We focus on causal discovery in the presence of measurement error in linear systems where the mixing matrix, i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables, is identified up to permutation and scaling of the columns. We demonstrate a somewhat surprising connection between this problem and causal discovery in the presence of unobserved parentless causes, in the sense that there is a mapping, given by the mixing matrix, between the underlying models to be inferred in these problems. Consequently, any identifiability result based on the mixing matrix for one model translates to an identifiability result for the other model. We characterize to what extent the causal models can be identified under a two-part faithfulness assumption. Under only the first part of the assumption (corresponding to the conventional definition of faithfulness), the structure can be learned up to the causal ordering among an ordered grouping of the variables but not all the edges across the groups can be identified. We further show that if both parts of the faithfulness assumption are imposed, the structure can be learned up to a more refined ordered grouping. As a result of this refinement, for the latent variable model with unobserved parentless causes, the structure can be identified. Based on our theoretical results, we propose causal structure learning methods for both models, and evaluate their performance on synthetic data.

我们建议在没有观察到的变量的情况下，提出基于订购的方法，用于学习结构方程模型（SEM）的最大祖先图（MAG），直到其Markov等效类（MEC）。文献中的现有基于订购的方法通过学习因果顺序（C-order）恢复图。我们提倡一个名为“可移动顺序”（R-rorder）的新颖订单，因为它们比结构学习的C端口有利。这是因为R-orders是适当定义的优化问题的最小化器，该问题可以准确解决（使用强化学习方法）或大约（使用爬山搜索）。此外，R-orders（与C-orders不同）在MEC中的所有图表中都是不变的，并将C-orders包括为子集。鉴于一组R-orders通常明显大于C-orders集，因此优化问题更容易找到R级而不是C级。我们评估了在现实世界和随机生成的网络上提出的方法的性能和可伸缩性。

因果鉴定是因果推理文献的核心，在该文献中提出了完整的算法来识别感兴趣的因果问题。这些算法的有效性取决于访问正确指定的因果结构的限制性假设。在这项工作中，我们研究了可获得因果结构概率模型的环境。具体而言，因果图中的边缘是分配的概率，例如，可能代表来自领域专家的信念程度。另外，关于边缘的不确定的可能反映了特定统计检验的置信度。在这种情况下自然出现的问题是：给定这样的概率图和感兴趣的特定因果效应，哪些具有最高合理性的子图是什么？我们表明回答这个问题减少了解决NP-HARD组合优化问题，我们称之为边缘ID问题。我们提出有效的算法来近似此问题，并评估我们针对现实世界网络和随机生成图的算法。

We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skeleton of causal graphs with cycles may not be possible from merely the observational distribution. Furthermore, intervening on a variable in such graphs does not necessarily lead to orienting all the edges incident to it. In this paper, we propose an experiment design approach that can learn both cyclic and acyclic graphs and hence, unifies the task of experiment design for both types of graphs. We provide a lower bound on the number of experiments required to guarantee the unique identification of the causal graph in the worst case, showing that the proposed approach is order-optimal in terms of the number of experiments up to an additive logarithmic term. Moreover, we extend our result to the setting where the size of each experiment is bounded by a constant. For this case, we show that our approach is optimal in terms of the size of the largest experiment required for uniquely identifying the causal graph in the worst case.

降低策略梯度方法方差的梯度估计器已成为近年来增强学习研究的主要重点之一，因为它们允许加速估算过程。我们提出了一种称为Sharp的方差降低的策略梯度方法，该方法将二阶信息纳入随机梯度下降（SGD）中，并使用动量和时间变化的学习率。 Sharp Algorithm无参数，实现$ \ Epsilon $ - Appro-Appro-Approximate固定点，带有$ O（\ Epsilon^{ - 3}）$的轨迹数，同时使用批量的大小为$ O（1）$迭代。与以前的大多数工作不同，我们提出的算法不需要重要的抽样，这可能会损害降低方差的优势。此外，估计错误的差异会以$ o（1/t^{2/3}）$的快速速率衰减，其中$ t $是迭代的数量。我们广泛的实验评估表明，拟议算法对各种控制任务的有效性及其对实践中最新状态的优势。

Pearl's Do Colculus是一种完整的公理方法，可以从观察数据中学习可识别的因果效应。如果无法识别这种效果，则有必要在系统中执行经常昂贵的干预措施以学习因果效应。在这项工作中，我们考虑了设计干预措施以最低成本来确定所需效果的问题。首先，我们证明了这个问题是NP-HARD，随后提出了一种可以找到最佳解或对数因子近似值的算法。这是通过在我们的问题和最小击球设置问题之间建立联系来完成的。此外，我们提出了几种多项式启发式算法来解决问题的计算复杂性。尽管这些算法可能会偶然发现亚最佳解决方案，但我们的模拟表明它们在随机图上产生了小的遗憾。

我们研究在有关系统的结构侧信息时学习一组变量的贝叶斯网络（BN）的问题。众所周知，学习一般BN的结构在计算上和统计上具有挑战性。然而，通常在许多应用中，关于底层结构的侧面信息可能会降低学习复杂性。在本文中，我们开发了一种基于递归约束的算法，其有效地将这些知识（即侧信息）纳入学习过程。特别地，我们研究了关于底层BN的两种类型的结构侧信息：（i）其集团数的上限是已知的，或者（ii）它是无菱形的。我们为学习算法提供理论保证，包括每个场景所需的最坏情况的测试数量。由于我们的工作，我们表明可以通过多项式复杂性学习有界树木宽度BNS。此外，我们评估了综合性和现实世界结构的算法的性能和可扩展性，并表明它们优于最先进的结构学习算法。

Linear structural causal models (SCMs)-- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources-- are pervasive in causal inference and casual discovery. However, for the task of causal discovery, existing work almost exclusively focus on the submodel where each observed variable is associated with a distinct source with non-zero variance. This results in the restriction that no observed variable can deterministically depend on other observed variables or latent confounders. In this paper, we extend the results on structure learning by focusing on a subclass of linear SCMs which do not have this property, i.e., models in which observed variables can be causally affected by any subset of the sources, and are allowed to be a deterministic function of other observed variables or latent confounders. This allows for a more realistic modeling of influence or information propagation in systems. We focus on the task of causal discovery form observational data generated from a member of this subclass. We derive a set of necessary and sufficient conditions for unique identifiability of the causal structure. To the best of our knowledge, this is the first work that gives identifiability results for causal discovery under both latent confounding and deterministic relationships. Further, we propose an algorithm for recovering the underlying causal structure when the aforementioned conditions are satisfied. We validate our theoretical results both on synthetic and real datasets.

6D object pose estimation problem has been extensively studied in the field of Computer Vision and Robotics. It has wide range of applications such as robot manipulation, augmented reality, and 3D scene understanding. With the advent of Deep Learning, many breakthroughs have been made; however, approaches continue to struggle when they encounter unseen instances, new categories, or real-world challenges such as cluttered backgrounds and occlusions. In this study, we will explore the available methods based on input modality, problem formulation, and whether it is a category-level or instance-level approach. As a part of our discussion, we will focus on how 6D object pose estimation can be used for understanding 3D scenes.

Predicting discrete events in time and space has many scientific applications, such as predicting hazardous earthquakes and outbreaks of infectious diseases. History-dependent spatio-temporal Hawkes processes are often used to mathematically model these point events. However, previous approaches have faced numerous challenges, particularly when attempting to forecast one or multiple future events. In this work, we propose a new neural architecture for multi-event forecasting of spatio-temporal point processes, utilizing transformers, augmented with normalizing flows and probabilistic layers. Our network makes batched predictions of complex history-dependent spatio-temporal distributions of future discrete events, achieving state-of-the-art performance on a variety of benchmark datasets including the South California Earthquakes, Citibike, Covid-19, and Hawkes synthetic pinwheel datasets. More generally, we illustrate how our network can be applied to any dataset of discrete events with associated markers, even when no underlying physics is known.