许多用于反问题和数据同化的现代算法都依赖于集成Kalman更新，以将先前的预测与观察到的数据融为一体。合奏Kalman方法通常具有小的合奏尺寸，这在生成每个粒子成本高昂的应用中至关重要。本文对合奏Kalman更新进行了非反应分析，该分析严格地解释了为什么由于快速衰减或近似稀疏性而导致先前的协方差具有适度的有效尺寸，那么小合奏的大小就足够了。我们在统一的框架中介绍了我们的理论，比较了使用扰动观测值，平方根滤波和本地化的集合卡尔曼更新的几个实现。作为我们分析的一部分，我们为可能具有独立感兴趣的大约稀疏矩阵开发了新的无维度协方差估计界限。

近几十年来，科学和工程的可用数据数量的重大增长彻底改变了。然而，尽管现在收集和存储数据的空前很容易，但通过补充每个功能的标签来标记数据仍然是具有挑战性的。标签过程需要专家知识或乏味且耗时的说明任务包括用诊断X射线标记X射线，具有蛋白质类型的蛋白质序列，其主题的文本，通过其情感推文或视频通过其类型的视频。在这些和许多其他示例中，由于成本和时间限制，只能手动标记一些功能。我们如何才能最好地将标签信息从少数昂贵的标签功能到大量未标记的标签信息传播？这是半监督学习（SSL）提出的问题。本文概述了基于图的贝叶斯SSL的最新基础发展，这是一种使用功能之间的相似性的标签传播概率框架。 SSL是一个活跃的研究领域，对现有文献的彻底回顾超出了本文的范围。我们的重点将放在我们自己的研究中得出的主题，这些主题说明了对基于图的贝叶斯SSL的统计准确性和计算效率进行严格研究的广泛数学工具和思想。

具有伽马超高提升的分层模型提供了一个灵活，稀疏的促销框架，用于桥接$ l ^ 1 $和$ l ^ 2 $ scalalizations在贝叶斯的配方中致正问题。尽管对这些模型具有贝叶斯动机，但现有的方法仅限于\ Textit {最大后验}估计。尚未实现执行不确定性量化的可能性。本文介绍了伽马超高图的分层逆问题的变分迭代交替方案。所提出的变分推理方法产生精确的重建，提供有意义的不确定性量化，易于实施。此外，它自然地引入了用于选择超参数的模型选择。我们说明了我们在几个计算的示例中的方法的性能，包括从时间序列数据的动态系统的解卷积问题和稀疏识别。

The performance of inertial navigation systems is largely dependent on the stable flow of external measurements and information to guarantee continuous filter updates and bind the inertial solution drift. Platforms in different operational environments may be prevented at some point from receiving external measurements, thus exposing their navigation solution to drift. Over the years, a wide variety of works have been proposed to overcome this shortcoming, by exploiting knowledge of the system current conditions and turning it into an applicable source of information to update the navigation filter. This paper aims to provide an extensive survey of information aided navigation, broadly classified into direct, indirect, and model aiding. Each approach is described by the notable works that implemented its concept, use cases, relevant state updates, and their corresponding measurement models. By matching the appropriate constraint to a given scenario, one will be able to improve the navigation solution accuracy, compensate for the lost information, and uncover certain internal states, that would otherwise remain unobservable.

We consider infinite horizon Markov decision processes (MDPs) with fast-slow structure, meaning that certain parts of the state space move "fast" (and in a sense, are more influential) while other parts transition more "slowly." Such structure is common in real-world problems where sequential decisions need to be made at high frequencies, yet information that varies at a slower timescale also influences the optimal policy. Examples include: (1) service allocation for a multi-class queue with (slowly varying) stochastic costs, (2) a restless multi-armed bandit with an environmental state, and (3) energy demand response, where both day-ahead and real-time prices play a role in the firm's revenue. Models that fully capture these problems often result in MDPs with large state spaces and large effective time horizons (due to frequent decisions), rendering them computationally intractable. We propose an approximate dynamic programming algorithmic framework based on the idea of "freezing" the slow states, solving a set of simpler finite-horizon MDPs (the lower-level MDPs), and applying value iteration (VI) to an auxiliary MDP that transitions on a slower timescale (the upper-level MDP). We also extend the technique to a function approximation setting, where a feature-based linear architecture is used. On the theoretical side, we analyze the regret incurred by each variant of our frozen-state approach. Finally, we give empirical evidence that the frozen-state approach generates effective policies using just a fraction of the computational cost, while illustrating that simply omitting slow states from the decision modeling is often not a viable heuristic.

In the present work we propose an unsupervised ensemble method consisting of oblique trees that can address the task of auto-encoding, namely Oblique Forest AutoEncoders (briefly OF-AE). Our method is a natural extension of the eForest encoder introduced in [1]. More precisely, by employing oblique splits consisting in multivariate linear combination of features instead of the axis-parallel ones, we will devise an auto-encoder method through the computation of a sparse solution of a set of linear inequalities consisting of feature values constraints. The code for reproducing our results is available at https://github.com/CDAlecsa/Oblique-Forest-AutoEncoders.

When robots learn reward functions using high capacity models that take raw state directly as input, they need to both learn a representation for what matters in the task -- the task ``features" -- as well as how to combine these features into a single objective. If they try to do both at once from input designed to teach the full reward function, it is easy to end up with a representation that contains spurious correlations in the data, which fails to generalize to new settings. Instead, our ultimate goal is to enable robots to identify and isolate the causal features that people actually care about and use when they represent states and behavior. Our idea is that we can tune into this representation by asking users what behaviors they consider similar: behaviors will be similar if the features that matter are similar, even if low-level behavior is different; conversely, behaviors will be different if even one of the features that matter differs. This, in turn, is what enables the robot to disambiguate between what needs to go into the representation versus what is spurious, as well as what aspects of behavior can be compressed together versus not. The notion of learning representations based on similarity has a nice parallel in contrastive learning, a self-supervised representation learning technique that maps visually similar data points to similar embeddings, where similarity is defined by a designer through data augmentation heuristics. By contrast, in order to learn the representations that people use, so we can learn their preferences and objectives, we use their definition of similarity. In simulation as well as in a user study, we show that learning through such similarity queries leads to representations that, while far from perfect, are indeed more generalizable than self-supervised and task-input alternatives.

While the capabilities of autonomous systems have been steadily improving in recent years, these systems still struggle to rapidly explore previously unknown environments without the aid of GPS-assisted navigation. The DARPA Subterranean (SubT) Challenge aimed to fast track the development of autonomous exploration systems by evaluating their performance in real-world underground search-and-rescue scenarios. Subterranean environments present a plethora of challenges for robotic systems, such as limited communications, complex topology, visually-degraded sensing, and harsh terrain. The presented solution enables long-term autonomy with minimal human supervision by combining a powerful and independent single-agent autonomy stack, with higher level mission management operating over a flexible mesh network. The autonomy suite deployed on quadruped and wheeled robots was fully independent, freeing the human supervision to loosely supervise the mission and make high-impact strategic decisions. We also discuss lessons learned from fielding our system at the SubT Final Event, relating to vehicle versatility, system adaptability, and re-configurable communications.

Deep learning models are known to put the privacy of their training data at risk, which poses challenges for their safe and ethical release to the public. Differentially private stochastic gradient descent is the de facto standard for training neural networks without leaking sensitive information about the training data. However, applying it to models for graph-structured data poses a novel challenge: unlike with i.i.d. data, sensitive information about a node in a graph cannot only leak through its gradients, but also through the gradients of all nodes within a larger neighborhood. In practice, this limits privacy-preserving deep learning on graphs to very shallow graph neural networks. We propose to solve this issue by training graph neural networks on disjoint subgraphs of a given training graph. We develop three random-walk-based methods for generating such disjoint subgraphs and perform a careful analysis of the data-generating distributions to provide strong privacy guarantees. Through extensive experiments, we show that our method greatly outperforms the state-of-the-art baseline on three large graphs, and matches or outperforms it on four smaller ones.

Machine learning models are typically evaluated by computing similarity with reference annotations and trained by maximizing similarity with such. Especially in the bio-medical domain, annotations are subjective and suffer from low inter- and intra-rater reliability. Since annotations only reflect the annotation entity's interpretation of the real world, this can lead to sub-optimal predictions even though the model achieves high similarity scores. Here, the theoretical concept of Peak Ground Truth (PGT) is introduced. PGT marks the point beyond which an increase in similarity with the reference annotation stops translating to better Real World Model Performance (RWMP). Additionally, a quantitative technique to approximate PGT by computing inter- and intra-rater reliability is proposed. Finally, three categories of PGT-aware strategies to evaluate and improve model performance are reviewed.