我们考虑了使用显微镜或X射线散射技术产生的图像数据自组装的模型的贝叶斯校准。为了说明BCP平衡结构中的随机远程疾病，我们引入了辅助变量以表示这种不确定性。然而，这些变量导致了高维图像数据的综合可能性，通常可以评估。我们使用基于测量运输的可能性方法以及图像数据的摘要统计数据来解决这一具有挑战性的贝叶斯推理问题。我们还表明，可以计算出有关模型参数的数据中的预期信息收益（EIG），而无需额外的成本。最后，我们介绍了基于二嵌段共聚物薄膜自组装和自上而下显微镜表征的ohta-kawasaki模型的数值案例研究。为了进行校准，我们介绍了一些基于域的能量和傅立叶的摘要统计数据，并使用EIG量化了它们的信息性。我们证明了拟议方法研究数据损坏和实验设计对校准结果的影响的力量。

我们介绍了一种新颖的几何形状不可逆的扰动，该扰动加速了langevin算法的贝叶斯计算的收敛性。有充分的文献证明，兰格文动力学存在扰动，该动力学在加速其收敛的同时保留其不变度的度量。不可逆的扰动和可逆扰动（例如Riemannian歧管Langevin Dynamics（RMLD））已被单独显示以改善Langevin Samplers的性能。我们同时考虑了这两种扰动，通过呈现一种新型的RMLD不可逆扰动形式，该形式由基础几何形状告知。通过数值示例，我们表明，这种新的不可逆扰动可以改善估计性性能，而不是不可逆的扰动，而这些扰动不会考虑到几何。此外，我们证明，不可逆转的扰动通常可以与Langevin算法的随机梯度版本结合使用。最后，尽管连续的不可逆扰动不能损害兰格文估计器的性能，但考虑离散化时，情况有时会更加复杂。为此，我们描述了一个离散的示例，其中不可逆性增加了所得估计量的偏差和差异。

我们研究基于度量传输的非参数密度估计器的收敛性和相关距离。这些估计量代表了利息的度量，作为传输图下选择的参考分布的推动力，其中地图是通过最大似然目标选择（等效地，将经验性的kullback-leibler损失）或其受惩罚版本选择。我们通过将M估计的技术与基于运输的密度表示的分析性能相结合，为一般惩罚措施估计量的一般类别的措施运输估计器建立了浓度不平等。然后，我们证明了我们的理论对三角形knothe-rosenblatt（kr）在$ d $维单元方面的运输的含义，并表明该估计器的惩罚和未化的版本都达到了Minimax最佳收敛速率，超过了H \ \ \'“较旧的密度类别。具体来说，我们建立了在有限的h \“较旧型球上，未确定的非参数最大似然估计，然后在某些sobolev-penalate的估计器和筛分的小波估计器中建立了最佳速率。

度量的运输提供了一种用于建模复杂概率分布的多功能方法，并具有密度估计，贝叶斯推理，生成建模及其他方法的应用。单调三角传输地图$ \ unicode {x2014} $近似值$ \ unicode {x2013} $ rosenblatt（kr）重新安排$ \ unicode {x2014} $是这些任务的规范选择。然而，此类地图的表示和参数化对它们的一般性和表现力以及对从数据学习地图学习（例如，通过最大似然估计）出现的优化问题的属性产生了重大影响。我们提出了一个通用框架，用于通过平滑函数的可逆变换来表示单调三角图。我们建立了有关转化的条件，以使相关的无限维度最小化问题没有伪造的局部最小值，即所有局部最小值都是全球最小值。我们展示了满足某些尾巴条件的目标分布，唯一的全局最小化器与KR地图相对应。鉴于来自目标的样品，我们提出了一种自适应算法，该算法估计了基础KR映射的稀疏半参数近似。我们证明了如何将该框架应用于关节和条件密度估计，无可能的推断以及有向图形模型的结构学习，并在一系列样本量之间具有稳定的概括性能。

The recent increase in public and academic interest in preserving biodiversity has led to the growth of the field of conservation technology. This field involves designing and constructing tools that utilize technology to aid in the conservation of wildlife. In this article, we will use case studies to demonstrate the importance of designing conservation tools with human-wildlife interaction in mind and provide a framework for creating successful tools. These case studies include a range of complexities, from simple cat collars to machine learning and game theory methodologies. Our goal is to introduce and inform current and future researchers in the field of conservation technology and provide references for educating the next generation of conservation technologists. Conservation technology not only has the potential to benefit biodiversity but also has broader impacts on fields such as sustainability and environmental protection. By using innovative technologies to address conservation challenges, we can find more effective and efficient solutions to protect and preserve our planet's resources.

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical parameters. The iMODE method learns meta-knowledge, the functional variations of the force field of dynamical system instances without knowing the physical parameters, by adopting a bi-level optimization framework: an outer level capturing the common force field form among studied dynamical system instances and an inner level adapting to individual system instances. A priori physical knowledge can be conveniently embedded in the neural network architecture as inductive bias, such as conservative force field and Euclidean symmetry. With the learned meta-knowledge, iMODE can model an unseen system within seconds, and inversely reveal knowledge on the physical parameters of a system, or as a Neural Gauge to "measure" the physical parameters of an unseen system with observed trajectories. We test the validity of the iMODE method on bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.

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.

Variational autoencoders model high-dimensional data by positing low-dimensional latent variables that are mapped through a flexible distribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from posterior collapse: the posterior of the latent variables is equal to its prior, rendering the variational autoencoder useless as a means to produce meaningful representations. Existing approaches to posterior collapse often attribute it to the use of neural networks or optimization issues due to variational approximation. In this paper, we consider posterior collapse as a problem of latent variable non-identifiability. We prove that the posterior collapses if and only if the latent variables are non-identifiable in the generative model. This fact implies that posterior collapse is not a phenomenon specific to the use of flexible distributions or approximate inference. Rather, it can occur in classical probabilistic models even with exact inference, which we also demonstrate. Based on these results, we propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. This model class resolves the problem of latent variable non-identifiability by leveraging bijective Brenier maps and parameterizing them with input convex neural networks, without special variational inference objectives or optimization tricks. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.

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/ .

We derive a set of causal deep neural networks whose architectures are a consequence of tensor (multilinear) factor analysis. Forward causal questions are addressed with a neural network architecture composed of causal capsules and a tensor transformer. The former estimate a set of latent variables that represent the causal factors, and the latter governs their interaction. Causal capsules and tensor transformers may be implemented using shallow autoencoders, but for a scalable architecture we employ block algebra and derive a deep neural network composed of a hierarchy of autoencoders. An interleaved kernel hierarchy preprocesses the data resulting in a hierarchy of kernel tensor factor models. Inverse causal questions are addressed with a neural network that implements multilinear projection and estimates the causes of effects. As an alternative to aggressive bottleneck dimension reduction or regularized regression that may camouflage an inherently underdetermined inverse problem, we prescribe modeling different aspects of the mechanism of data formation with piecewise tensor models whose multilinear projections are well-defined and produce multiple candidate solutions. Our forward and inverse neural network architectures are suitable for asynchronous parallel computation.