Unlimited sampling was recently introduced to deal with the clipping or saturation of measurements where a modulo operator is applied before sampling. In this paper, we investigate the identifiability of the model where measurements are acquired under a discrete Fourier transform (DFT) sensing matrix first followed by a modulo operator (modulo-DFT). Firstly, based on the theorems of cyclotomic polynomials, we derive a sufficient condition for uniquely identifying the original signal in modulo-DFT. Additionally, for periodic bandlimited signals (PBSs) under unlimited sampling which can be viewed as a special case of modulo-DFT, the necessary and sufficient condition for the unique recovery of the original signal are provided. Moreover, we show that when the oversampling factor exceeds $3(1+1/P)$, PBS is always identifiable from the modulo samples, where $P$ is the number of harmonics including the fundamental component in the positive frequency part.
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Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i.e. the function spaces over which they define a probability measure, is lacking. In practice, GPs are not constructed through a probability measure, but instead through a mean function and a covariance kernel. In this paper we provide necessary and sufficient conditions on the covariance kernel for the sample paths of the corresponding GP to attain a given regularity. We use the framework of H\"older regularity as it grants particularly straightforward conditions, which simplify further in the cases of stationary and isotropic GPs. We then demonstrate that our results allow for novel and unusually tight characterisations of the sample path regularities of the GPs commonly used in machine learning applications, such as the Mat\'ern GPs.
Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states, remains challenging. We propose stabilized neural differential equations (SNDEs), a method to enforce arbitrary manifold constraints for neural differential equations. Our approach is based on a stabilization term that, when added to the original dynamics, renders the constraint manifold provably asymptotically stable. Due to its simplicity, our method is compatible with all common neural differential equation (NDE) models and broadly applicable. In extensive empirical evaluations, we demonstrate that SNDEs outperform existing methods while broadening the types of constraints that can be incorporated into NDE training.
While myoelectric control has recently become a focus of increased research as a possible flexible hands-free input modality, current control approaches are prone to inadvertent false activations in real-world conditions. In this work, a novel myoelectric control paradigm -- on-demand myoelectric control -- is proposed, designed, and evaluated, to reduce the number of unrelated muscle movements that are incorrectly interpreted as input gestures . By leveraging the concept of wake gestures, users were able to switch between a dedicated control mode and a sleep mode, effectively eliminating inadvertent activations during activities of daily living (ADLs). The feasibility of wake gestures was demonstrated in this work through two online ubiquitous EMG control tasks with varying difficulty levels; dismissing an alarm and controlling a robot. The proposed control scheme was able to appropriately ignore almost all non-targeted muscular inputs during ADLs (>99.9%) while maintaining sufficient sensitivity for reliable mode switching during intentional wake gesture elicitation. These results highlight the potential of wake gestures as a critical step towards enabling ubiquitous myoelectric control-based on-demand input for a wide range of applications.
Efficient exploration is a key challenge in contextual bandits due to the large size of their action space, where uninformed exploration can result in computational and statistical inefficiencies. Fortunately, the rewards of actions are often correlated and this can be leveraged to explore them efficiently. In this work, we capture such correlations using pre-trained diffusion models; upon which we design diffusion Thompson sampling (dTS). Both theoretical and algorithmic foundations are developed for dTS, and empirical evaluation also shows its favorable performance.
Anomaly detection is a critical challenge across various research domains, aiming to identify instances that deviate from normal data distributions. This paper explores the application of Generative Adversarial Networks (GANs) in fraud detection, comparing their advantages with traditional methods. GANs, a type of Artificial Neural Network (ANN), have shown promise in modeling complex data distributions, making them effective tools for anomaly detection. The paper systematically describes the principles of GANs and their derivative models, emphasizing their application in fraud detection across different datasets. And by building a collection of adversarial verification graphs, we will effectively prevent fraud caused by bots or automated systems and ensure that the users in the transaction are real. The objective of the experiment is to design and implement a fake face verification code and fraud detection system based on Generative Adversarial network (GANs) algorithm to enhance the security of the transaction process.The study demonstrates the potential of GANs in enhancing transaction security through deep learning techniques.
A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered to be an efficient interval estimation technique. In this paper, we offer a first attempt at computing the coverage probability and expected length of a parametric or percentile bootstrap interval by exact probabilistic calculation for any fixed sample size. This method is applied to the basic bootstrap intervals for functions of binomial proportions and a normal mean. None of these intervals, however, are found to have a correct confidence coefficient, which leads to illogical conclusions including that the bootstrap interval is narrower than the z-interval when estimating a normal mean. This raises a general question of how to utilize bootstrap intervals appropriately in practice since the sample size is typically fixed.
Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we would like to compute $\frac{1}{n}\sum_{i=1}^{n} f(x_i,y)$ for any query point $y \in \mathbb{R}^d$. Recently, there has been a growing trend of using data structures for efficient KDE. However, the proposed KDE data structures focus on static settings. The robustness of KDE data structures over dynamic changing data distributions is not addressed. In this work, we focus on the dynamic maintenance of KDE data structures with robustness to adversarial queries. Especially, we provide a theoretical framework of KDE data structures. In our framework, the KDE data structures only require subquadratic spaces. Moreover, our data structure supports the dynamic update of the dataset in sublinear time. Furthermore, we can perform adaptive queries with the potential adversary in sublinear time.
As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.
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