealed. In this paper, we focus our investigation on the recently designed SDG method and derive its explicit scheme from a correction process based on the DG weak formulation. We also introduce another similar technique, namely the spectral deferred correction (SDC) method. A comparison is made among both proposed time discretization techniques with the standard third-order Runge-Kutta method through several numerical examples, to conclude that both the SDG and SDC methods are efficient time discretization techniques for exploiting the spatial superconvergence of the DG methods.

Purpose: Manual annotations for training deep learning (DL) models in auto-segmentation are time-intensive. This study introduces a hybrid representation-enhanced sampling strategy that integrates both density and diversity criteria within an uncertainty-based Bayesian active learning (BAL) framework to reduce annotation efforts by selecting the most informative training samples. Methods: The experiments are performed on two lower extremity (LE) datasets of MRI and CT images, focusing on the segmentation of the femur, pelvis, sacrum, quadriceps femoris, hamstrings, adductors, sartorius, and iliopsoas, utilizing a U-net-based BAL framework. Our method selects uncertain samples with high density and diversity for manual revision, optimizing for maximal similarity to unlabeled instances and minimal similarity to existing training data. We assess the accuracy and efficiency using Dice and a proposed metric called reduced annotation cost (RAC), respectively. We further evaluate the impact of various acquisition rules on BAL performance and design an ablation study for effectiveness estimation. Results: In MRI and CT datasets, our method was superior or comparable to existing ones, achieving a 0.8\% Dice and 1.0\% RAC increase in CT (statistically significant), and a 0.8\% Dice and 1.1\% RAC increase in MRI (not statistically significant) in volume-wise acquisition. Our ablation study indicates that combining density and diversity criteria enhances the efficiency of BAL in musculoskeletal segmentation compared to using either criterion alone. Conclusion: Our sampling method is proven efficient in reducing annotation costs in image segmentation tasks. The combination of the proposed method and our BAL framework provides a semi-automatic way for efficient annotation of medical image datasets.

State space models (SSMs) are widely used to describe dynamic systems. However, when the likelihood of the observations is intractable, parameter inference for SSMs cannot be easily carried out using standard Markov chain Monte Carlo or sequential Monte Carlo methods. In this paper, we propose a particle Gibbs sampler as a general strategy to handle SSMs with intractable likelihoods in the approximate Bayesian computation (ABC) setting. The proposed sampler incorporates a conditional auxiliary particle filter, which can help mitigate the weight degeneracy often encountered in ABC. To illustrate the methodology, we focus on a classic stochastic volatility model (SVM) used in finance and econometrics for analyzing and interpreting volatility. Simulation studies demonstrate the accuracy of our sampler for SVM parameter inference, compared to existing particle Gibbs samplers based on the conditional bootstrap filter. As a real data application, we apply the proposed sampler for fitting an SVM to S&P 500 Index time-series data during the 2008 financial crisis.

Slow concept drift is a ubiquitous, yet under-studied problem in practical machine learning systems. In such settings, although recent data is more indicative of future data, naively prioritizing recent instances runs the risk of losing valuable information from the past. We propose an optimization-driven approach towards balancing instance importance over large training windows. First, we model instance relevance using a mixture of multiple timescales of decay, allowing us to capture rich temporal trends. Second, we learn an auxiliary scorer model that recovers the appropriate mixture of timescales as a function of the instance itself. Finally, we propose a nested optimization objective for learning the scorer, by which it maximizes forward transfer for the learned model. Experiments on a large real-world dataset of 39M photos over a 9 year period show upto 15% relative gains in accuracy compared to other robust learning baselines. We replicate our gains on two collections of real-world datasets for non-stationary learning, and extend our work to continual learning settings where, too, we beat SOTA methods by large margins.

Contrastive learning has achieved state-of-the-art performance in various self-supervised learning tasks and even outperforms its supervised counterpart. Despite its empirical success, theoretical understanding of the superiority of contrastive learning is still limited. In this paper, under linear representation settings, (i) we provably show that contrastive learning outperforms the standard autoencoders and generative adversarial networks, two classical generative unsupervised learning methods, for both feature recovery and in-domain downstream tasks; (ii) we also illustrate the impact of labeled data in supervised contrastive learning. This provides theoretical support for recent findings that contrastive learning with labels improves the performance of learned representations in the in-domain downstream task, but it can harm the performance in transfer learning. We verify our theory with numerical experiments.

Recently, reputation-based indirect reciprocity has been widely applied to the study on fairness behavior. Previous works mainly investigate indirect reciprocity by considering compulsory participation. While in reality, individuals may choose voluntary participation according to the opponent's reputation. It is still unclear how such reputation-based voluntary participation influences the evolution of fairness. To address this question, we introduce indirect reciprocity with voluntary participation into the dictator game (DG). We respectively consider good dictators or recipients can voluntarily participate in games when the opponents are assessed as bad. We theoretically calculate the fairness level under all social norms of third-order information. Our findings reveal that several social norms induce the high fairness level in both scenarios. However, more social norms lead to a high fairness level for voluntary participation of recipients, compared with the one of good dictators. The results also hold when the probability of voluntary participation is not low. Our results demonstrate that recipients' voluntary participation is more effective in promoting the emergence of fairness behavior.

Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.

In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.

Despite its great success, machine learning can have its limits when dealing with insufficient training data. A potential solution is the additional integration of prior knowledge into the training process which leads to the notion of informed machine learning. In this paper, we present a structured overview of various approaches in this field. We provide a definition and propose a concept for informed machine learning which illustrates its building blocks and distinguishes it from conventional machine learning. We introduce a taxonomy that serves as a classification framework for informed machine learning approaches. It considers the source of knowledge, its representation, and its integration into the machine learning pipeline. Based on this taxonomy, we survey related research and describe how different knowledge representations such as algebraic equations, logic rules, or simulation results can be used in learning systems. This evaluation of numerous papers on the basis of our taxonomy uncovers key methods in the field of informed machine learning.

Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.