由于其高质量的重建以及将现有迭代求解器结合起来的易于性,因此最近将扩散模型作为强大的生成反问题解决器研究。但是,大多数工作都专注于在无噪声设置中解决简单的线性逆问题,这显着不足以使实际问题的复杂性不足。在这项工作中,我们将扩散求解器扩展求解器,以通过后采样的拉普拉斯近似有效地处理一般噪声(非)线性反问题。有趣的是,所得的后验采样方案是扩散采样的混合版本,具有歧管约束梯度,而没有严格的测量一致性投影步骤,与先前的研究相比,在嘈杂的设置中产生了更可取的生成路径。我们的方法表明,扩散模型可以结合各种测量噪声统计量,例如高斯和泊松,并且还有效处理嘈杂的非线性反问题,例如傅立叶相检索和不均匀的脱毛。
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放射造影通常用于探测动态系统中的复杂,不断发展的密度字段,以便在潜在的物理学中实现进入洞察力。该技术已用于许多领域,包括材料科学,休克物理,惯性监禁融合和其他国家安全应用。然而,在许多这些应用中,噪声,散射,复杂光束动力学等的并发症防止了密度的重建足以足以识别具有足够置信度的底层物理。因此,来自静态/动态射线照相的密度重建通常限于在许多这些应用中识别诸如裂缝和空隙的不连续特征。在这项工作中,我们提出了一种从基本上重建密度的基本上新的射线照片序列的密度。仅使用射线照相识别的稳健特征,我们将它们与使用机器学习方法的底层流体动力方程组合,即条件生成对冲网络(CGAN),以从射线照片的动态序列确定密度字段。接下来,我们寻求通过参数估计和投影的过程进一步提高ML的密度重建的流体动力学一致性,并进入流体动力歧管。在这种情况下,我们注意到,训练数据给出的流体动力歧管在被认为的参数空间中给出的测试数据是用于预测的稳定性的诊断,并用于增强培训数据库,期望后者将进一步降低未来的密度重建错误。最后,我们展示了这种方法优于传统的射线照相重建在捕获允许的流体动力学路径中的能力,即使存在相对少量的散射。
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While the brain connectivity network can inform the understanding and diagnosis of developmental dyslexia, its cause-effect relationships have not yet enough been examined. Employing electroencephalography signals and band-limited white noise stimulus at 4.8 Hz (prosodic-syllabic frequency), we measure the phase Granger causalities among channels to identify differences between dyslexic learners and controls, thereby proposing a method to calculate directional connectivity. As causal relationships run in both directions, we explore three scenarios, namely channels' activity as sources, as sinks, and in total. Our proposed method can be used for both classification and exploratory analysis. In all scenarios, we find confirmation of the established right-lateralized Theta sampling network anomaly, in line with the temporal sampling framework's assumption of oscillatory differences in the Theta and Gamma bands. Further, we show that this anomaly primarily occurs in the causal relationships of channels acting as sinks, where it is significantly more pronounced than when only total activity is observed. In the sink scenario, our classifier obtains 0.84 and 0.88 accuracy and 0.87 and 0.93 AUC for the Theta and Gamma bands, respectively.
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There are multiple scales of abstraction from which we can describe the same image, depending on whether we are focusing on fine-grained details or a more global attribute of the image. In brain mapping, learning to automatically parse images to build representations of both small-scale features (e.g., the presence of cells or blood vessels) and global properties of an image (e.g., which brain region the image comes from) is a crucial and open challenge. However, most existing datasets and benchmarks for neuroanatomy consider only a single downstream task at a time. To bridge this gap, we introduce a new dataset, annotations, and multiple downstream tasks that provide diverse ways to readout information about brain structure and architecture from the same image. Our multi-task neuroimaging benchmark (MTNeuro) is built on volumetric, micrometer-resolution X-ray microtomography images spanning a large thalamocortical section of mouse brain, encompassing multiple cortical and subcortical regions. We generated a number of different prediction challenges and evaluated several supervised and self-supervised models for brain-region prediction and pixel-level semantic segmentation of microstructures. Our experiments not only highlight the rich heterogeneity of this dataset, but also provide insights into how self-supervised approaches can be used to learn representations that capture multiple attributes of a single image and perform well on a variety of downstream tasks. Datasets, code, and pre-trained baseline models are provided at: https://mtneuro.github.io/ .
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Partial differential equations (PDEs) are important tools to model physical systems, and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works like a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDE, the heat equation, wave equation, and Maxwell's equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.
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Unbiased learning to rank (ULTR) studies the problem of mitigating various biases from implicit user feedback data such as clicks, and has been receiving considerable attention recently. A popular ULTR approach for real-world applications uses a two-tower architecture, where click modeling is factorized into a relevance tower with regular input features, and a bias tower with bias-relevant inputs such as the position of a document. A successful factorization will allow the relevance tower to be exempt from biases. In this work, we identify a critical issue that existing ULTR methods ignored - the bias tower can be confounded with the relevance tower via the underlying true relevance. In particular, the positions were determined by the logging policy, i.e., the previous production model, which would possess relevance information. We give both theoretical analysis and empirical results to show the negative effects on relevance tower due to such a correlation. We then propose three methods to mitigate the negative confounding effects by better disentangling relevance and bias. Empirical results on both controlled public datasets and a large-scale industry dataset show the effectiveness of the proposed approaches.
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G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the Minimum Description Length principle (MDL) to derive two different model selection criteria. Several proven theoretical results about these criteria give insights about their asymptotic behavior and are used to speed up their optimisation. These insights, combined to a greedy search heuristic, are used to construct histograms in linearithmic time rather than the polynomial time incurred by previous works. The capabilities of the proposed MDL density estimation method are illustrated with reference to other fully automated methods in the literature, both on synthetic and large real-world data sets.
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The ability to convert reciprocating, i.e., alternating, actuation into rotary motion using linkages is hindered fundamentally by their poor torque transmission capability around kinematic singularity configurations. Here, we harness the elastic potential energy of a linear spring attached to the coupler link of four-bar mechanisms to manipulate force transmission around the kinematic singularities. We developed a theoretical model to explore the parameter space for proper force transmission in slider-crank and rocker-crank four-bar kinematics. Finally, we verified the proposed model and methodology by building and testing a macro-scale prototype of a slider-crank mechanism. We expect this approach to enable the development of small-scale rotary engines and robotic devices with closed kinematic chains dealing with serial kinematic singularities, such as linkages and parallel manipulators.
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This paper considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing and direct kinematics of continuum robots. Assuming general string routing, a methodical Lie group formulation for the shape sensing of these robots is presented. The shape kinematics is expressed using arc-length-dependent curvature distributions parameterized by modal functions, and the Magnus expansion for Lie group integration is used to express the shape as a product of exponentials. The tendon and string length kinematic constraints are solved for the modal coefficients and the configuration space and body Jacobian are derived. The noise amplification index for the shape reconstruction problem is defined and used for optimizing the string/tendon routing paths, and a planar simulation study shows the minimal number of strings/tendons needed for accurate shape reconstruction. A torsionally stiff continuum segment is used for experimental evaluation, demonstrating mean (maximal) end-effector absolute position error of less than 2% (5%) of total length. Finally, a simulation study of a torsionally compliant segment demonstrates the approach for general deflections and string routings. We believe that the methods of this paper can benefit the design process, sensing and control of continuum and soft robots.
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Image classification with small datasets has been an active research area in the recent past. However, as research in this scope is still in its infancy, two key ingredients are missing for ensuring reliable and truthful progress: a systematic and extensive overview of the state of the art, and a common benchmark to allow for objective comparisons between published methods. This article addresses both issues. First, we systematically organize and connect past studies to consolidate a community that is currently fragmented and scattered. Second, we propose a common benchmark that allows for an objective comparison of approaches. It consists of five datasets spanning various domains (e.g., natural images, medical imagery, satellite data) and data types (RGB, grayscale, multispectral). We use this benchmark to re-evaluate the standard cross-entropy baseline and ten existing methods published between 2017 and 2021 at renowned venues. Surprisingly, we find that thorough hyper-parameter tuning on held-out validation data results in a highly competitive baseline and highlights a stunted growth of performance over the years. Indeed, only a single specialized method dating back to 2019 clearly wins our benchmark and outperforms the baseline classifier.
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