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5G cellular networks are now a reality and promise to improve key performance indicators (KPIs), such as Gbps data rates and latencies in the order of milliseconds. While some of these KPIs are achievable in urban scenarios, rural areas often face challenging connectivity conditions due to the lack of terrestrial network (TN) infrastructure. To solve this problem, non-terrestrial networks (NTNs) such as satellite-based solutions, have been introduced to provide coverage in remote regions. Therefore, a multi-connectivity approach can be integrated to simultaneously serve an end-user by merging satellite and cellular links in a joint approach. This study explores, using experimental data, the benefits of both TN-TN and TN-NTN multi-connectivity in rural environments. The results obtained demonstrate that a traditional single-connectivity approach may not be sufficient to provide service to rural environments due to the KPIs requirements given several use cases within these rural areas. The multi-connectivity strategy, which jointly integrates 5G and satellite networks, meets the network availability requirements for latency, downlink throughput, and uplink throughput KPIs at least 98%, 99%, and 95% of the time, respectively, for several use cases, such as precision agriculture, livestock monitoring, and forest management. These include applications like microclimate monitoring, remote operational support, early pest detection, and real-time tracking of livestock transport., Comment: 12 pages, 9 figures

This letter presents a measurement campaign carried out in an FR2 urban outdoor environment in a live experimental network deployment. The radio propagation analysis from a physical perspective at 26 GHz is essential for the correct deployment and dimensioning of future communication networks. This study performs a walk test emulating realistic conditions under which a pedestrian may be affected, summarizing and evaluating some of the typical effects encountered in a communications scenario such as penetration losses in a building, losses due to vegetation or the human body, or diffraction/scattering propagation around corners in street canyon-like environments. The operational conditions of the 5G network, the urban micro-cell scenario, and the use of omnidirectional antennas on the UE side validate the channel conditions from a perspective closer to a realistic scenario for a pedestrian within a FR2 live network., Comment: Published in IEEE Wireless Communications Letters

Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such processes can often be accurately modeled via stochastic differential equations (SDEs), which naturally imply causal relationships via "which variables enter the differential of which other variables". In this paper, we develop conditional independence (CI) constraints on coordinate processes over selected intervals that are Markov with respect to the acyclic dependence graph (allowing self-loops) induced by a general SDE model. We then provide a sound and complete causal discovery algorithm, capable of handling both fully and partially observed data, and uniquely recovering the underlying or induced ancestral graph by exploiting time directionality assuming a CI oracle. Finally, to make our algorithm practically usable, we also propose a flexible, consistent signature kernel-based CI test to infer these constraints from data. We extensively benchmark the CI test in isolation and as part of our causal discovery algorithms, outperforming existing approaches in SDE models and beyond.

Causal discovery outputs a causal structure, represented by a graph, from observed data. For time series data, there is a variety of methods, however, it is difficult to evaluate these on real data as realistic use cases very rarely come with a known causal graph to which output can be compared. In this paper, we present a dataset from an industrial subsystem at the European Spallation Source along with its causal graph which has been constructed from expert knowledge. This provides a testbed for causal discovery from time series observations of complex systems, and we believe this can help inform the development of causal discovery methodology., Comment: 18 pages, 9 figures, 1 table

Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some regularity conditions, a local independence graph implies a set of independences using a graphical criterion known as $\delta$-separation, or using its generalization, $\mu$-separation. This is a stochastic process analogue of $d$-separation in DAGs. However, there may be more independences than implied by this graph and this is a violation of so-called faithfulness. We characterize faithfulness in local independence graphs and give a method to construct a faithful graph from any local independence model such that the output equals the true graph when Markov and faithfulness assumptions hold. We discuss various assumptions that are weaker than faithfulness, and we explore different structure learning algorithms and their properties under varying assumptions., Comment: 17 pages, 3 figures

We study time-dependent mediators in survival analysis using a treatment separation approach due to Didelez [2019] and based on earlier work by Robins and Richardson [2011]. This approach avoids nested counterfactuals and crossworld assumptions which are otherwise common in mediation analysis. The causal model of treatment, mediators, covariates, confounders and outcome is represented by causal directed acyclic graphs (DAGs). However, the DAGs tend to be very complex when we have measurements at a large number of time points. We therefore suggest using so-called rolled graphs in which a node represents an entire coordinate process instead of a single random variable, leading us to far simpler graphical representations. The rolled graphs are not necessarily acyclic; they can be analyzed by $\delta$-separation which is the appropriate graphical separation criterion in this class of graphs and analogous to $d$-separation. In particular, $\delta$-separation is a graphical tool for evaluating if the conditions of the mediation analysis are met or if unmeasured confounders influence the estimated effects. We also state a mediational g-formula. This is similar to the approach in Vansteelandt et al. [2019] although that paper has a different conceptual basis. Finally, we apply this framework to a statistical model based on a Cox model with an added treatment effect.survival analysis; mediation; causal inference; graphical models; local independence graphs, Comment: 40 pages, 9 figures

Interacting systems of events may exhibit cascading behavior where events tend to be temporally clustered. While the cascades themselves may be obvious from the data, it is important to understand which states of the system trigger them. For this purpose, we propose a modeling framework based on continuous-time Bayesian networks (CTBNs) to analyze cascading behavior in complex systems. This framework allows us to describe how events propagate through the system and to identify likely sentry states, that is, system states that may lead to imminent cascading behavior. Moreover, CTBNs have a simple graphical representation and provide interpretable outputs, both of which are important when communicating with domain experts. We also develop new methods for knowledge extraction from CTBNs and we apply the proposed methodology to a data set of alarms in a large industrial system., Comment: 21 pages, 11 figures

Industrial environments constitute a challenge in terms of radio propagation due to the presence of machinery and the mobility of the different agents, especially at mmWave bands. This paper presents an experimental evaluation of a FR2 5G network deployed in an operational factory scenario at 26 GHz. The experimental characterization, performed with autonomous mobile robots that self-navigate the industrial lab, leads to the analysis of the received power along the factory and the evaluation of reference path gain models. The proposed assessment deeply analyzes the physical layer of the communication network under operational conditions. Thus, two different network configurations are assessed by measuring the power received in the entire factory, providing a comparison between deployments. Additionally, beam management procedures, such as beam recovery, beam sweeping or beam switching, are analyzed since they are crucial in environments where mobile agents are involved. They aim for a zero interruption approach based on reliable communications. The results analysis shows that beam recovery procedures can perform a beam switching to an alternative serving beam with power losses of less than 1.6 dB on average. Beam sweeping analysis demonstrates the prevalence of the direct component in Line-of-Sight conditions despite the strong scattering component and large-scale fading in the environment., Comment: Published in IEEE Transactions on Vehicular Technology, 2024

Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some coordinate processes of the multivariate stochastic process are unobserved, the local independence graph of the observed coordinate processes is a directed mixed graph (DMG). Two DMGs may encode the same local independences in which case we say that they are Markov equivalent. Markov equivalence is a central notion in graphical modeling. We show that deciding Markov equivalence of DMGs is coNP-complete, even under a sparsity assumption. As a remedy, we introduce a collection of equivalence relations on DMGs that are all less granular than Markov equivalence and we say that they are weak equivalence relations. This leads to feasible algorithms for naturally occurring computational problems related to weak equivalence of DMGs. The equivalence classes of a weak equivalence relation have attractive properties. In particular, each equivalence class has a greatest element which leads to a concise representation of an equivalence class. Moreover, these equivalence relations define a hierarchy of granularity in the graphical modeling which leads to simple and interpretable connections between equivalence relations corresponding to different levels of granularity., Comment: 50 pages, 22 figures

Instrumental variable methods are often used for parameter estimation in the presence of confounding. They can also be applied in stochastic processes. Instrumental variable analysis exploits moment equations to obtain estimators for causal parameters. We show that in stochastic processes one can find such moment equations using an integrated covariance matrix. This provides new instrumental variable methods, instrumental variable methods in a class of continuous-time processes as well as a unified treatment of discrete- and continuous-time processes.

Questions in causality, control, and reinforcement learning go beyond the classical machine learning task of prediction under i.i.d. observations. Instead, these fields consider the problem of learning how to actively perturb a system to achieve a certain effect on a response variable. Arguably, they have complementary views on the problem: In control, one usually aims to first identify the system by excitation strategies to then apply model-based design techniques to control the system. In (non-model-based) reinforcement learning, one directly optimizes a reward. In causality, one focus is on identifiability of causal structure. We believe that combining the different views might create synergies and this competition is meant as a first step toward such synergies. The participants had access to observational and (offline) interventional data generated by dynamical systems. Track CHEM considers an open-loop problem in which a single impulse at the beginning of the dynamics can be set, while Track ROBO considers a closed-loop problem in which control variables can be set at each time step. The goal in both tracks is to infer controls that drive the system to a desired state. Code is open-sourced ( https://github.com/LearningByDoingCompetition/learningbydoing-comp ) to reproduce the winning solutions of the competition and to facilitate trying out new methods on the competition tasks., Comment: https://learningbydoingcompetition.github.io/

Recently, methods have been proposed that exploit the invariance of prediction models with respect to changing environments to infer subsets of the causal parents of a response variable. If the environments influence only few of the underlying mechanisms, the subset identified by invariant causal prediction (ICP), for example, may be small, or even empty. We introduce the concept of minimal invariance and propose invariant ancestry search (IAS). In its population version, IAS outputs a set which contains only ancestors of the response and is a superset of the output of ICP. When applied to data, corresponding guarantees hold asymptotically if the underlying test for invariance has asymptotic level and power. We develop scalable algorithms and perform experiments on simulated and real data., Comment: International Conference of Machine Learning (ICML) 2022

Radio channel modeling is one of the most fundamental aspects in the process of designing, optimizing, and simulating wireless communication networks. In this field, long-established approaches such as analytical channel models and ray tracing techniques represent the de-facto standard methodologies. However, as demonstrated by recent results, there remains an untapped potential to innovate this research field by enriching model-based approaches with machine learning techniques. In this paper, we present Deep RAdio channel modeling from GeOinformatioN (DRaGon) as a novel machine learning-enabled method for automatic generation of Radio Environmental Maps (REMs) from geographical data. For achieving accurate path loss prediction results, DRaGon combines determining features extracted from a three-dimensional model of the radio propagation environment with raw images of the receiver area within a deep learning model. In a comprehensive performance evaluation and validation campaign, we compare the accuracy of the proposed approach with real world measurements, ray tracing analyses, and well-known channel models. It is found that the combination of expert knowledge from the communications domain and the data analysis capabilities of deep learning allows to achieve a significantly higher prediction accuracy than the reference methods.