不观察到的混淆是估算因果效应时的主要挑战之一。我们提出了一种因果还原方法，给出因果模型，用一个潜在的混淆器取代了一个任意数量的可能的高维潜在混淆，这些混淆是在同一空间中的价值观，而不改变原因的观察和介入分布模特需要。这使我们能够以合并数据的原则方式估计因果效应而不依赖于普遍但往往不切实际的假设，即所有的混乱。我们在三种不同的设置中应用了我们的因果化。在第一个设置中，我们假设治疗和结果是离散的。随后的因果还原暗示可以利用估计目的的观察和介入分布之间的界限。在某些情况下具有高度不平衡的观察样本的情况下，通过掺入观察数据，可以提高因果效应估计的准确性。其次，对于连续变量并假设线性高斯模型，我们导出了对观察和介入分布的参数的平等约束。第三，对于一般连续设置（可能是非线性或非高斯），我们使用标准化流量参数化减少的因果模型，灵活的易于可逆的非线性变换。我们对合成数据进行一系列实验，发现在几个情况下，在不牺牲精度的情况下添加观察训练样本时，可以减少介入样本的数量。

动态系统中的完美适应性是一个或多个变量具有对外部刺激的持续变化的初始短暂响应的现象，但随着系统收敛到平衡，其原始值还原为原始值。借助因果有序算法，可以构建代表变量之间的因果关系和平衡分布中条件独立性之间的因果关系的图形表示。我们应用这些工具来制定足够的图形条件，以识别一组一阶微分方程的完美适应。此外，我们提供了足够的条件来测试实验平衡数据中完美适应的情况。我们将此方法应用于蛋白质信号通路的简单模型，并在模拟和使用现实世界中的蛋白质表达数据中测试其预测。我们证明，完美的适应会导致因果发现算法输出中边缘的误导方向。

现实世界的数学模型是复杂系统的简化表示。使用数学模型的警告是，在模型扩展下，预测的因果效应和条件独立性可能不健壮，从而限制了此类模型的适用性。在这项工作中，我们考虑将两个模型组合在一起时保留定性模型预测的条件。在温和的假设下，我们展示了如何使用因果秩序的技术来有效评估定性模型预测的鲁棒性。我们还表征了一大批模型扩展，以保留定性模型预测。对于平衡的动态系统，我们演示了新颖的见解如何有助于选择适当的模型扩展，并理解反馈回路的存在。我们用具有免疫反应的病毒感染模型来说明我们的想法。

因果匪是经典匪徒问题的变体，在该问题中，代理必须在顺序决策过程中识别最佳动作，其中动作的奖励分布显示由因果模型控制的非平凡依赖性结构。到目前为止，文献中针对此问题提出的方法取决于完整因果图的精确知识。我们制定了不再依赖先前因果知识的新因果匪徒。相反，他们利用基于分离集的估计量，我们可以使用简单的条件独立性测试或因果发现方法找到。我们证明，给定一个真正的分离集，用于离散的I.I.D.数据，该估计量是公正的，并且具有差异，该方差受样本平均值的上限。我们分别基于Thompson采样和UCB开发算法，分别用于离散和高斯模型，并显示了模拟数据以及来自现实世界中蛋白质信号数据的强盗图上的性能提高。

动态系统广泛用于科学和工程，以模拟由多个交互组件组成的系统。通常，它们可以在意义上给出因果解释，因为它们不仅模拟了系统组件状态随时间的演变，而且描述了他们的进化如何受到动态的系统的外部干预的影响。我们介绍了结构动态因果模型（SDCMS）的正式框架，其将系统组件的因果语言作为模型的一部分来阐述。 SDCMS表示动态系统作为随机过程的集合，并指定了管理每个组件的动态的基本因果机制，作为任意顺序的随机微分方程的结构化系统。 SDCMS扩展了结构因果模型（SCM）的多功能因果建模框架，也称为结构方程模型（SEM），通过显式允许时间依赖。 SDCM可以被认为是SCM的随机过程版本，其中SCM的静态随机变量由动态随机过程及其衍生物代替。我们为SDCMS理论提供基础，（i）正式定义SDCMS，其解决方案，随机干预和图形表示; （ii）对初始条件的解决方案的存在性和独特性; （iii）随着时间的推移倾向于无穷大，讨论SDCMS平衡的条件下降; （iv）将SDCM的性质与平衡SCM的性质相关联。这封对应关系使人们能够在研究大类随机动力系统的因果语义时利用SCM的大量统计工具和发现方法。该理论用来自不同科学域的几个众所周知的示例进行说明。

也称为（非参数）结构方程模型（SEMS）的结构因果模型（SCM）被广泛用于因果建模目的。特别是，也称为递归SEM的无循环SCMS，形成了一个研究的SCM的良好的子类，概括了因果贝叶斯网络来允许潜在混淆。在本文中，我们调查了更多普通环境中的SCM，允许存在潜在混杂器和周期。我们展示在存在周期中，无循环SCM的许多方便的性质通常不会持有：它们并不总是有解决方案;它们并不总是诱导独特的观察，介入和反事实分布;边缘化并不总是存在，如果存在边缘模型并不总是尊重潜在的投影;他们并不总是满足马尔可夫财产;他们的图表并不总是与他们的因果语义一致。我们证明，对于SCM一般，这些属性中的每一个都在某些可加工条件下保持。我们的工作概括了SCM的结果，迄今为止仅针对某些特殊情况所知的周期。我们介绍了将循环循环设置扩展到循环设置的简单SCM的类，同时保留了许多方便的无环SCM的性能。用本文，我们的目标是为SCM提供统计因果建模的一般理论的基础。

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.