We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a collection of latent variables. A key innovation for this algorithm is a method for optimally weighing and combining multiple estimates in each iteration. Building upon an AMP convergence theorem for non-separable functions, we prove a state evolution for non-separable functions that provides an asymptotically exact description of its performance in the high-dimensional limit. We leverage this state evolution result to provide necessary and sufficient conditions for recovery of the signal of interest. Such conditions depend on the singular values of a linear operator derived from an appropriate generalization of a signal-to-noise ratio for our model. Our results recover as special cases a number of recently proposed methods for contextual models (e.g., covariate assisted clustering) as well as inhomogeneous noise models.
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ACM/IEEE第23屆模型驅動工程語言和系統國際會議，是模型驅動軟件和系統工程的首要會議系列，由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來，模型涵蓋了建模的各個方面，從語言和方法到工具和應用程序。模特的參加者來自不同的背景，包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇，參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會，并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。
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Recently, denoising diffusion probabilistic models (DDPM) have been applied to image segmentation by generating segmentation masks conditioned on images, while the applications were mainly limited to 2D networks without exploiting potential benefits from the 3D formulation. In this work, we studied the DDPM-based segmentation model for 3D multiclass segmentation on two large multiclass data sets (prostate MR and abdominal CT). We observed that the difference between training and test methods led to inferior performance for existing DDPM methods. To mitigate the inconsistency, we proposed a recycling method which generated corrupted masks based on the model's prediction at a previous time step instead of using ground truth. The proposed method achieved statistically significantly improved performance compared to existing DDPMs, independent of a number of other techniques for reducing train-test discrepancy, including performing mask prediction, using Dice loss, and reducing the number of diffusion time steps during training. The performance of diffusion models was also competitive and visually similar to non-diffusion-based U-net, within the same compute budget. The JAX-based diffusion framework has been released at //github.com/mathpluscode/ImgX-DiffSeg.
The log-conformation formulation, although highly successful, was from the beginning formulated as a partial differential equation that contains an, for PDEs unusual, eigenvalue decomposition of the unknown field. To this day, most numerical implementations have been based on this or a similar eigenvalue decomposition, with Knechtges et al. (2014) being the only notable exception for two-dimensional flows. In this paper, we present an eigenvalue-free algorithm to compute the constitutive equation of the log-conformation formulation that works for two- and three-dimensional flows. Therefore, we first prove that the challenging terms in the constitutive equations are representable as a matrix function of a slightly modified matrix of the log-conformation field. We give a proof of equivalence of this term to the more common log-conformation formulations. Based on this formulation, we develop an eigenvalue-free algorithm to evaluate this matrix function. The resulting full formulation is first discretized using a finite volume method, and then tested on the confined cylinder and sedimenting sphere benchmarks.
The learned denoising-based approximate message passing (LDAMP) algorithm has attracted great attention for image compressed sensing (CS) tasks. However, it has two issues: first, its global measurement model severely restricts its applicability to high-dimensional images, and its block-based measurement method exhibits obvious block artifacts; second, the denoiser in the LDAMP is too simple, and existing denoisers have limited ability in detail recovery. In this paper, to overcome the issues and develop a high-performance LDAMP method for image block compressed sensing (BCS), we propose a novel sparsity and coefficient permutation-based AMP (SCP-AMP) method consisting of the block-based sampling and the two-domain reconstruction modules. In the sampling module, SCP-AMP adopts a discrete cosine transform (DCT) based sparsity strategy to reduce the impact of the high-frequency coefficient on the reconstruction, followed by a coefficient permutation strategy to avoid block artifacts. In the reconstruction module, a two-domain AMP method with DCT domain noise correction and pixel domain denoising is proposed for iterative reconstruction. Regarding the denoiser, we proposed a multi-level deep attention network (MDANet) to enhance the texture details by employing multi-level features and multiple attention mechanisms. Extensive experiments demonstrated that the proposed SCP-AMP method achieved better reconstruction accuracy than other state-of-the-art BCS algorithms in terms of both visual perception and objective metrics.
The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most efficient plan for a fleet of vehicles to deliver goods to a set of customers, subject to the limited carrying capacity of each vehicle. As the number of possible solutions skyrockets when the number of customers increases, finding the optimal solution remains a significant challenge. Recently, a quantum-classical hybrid algorithm known as Quantum Approximate Optimization Algorithm (QAOA) can provide better solutions in some cases of combinatorial optimization problems, compared to classical heuristics. However, the QAOA exhibits a diminished ability to produce high-quality solutions for some constrained optimization problems including the CVRP. One potential approach for improvement involves a variation of the QAOA known as the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA). In this work, we attempt to use GM-QAOA to solve the CVRP. We present a new binary encoding for the CVRP, with an alternative objective function of minimizing the shortest path that bypasses the vehicle capacity constraint of the CVRP. The search space is further restricted by the Grover-Mixer. We examine and discuss the effectiveness of the proposed solver through its application to several illustrative examples.
RF fingerprinting is emerging as a physical layer security scheme to identify illegitimate and/or unauthorized emitters sharing the RF spectrum. However, due to the lack of publicly accessible real-world datasets, most research focuses on generating synthetic waveforms with software-defined radios (SDRs) which are not suited for practical deployment settings. On other hand, the limited datasets that are available focus only on chipsets that generate only one kind of waveform. Commercial off-the-shelf (COTS) combo chipsets that support two wireless standards (for example WiFi and Bluetooth) over a shared dual-band antenna such as those found in laptops, adapters, wireless chargers, Raspberry Pis, among others are becoming ubiquitous in the IoT realm. Hence, to keep up with the modern IoT environment, there is a pressing need for real-world open datasets capturing emissions from these combo chipsets transmitting heterogeneous communication protocols. To this end, we capture the first known emissions from the COTS IoT chipsets transmitting WiFi and Bluetooth under two different time frames. The different time frames are essential to rigorously evaluate the generalization capability of the models. To ensure widespread use, each capture within the comprehensive 72 GB dataset is long enough (40 MSamples) to support diverse input tensor lengths and formats. Finally, the dataset also comprises emissions at varying signal powers to account for the feeble to high signal strength emissions as encountered in a real-world setting.
Linear mixed models (LMMs) are suitable for clustered data and are common in biometrics, medicine, survey statistics and many other fields. In those applications, it is essential to carry out valid inference after selecting a subset of the available variables. We construct confidence sets for the fixed effects in Gaussian LMMs that are based on Lasso-type estimators. Aside from providing confidence regions, this also allows to quantify the joint uncertainty of both variable selection and parameter estimation in the procedure. To show that the resulting confidence sets for the fixed effects are uniformly valid over the parameter spaces of both the regression coefficients and the covariance parameters, we also prove the novel result on uniform Cramer consistency of the restricted maximum likelihood (REML) estimators of the covariance parameters. The superiority of the constructed confidence sets to naive post-selection procedures is validated in simulations and illustrated with a study of the acid neutralization capacity of lakes in the United States.
The field of robotic Flexible Endoscopes (FEs) has progressed significantly, offering a promising solution to reduce patient discomfort. However, the limited autonomy of most robotic FEs results in non-intuitive and challenging manoeuvres, constraining their application in clinical settings. While previous studies have employed lumen tracking for autonomous navigation, they fail to adapt to the presence of obstructions and sharp turns when the endoscope faces the colon wall. In this work, we propose a Deep Reinforcement Learning (DRL)-based navigation strategy that eliminates the need for lumen tracking. However, the use of DRL methods poses safety risks as they do not account for potential hazards associated with the actions taken. To ensure safety, we exploit a Constrained Reinforcement Learning (CRL) method to restrict the policy in a predefined safety regime. Moreover, we present a model selection strategy that utilises Formal Verification (FV) to choose a policy that is entirely safe before deployment. We validate our approach in a virtual colonoscopy environment and report that out of the 300 trained policies, we could identify three policies that are entirely safe. Our work demonstrates that CRL, combined with model selection through FV, can improve the robustness and safety of robotic behaviour in surgical applications.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
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.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
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