In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here, under the assumption of compactness in the coefficient operators, that the error of the approximate solution to the operator-valued Riccati equation is bounded above by the approximation error of the governing semigroup. One significant outcome of this result is the correct prediction of optimal convergence for finite element approximations of the operator-valued Riccati equations for when the governing semigroup involves parabolic, as well as hyperbolic processes. We derive the abstract theory for the time-dependent and time-independent operator-valued Riccati equations in the first part of this work. In the second part, we prove optimal convergence rates for the finite element approximation of the functional gain associated with model one-dimensional weakly damped wave and thermal LQR control systems. These theoretical claims are then corroborated with computational evidence.
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In this work, we study the out-of-distribution (OOD) detection problem through the use of the feature space of a pre-trained deep classifier. We show that learning the density of in-distribution (ID) features with an energy-based models (EBM) leads to competitive detection results. However, we found that the non-mixing of MCMC sampling during the EBM's training undermines its detection performance. To overcome this an energy-based correction of a mixture of class-conditional Gaussian distributions. We obtains favorable results when compared to a strong baseline like the KNN detector on the CIFAR-10/CIFAR-100 OOD detection benchmarks.
In this work, we consider the problem of localizing multiple signal sources based on time-difference of arrival (TDOA) measurements. In the blind setting, in which the source signals are not known, the localization task is challenging due to the data association problem. That is, it is not known which of the TDOA measurements correspond to the same source. Herein, we propose to perform joint localization and data association by means of an optimal transport formulation. The method operates by finding optimal groupings of TDOA measurements and associating these with candidate source locations. To allow for computationally feasible localization in three-dimensional space, an efficient set of candidate locations is constructed using a minimal multilateration solver based on minimal sets of receiver pairs. In numerical simulations, we demonstrate that the proposed method is robust both to measurement noise and TDOA detection errors. Furthermore, it is shown that the data association provided by the proposed method allows for statistically efficient estimates of the source locations.
In this work, we propose fully nonconforming, locally exactly divergence-free discretizations based on lowest order Crouziex-Raviart finite element and piecewise constant spaces to study the optimal control of stationary double diffusion model presented in [B\"urger, M\'endez, Ruiz-Baier, SINUM (2019), 57:1318-1343]. The well-posedness of the discrete uncontrolled state and adjoint equations are discussed using discrete lifting and fixed point arguments, and convergence results are derived rigorously under minimal regularity. Building upon our recent work [Tushar, Khan, Mohan arXiv (2023)], we prove the local optimality of a reference control using second-order sufficient optimality condition for the control problem, and use it along with an optimize-then-discretize approach to prove optimal order a priori error estimates for the control, state and adjoint variables upto the regularity of the solution. The optimal control is computed using a primal-dual active set strategy as a semi-smooth Newton method and computational tests validate the predicted error decay rates and illustrate the proposed scheme's applicability to optimal control of thermohaline circulation problems.
Computational argumentation has become an essential tool in various fields, including artificial intelligence, law, and public policy. It is an emerging research field in natural language processing that attracts increasing attention. Research on computational argumentation mainly involves two types of tasks: argument mining and argument generation. As large language models have demonstrated strong abilities in understanding context and generating natural language, it is worthwhile to evaluate the performance of LLMs on various computational argumentation tasks. This work aims to embark on an assessment of LLMs, such as ChatGPT, Flan models and LLaMA2 models, under zero-shot and few-shot settings within the realm of computational argumentation. We organize existing tasks into six main categories and standardise the format of fourteen open-sourced datasets. In addition, we present a new benchmark dataset on counter speech generation, that aims to holistically evaluate the end-to-end performance of LLMs on argument mining and argument generation. Extensive experiments show that LLMs exhibit commendable performance across most of these datasets, demonstrating their capabilities in the field of argumentation. Our analysis offers valuable suggestions for evaluating computational argumentation and its integration with LLMs in future research endeavors.
Vessel trajectory clustering, which aims to find similar trajectory patterns, has been widely leveraged in overwater applications. Most traditional methods use predefined rules and thresholds to identify discrete vessel behaviors. They aim for high-quality clustering and conduct clustering on entire sequences, whether the original trajectory or its sub-trajectories, failing to represent their evolution. To resolve this problem, we propose a Predictive Clustering of Hierarchical Vessel Behavior (PC-HiV). PC-HiV first uses hierarchical representations to transform every trajectory into a behavioral sequence. Then, it predicts evolution at each timestamp of the sequence based on the representations. By applying predictive clustering and latent encoding, PC-HiV improves clustering and predictions simultaneously. Experiments on real AIS datasets demonstrate PC-HiV's superiority over existing methods, showcasing its effectiveness in capturing behavioral evolution discrepancies between vessel types (tramp vs. liner) and within emission control areas. Results show that our method outperforms NN-Kmeans and Robust DAA by 3.9% and 6.4% of the purity score.
Classification algorithms using Transformer architectures can be affected by the sequence length learning problem whenever observations from different classes have a different length distribution. This problem causes models to use sequence length as a predictive feature instead of relying on important textual information. Although most public datasets are not affected by this problem, privately owned corpora for fields such as medicine and insurance may carry this data bias. The exploitation of this sequence length feature poses challenges throughout the value chain as these machine learning models can be used in critical applications. In this paper, we empirically expose this problem and present approaches to minimize its impacts.
Most diffusion models assume that the reverse process adheres to a Gaussian distribution. However, this approximation has not been rigorously validated, especially at singularities, where t=0 and t=1. Improperly dealing with such singularities leads to an average brightness issue in applications, and limits the generation of images with extreme brightness or darkness. We primarily focus on tackling singularities from both theoretical and practical perspectives. Initially, we establish the error bounds for the reverse process approximation, and showcase its Gaussian characteristics at singularity time steps. Based on this theoretical insight, we confirm the singularity at t=1 is conditionally removable while it at t=0 is an inherent property. Upon these significant conclusions, we propose a novel plug-and-play method SingDiffusion to address the initial singular time step sampling, which not only effectively resolves the average brightness issue for a wide range of diffusion models without extra training efforts, but also enhances their generation capability in achieving notable lower FID scores. Code and models are released at //github.com/PangzeCheung/SingDiffusion.
This work delves into the complexities of machine unlearning in the face of distributional shifts, particularly focusing on the challenges posed by non-uniform feature and label removal. With the advent of regulations like the GDPR emphasizing data privacy and the right to be forgotten, machine learning models face the daunting task of unlearning sensitive information without compromising their integrity or performance. Our research introduces a novel approach that leverages influence functions and principles of distributional independence to address these challenges. By proposing a comprehensive framework for machine unlearning, we aim to ensure privacy protection while maintaining model performance and adaptability across varying distributions. Our method not only facilitates efficient data removal but also dynamically adjusts the model to preserve its generalization capabilities. Through extensive experimentation, we demonstrate the efficacy of our approach in scenarios characterized by significant distributional shifts, making substantial contributions to the field of machine unlearning. This research paves the way for developing more resilient and adaptable unlearning techniques, ensuring models remain robust and accurate in the dynamic landscape of data privacy and machine learning.
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.
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.
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