Analyses of causal mediation often involve exposure-induced confounders or, relatedly, multiple mediators. In such applications, researchers aim to estimate a variety of different quantities, including interventional direct and indirect effects, multivariate natural direct and indirect effects, and/or path-specific effects. This study introduces a general approach to estimating all these quantities by simulating potential outcomes from a series of distribution models for each mediator and the outcome. Building on similar methods developed for analyses with only a single mediator (Imai et al. 2010), we first outline how to implement this approach with parametric models. The parametric implementation can accommodate linear and nonlinear relationships, both continuous and discrete mediators, and many different types of outcomes. However, it depends on correct specification of each model used to simulate the potential outcomes. To address the risk of misspecification, we also introduce an alternative implementation using a novel class of nonparametric models, which leverage deep neural networks to approximate the relevant distributions without relying on strict assumptions about functional form. We illustrate both methods by reanalyzing the effects of media framing on attitudes toward immigration (Brader et al. 2008) and the effects of prenatal care on preterm birth (VanderWeele et al. 2014).

Potential-based reward shaping is commonly used to incorporate prior knowledge of how to solve the task into reinforcement learning because it can formally guarantee policy invariance. As such, the optimal policy and the ordering of policies by their returns are not altered by potential-based reward shaping. In this work, we highlight the dependence of effective potential-based reward shaping on the initial Q-values and external rewards, which determine the agent's ability to exploit the shaping rewards to guide its exploration and achieve increased sample efficiency. We formally derive how a simple linear shift of the potential function can be used to improve the effectiveness of reward shaping without changing the encoded preferences in the potential function, and without having to adjust the initial Q-values, which can be challenging and undesirable in deep reinforcement learning. We show the theoretical limitations of continuous potential functions for correctly assigning positive and negative reward shaping values. We verify our theoretical findings empirically on Gridworld domains with sparse and uninformative reward functions, as well as on the Cart Pole and Mountain Car environments, where we demonstrate the application of our results in deep reinforcement learning.

Construction robotics increasingly relies on natural language processing for task execution, creating a need for robust methods to interpret commands in complex, dynamic environments. While existing research primarily focuses on what tasks robots should perform, less attention has been paid to how these tasks should be executed safely and efficiently. This paper presents a novel probabilistic framework that uses sentiment analysis from natural language commands to dynamically adjust robot navigation policies in construction environments. The framework leverages Building Information Modeling (BIM) data and natural language prompts to create adaptive navigation strategies that account for varying levels of environmental risk and uncertainty. We introduce an object-aware path planning approach that combines exponential potential fields with a grid-based representation of the environment, where the potential fields are dynamically adjusted based on the semantic analysis of user prompts. The framework employs Bayesian inference to consolidate multiple information sources: the static data from BIM, the semantic content of natural language commands, and the implied safety constraints from user prompts. We demonstrate our approach through experiments comparing three scenarios: baseline shortest-path planning, safety-oriented navigation, and risk-aware routing. Results show that our method successfully adapts path planning based on natural language sentiment, achieving a 50\% improvement in minimum distance to obstacles when safety is prioritized, while maintaining reasonable path lengths. Scenarios with contrasting prompts, such as "dangerous" and "safe", demonstrate the framework's ability to modify paths. This approach provides a flexible foundation for integrating human knowledge and safety considerations into construction robot navigation.

Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes of logical variables. We found that the current state-of-the-art algorithm to construct a lifted representation in form of a parametric factor graph misses symmetries between factors that are exchangeable but scaled differently, thereby leading to a less compact representation. In this paper, we propose a generalisation of the advanced colour passing (ACP) algorithm, which is the state of the art to construct a parametric factor graph. Our proposed algorithm allows for potentials of factors to be scaled arbitrarily and efficiently detects more symmetries than the original ACP algorithm. By detecting strictly more symmetries than ACP, our algorithm significantly reduces online query times for probabilistic inference when the resulting model is applied, which we also confirm in our experiments.

Updates of extensive Internet of Things (IoT) data are critical to the immersion of vehicular metaverse services. However, providing high-quality and sustainable data in unstable and resource-constrained vehicular networks remains a significant challenge. To address this problem, we put forth a novel immersion-aware model trading framework that incentivizes metaverse users (MUs) to contribute learning models trained by their latest local data for augmented reality (AR) services in the vehicular metaverse, while preserving their privacy through federated learning. To comprehensively evaluate the contribution of locally trained learning models provided by MUs to AR services, we design a new immersion metric that captures service immersion by considering the freshness and accuracy of learning models, as well as the amount and potential value of raw data used for training. We model the trading interactions between metaverse service providers (MSPs) and MUs as an equilibrium problem with equilibrium constraints (EPEC) to analyze and balance their costs and gains. Moreover, considering dynamic network conditions and privacy concerns, we formulate the reward decisions of MSPs as a multi-agent Markov decision process. Then, a fully distributed dynamic reward method based on deep reinforcement learning is presented, which operates without any private information about MUs and other MSPs. Experimental results demonstrate that the proposed framework can effectively provide higher-value models for object detection and classification in AR services on real AR-related vehicle datasets compared to benchmark schemes.

Lifted probabilistic inference exploits symmetries in probabilistic graphical models to allow for tractable probabilistic inference with respect to domain sizes. To exploit symmetries in, e.g., factor graphs, it is crucial to identify commutative factors, i.e., factors having symmetries within themselves due to their arguments being exchangeable. The current state of the art to check whether a factor is commutative with respect to a subset of its arguments iterates over all possible subsets of the factor's arguments, i.e., $O(2^n)$ iterations for a factor with $n$ arguments in the worst case. In this paper, we efficiently solve the problem of detecting commutative factors in a factor graph. In particular, we introduce the detection of commutative factors (DECOR) algorithm, which allows us to drastically reduce the computational effort for checking whether a factor is commutative in practice. We prove that DECOR efficiently identifies restrictions to drastically reduce the number of required iterations and validate the efficiency of DECOR in our empirical evaluation.

Swarm robots, inspired by the emergence of animal herds, are robots that assemble a large number of modules and self-organize themselves to form specific morphologies and exhibit specific functions. These modular robots perform relatively simple actions and controls, and create macroscopic morphologies and functions through the interaction of a large number of modular robots. This research focuses on such self-organizing robots or swarm robots. The proposed algorithm is a model that applies the Turing pattern, one of the self-organization models, to make a group of modules accumulate and stay within a certain region. The proposed method utilizes the area within the spots of the Turing pattern as the aggregation region of the modules. Furthermore, it considers the value corresponding to the concentration distribution within the spotted pattern of the Turing pattern model (referred to as the potential value in this research), identifies the center of the region (spotted pattern), and makes it the center of the module group. By controlling the modules in the direction of the higher potential value, it succeeds in maintaining the shape of the module group as a whole while moving. The algorithm was validated using a two-dimensional simulation model. The unit module robot was assumed to have the following properties: 1) limited self-drive, 2) no module identifier, 3) information exchange only with adjacent modules, 4) no coordinate system, and 5) only simple arithmetic and memory functions. Using these modules, the devised algorithm was able to achieve not only the creation of static forms but also the realization of the following movements: 1) modules accumulate and grow, 2) modules move to the light source, 3) exit the gap while maintaining its shape, and 4) self-replication.

To allow for tractable probabilistic inference with respect to domain sizes, lifted probabilistic inference exploits symmetries in probabilistic graphical models. However, checking whether two factors encode equivalent semantics and hence are exchangeable is computationally expensive. In this paper, we efficiently solve the problem of detecting exchangeable factors in a factor graph. In particular, we introduce the detection of exchangeable factors (DEFT) algorithm, which allows us to drastically reduce the computational effort for checking whether two factors are exchangeable in practice. While previous approaches iterate all $O(n!)$ permutations of a factor's argument list in the worst case (where $n$ is the number of arguments of the factor), we prove that DEFT efficiently identifies restrictions to drastically reduce the number of permutations and validate the efficiency of DEFT in our empirical evaluation.

Mobile manipulators always need to determine feasible base positions prior to carrying out navigation-manipulation tasks. Real-world environments are often cluttered with various furniture, obstacles, and dozens of other objects. Efficiently computing base positions poses a challenge. In this work, we introduce a framework named MoMa-Pos to address this issue. MoMa-Pos first learns to predict a small set of objects that, taken together, would be sufficient for finding base positions using a graph embedding architecture. MoMa-Pos then calculates standing positions by considering furniture structures, robot models, and obstacles comprehensively. We have extensively evaluated the proposed MoMa-Pos across different settings (e.g., environment and algorithm parameters) and with various mobile manipulators. Our empirical results show that MoMa-Pos demonstrates remarkable effectiveness and efficiency in its performance, surpassing the methods in the literature. %, but also is adaptable to cluttered environments and different robot models. Supplementary material can be found at \url{https://yding25.com/MoMa-Pos}.

In reinforcement learning, reward shaping is an efficient way to guide the learning process of an agent, as the reward can indicate the optimal policy of the task. The potential-based reward shaping framework was proposed to guarantee policy invariance after reward shaping, where a potential function is used to calculate the shaping reward. In former work, we proposed a novel adaptive potential function (APF) method to learn the potential function concurrently with training the agent based on information collected by the agent during the training process, and examined the APF method in discrete action space scenarios. This paper investigates the feasibility of using APF in solving continuous-reaching tasks in a real-world robotic scenario with continuous action space. We combine the Deep Deterministic Policy Gradient (DDPG) algorithm and our proposed method to form a new algorithm called APF-DDPG. To compare APF-DDPG with DDPG, we designed a task where the agent learns to control Baxter's right arm to reach a goal position. The experimental results show that the APF-DDPG algorithm outperforms the DDPG algorithm on both learning speed and robustness.