A filter for inertial-based odometry is a recursive method used to estimate the pose from measurements of ego-motion and relative pose. Currently, there is no known filter that guarantees the computation of a globally optimal solution for the non-linear measurement model. In this paper, we demonstrate that an innovative filter, with the state being $SE_2(3)$ and the $\sqrt{n}$-\textit{consistent} pose as the initialization, efficiently achieves \textit{asymptotic optimality} in terms of minimum mean square error. This approach is tailored for real-time SLAM and inertial-based odometry applications. Our first contribution is that we propose an iterative filtering method based on the Gauss-Newton method on Lie groups which is numerically to solve the estimation of states from a priori and non-linear measurements. The filtering stands out due to its iterative mechanism and adaptive initialization. Second, when dealing with environmental measurements of the surroundings, we utilize a $\sqrt{n}$-consistent pose as the initial value for the update step in a single iteration. The solution is closed in form and has computational complexity $O(n)$. Third, we theoretically show that the approach can achieve asymptotic optimality in the sense of minimum mean square error from the a priori and virtual relative pose measurements (see Problem~\ref{prob:new update problem}). Finally, to validate our method, we carry out extensive numerical and experimental evaluations. Our results consistently demonstrate that our approach outperforms other state-of-the-art filter-based methods, including the iterated extended Kalman filter and the invariant extended Kalman filter, in terms of accuracy and running time.

In these settings, such as communicable disease management (Tuldrà et al., the underlying transition dynamics are often unknown 1999; Killian et al., 2019), prenatal and infant care (Hegde a priori, requiring online reinforcement & Doshi, 2016; Ope, 2020; Bashingwa et al., 2021), and learning (RL). However, existing methods in online cancer prevention (Wells et al., 2011; Lee et al., 2019), beneficiaries RL for RMABs cannot incorporate properties may at any time enter an adhering (e.g., following often present in real-world public health applications, their treatment regimen) or non-adhering (e.g., missing a such as contextual information and treatment) state. As adherence is often vital for ensuring non-stationarity. We present Bayesian Learning certain health outcomes, programs may allocate resources for Contextual RMABs (BCoR), an online or interventions to patients at risk of drop-out from the program RL approach for RMABs that novelly combines due to continued non-adherence. We can model this techniques in Bayesian modeling with Thompson problem as an RMAB by representing each beneficiary as an sampling to flexibly model a wide range of arm, their adherence status as the state of the corresponding complex RMAB settings, such as contextual and MDP, and the allocation of an intervention as the action.

Partial label learning (PLL) is a weakly-supervised learning paradigm where each training instance is paired with a set of candidate labels (partial label), one of which is the true label. Noisy PLL (NPLL) relaxes this constraint by allowing some partial labels to not contain the true label, enhancing the practicality of the problem. Our work centers on NPLL and presents a minimalistic framework called SARI that initially assigns pseudo-labels to images by exploiting the noisy partial labels through a weighted nearest neighbour algorithm. These pseudo-label and image pairs are then used to train a deep neural network classifier with label smoothing and standard regularization techniques. The classifier's features and predictions are subsequently employed to refine and enhance the accuracy of pseudo-labels. SARI combines the strengths of Average Based Strategies (in pseudo labelling) and Identification Based Strategies (in classifier training) from the literature. We perform thorough experiments on seven datasets and compare SARI against nine NPLL and PLL methods from the prior art. SARI achieves state-of-the-art results in almost all studied settings, obtaining substantial gains in fine-grained classification and extreme noise settings.

The self-rationalising capabilities of LLMs are appealing because the generated explanations can give insights into the plausibility of the predictions. However, how faithful the explanations are to the predictions is questionable, raising the need to explore the patterns behind them further. To this end, we propose a hypothesis-driven statistical framework. We use a Bayesian network to implement a hypothesis about how a task (in our example, natural language inference) is solved, and its internal states are translated into natural language with templates. Those explanations are then compared to LLM-generated free-text explanations using automatic and human evaluations. This allows us to judge how similar the LLM's and the Bayesian network's decision processes are. We demonstrate the usage of our framework with an example hypothesis and two realisations in Bayesian networks. The resulting models do not exhibit a strong similarity to GPT-3.5. We discuss the implications of this as well as the framework's potential to approximate LLM decisions better in future work.

Causal discovery is an essential part of causal inference (Spirtes et al., 2000; Peters et al., 2017), but estimating causal effects is extremely challenging if the underlying causal graph is unknown. Algorithms for learning causal graphs are many and varied, using different parametric structure, classes of graphical models, and assumptions about whether all relevant variables are measured (Spirtes et al., 2000; Kaltenpoth and Vreeken, 2023; Claassen and Bucur, 2022; Nowzohour et al., 2017; Zhang and Hyvarinen, 2009; Peters et al., 2017). In this paper, we consider only nonparametric assumptions, i.e. conditional independences in distributions that are represented by graphs. The primary graphical model used in causal inference is the directed acyclic graph, also known as a DAG. These offer a clear interpretation and are straightforward to conduct inference with, and are associated with probabilistic distributions by encoding conditional independence constraints.

In tasks aiming for long-term returns, planning becomes necessary. We study generative modeling for planning with datasets repurposed from offline reinforcement learning. Specifically, we identify temporal consistency in the absence of step-wise rewards as one key technical challenge. We introduce the Latent Plan Transformer (LPT), a novel model that leverages a latent space to connect a Transformer-based trajectory generator and the final return. LPT can be learned with maximum likelihood estimation on trajectory-return pairs. In learning, posterior sampling of the latent variable naturally gathers sub-trajectories to form a consistent abstraction despite the finite context. During test time, the latent variable is inferred from an expected return before policy execution, realizing the idea of planning as inference. It then guides the autoregressive policy throughout the episode, functioning as a plan. Our experiments demonstrate that LPT can discover improved decisions from suboptimal trajectories. It achieves competitive performance across several benchmarks, including Gym-Mujoco, Maze2D, and Connect Four, exhibiting capabilities of nuanced credit assignments, trajectory stitching, and adaptation to environmental contingencies. These results validate that latent variable inference can be a strong alternative to step-wise reward prompting.

This paper introduces a novel prior called Diversified Block Sparse Prior to characterize the widespread block sparsity phenomenon in real-world data. By allowing diversification on variance and correlation matrix, we effectively address the sensitivity issue of existing block sparse learning methods to pre-defined block information, which enables adaptive block estimation while mitigating the risk of overfitting. Based on this, a diversified block sparse Bayesian learning method (DivSBL) is proposed, utilizing EM algorithm and dual ascent method for hyperparameter estimation. Moreover, we establish the global and local optimality theory of our model. Experiments validate the advantages of DivSBL over existing algorithms.

With the rise of complex cyber devices Cyber Forensics (CF) is facing many new challenges. For example, there are dozens of systems running on smartphones, each with more than millions of downloadable applications. Sifting through this large amount of data and making sense requires new techniques, such as from the field of Artificial Intelligence (AI). To apply these techniques successfully in CF, we need to justify and explain the results to the stakeholders of CF, such as forensic analysts and members of the court, for them to make an informed decision. If we want to apply AI successfully in CF, there is a need to develop trust in AI systems. Some other factors in accepting the use of AI in CF are to make AI authentic, interpretable, understandable, and interactive. This way, AI systems will be more acceptable to the public and ensure alignment with legal standards. An explainable AI (XAI) system can play this role in CF, and we call such a system XAI-CF. XAI-CF is indispensable and is still in its infancy. In this paper, we explore and make a case for the significance and advantages of XAI-CF. We strongly emphasize the need to build a successful and practical XAI-CF system and discuss some of the main requirements and prerequisites of such a system. We present a formal definition of the terms CF and XAI-CF and a comprehensive literature review of previous works that apply and utilize XAI to build and increase trust in CF. We discuss some challenges facing XAI-CF. We also provide some concrete solutions to these challenges. We identify key insights and future research directions for building XAI applications for CF. This paper is an effort to explore and familiarize the readers with the role of XAI applications in CF, and we believe that our work provides a promising basis for future researchers interested in XAI-CF.

Facing climate change, the already limited availability of drinking water will decrease in the future rendering drinking water an increasingly scarce resource. Considerable amounts of it are lost through leakages in water transportation and distribution networks. Thus, anomaly detection and localization, in particular for leakages, are crucial but challenging tasks due to the complex interactions and changing demands in water distribution networks. In this work, we analyze the effects of anomalies on the dynamics of critical infrastructure systems by modeling the networks employing Bayesian networks. We then discuss how the problem is connected to and can be considered through the lens of concept drift. In particular, we argue that model-based explanations of concept drift are a promising tool for localizing anomalies given limited information about the network. The methodology is experimentally evaluated using realistic benchmark scenarios. To showcase that our methodology applies to critical infrastructure more generally, in addition to considering leakages and sensor faults in water systems, we showcase the suitability of the derived technique to localize sensor faults in power systems.

We propose a diffusion approximation method to the continuous-state Markov Decision Processes (MDPs) that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most decision-theoretic planning frameworks that assume fully known state transition models, we design a method that eliminates such a strong assumption that is often extremely difficult to engineer in reality. We first take the second-order Taylor expansion of the value function. The Bellman optimality equation is then approximated by a partial differential equation, which only relies on the first and second moments of the transition model. By combining the kernel representation of the value function, we design an efficient policy iteration algorithm whose policy evaluation step can be represented as a linear system of equations characterized by a finite set of supporting states. We first validate the proposed method through extensive simulations in 2D obstacle avoidance and 2.5D terrain navigation problems. The results show that the proposed approach leads to a much superior performance over several baselines. We then develop a system that integrates our decision-making framework with onboard perception and conduct real-world experiments in both cluttered indoor and unstructured outdoor environments. The results from the physical systems further demonstrate the applicability of our method in challenging real-world environments.