Commonly adopted in the manufacturing and aerospace sectors, digital twin (DT) platforms are increasingly seen as a promising paradigm to control, monitor, and analyze software-based, "open", communication systems. Notably, DT platforms provide a sandbox in which to test artificial intelligence (AI) solutions for communication systems, potentially reducing the need to collect data and test algorithms in the field, i.e., on the physical twin (PT). A key challenge in the deployment of DT systems is to ensure that virtual control optimization, monitoring, and analysis at the DT are safe and reliable, avoiding incorrect decisions caused by "model exploitation". To address this challenge, this paper presents a general Bayesian framework with the aim of quantifying and accounting for model uncertainty at the DT that is caused by limitations in the amount and quality of data available at the DT from the PT. In the proposed framework, the DT builds a Bayesian model of the communication system, which is leveraged to enable core DT functionalities such as control via multi-agent reinforcement learning (MARL), monitoring of the PT for anomaly detection, prediction, data-collection optimization, and counterfactual analysis. To exemplify the application of the proposed framework, we specifically investigate a case-study system encompassing multiple sensing devices that report to a common receiver. Experimental results validate the effectiveness of the proposed Bayesian framework as compared to standard frequentist model-based solutions.

Identifying causality is a challenging task in many data-intensive scenarios. Many algorithms have been proposed for this critical task. However, most of them consider the learning algorithms for directed acyclic graph (DAG) of Bayesian network (BN). These BN-based models only have limited causal explainability because of the issue of Markov equivalence class. Moreover, they are dependent on the assumption of stationarity, whereas many sampling time series from complex system are nonstationary. The nonstationary time series bring dataset shift problem, which leads to the unsatisfactory performances of these algorithms. To fill these gaps, a novel causation model named Unique Causal Network (UCN) is proposed in this paper. Different from the previous BN-based models, UCN considers the influence of time delay, and proves the uniqueness of obtained network structure, which addresses the issue of Markov equivalence class. Furthermore, based on the decomposability property of UCN, a higher-order causal entropy (HCE) algorithm is designed to identify the structure of UCN in a distributed way. HCE algorithm measures the strength of causality by using nearest-neighbors entropy estimator, which works well on nonstationary time series. Finally, lots of experiments validate that HCE algorithm achieves state-of-the-art accuracy when time series are nonstationary, compared to the other baseline algorithms.

We consider random forests and LASSO methods for model-based small area estimation when the number of areas with sampled data is a small fraction of the total areas for which estimates are required. Abundant auxiliary information is available for the sampled areas, from the survey, and for all areas, from an exterior source, and the goal is to use auxiliary variables to predict the outcome of interest. We compare areallevel random forests and LASSO approaches to a frequentist forward variable selection approach and a Bayesian shrinkage method. This work is motivated by Ghanaian data available from the sixth Living Standard Survey (GLSS) and the 2010 Population and Housing Census. We estimate the areal mean household log consumption using both datasets. The outcome variable is measured only in the GLSS for 3% of all the areas (136 out of 5019) and more than 170 potential covariates are available from both datasets. Among the four modelling methods considered, the Bayesian shrinkage performed the best in terms of bias, MSE and prediction interval coverages and scores, as assessed through a cross-validation study. We find substantial between-area variation, the log consumption areal point estimates showing a 1.3-fold variation across the GAMA region. The western areas are the poorest while the Accra Metropolitan Area district gathers the richest areas. In 2015, the United Nations (UN) released their 2030 agenda for sustainable development goals (SDGs) consisting of 17 goals, the first of which was to end poverty worldwide (Resolution, General Assembly and others, 2015). For their first SDG, the UN made seven guidelines explicit, including the implementation of "poverty eradication policies" at a disaggregated level. To that end, producing reliable and fine-grained pictures of socioeconomic status and income inequality is fundamental to help decision makers prioritise and target certain areas. These detailed maps help local communities understand their situation compared to their neighbours, which also helps when planning interventions (Bedi et al., 2007). In Ghana, household surveys are collected every few years to measure the living conditions of households across Ghanaian regions and districts and to monitor poverty.

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based methods have been proposed. As these methods need a great number of forward and backward computations, they become costly in computation, in particular, when the forward or generative models are complex and the evaluation of the likelihood becomes very costly. Using Deep Neural Network surrogate models and approximate computation can become very helpful. However, accounting for the uncertainties, we need first understand the Bayesian Deep Learning and then, we can see how we can use them for inverse problems. In this work, we focus on NN, DL and more specifically the Bayesian DL particularly adapted for inverse problems. We first give details of Bayesian DL approximate computations with exponential families, then we will see how we can use them for inverse problems. We consider two cases: First the case where the forward operator is known and used as physics constraint, the second more general data driven DL methods. keyword: Neural Network, Variational Bayesian inference, Bayesian Deep Learning (DL), Inverse problems, Physics based DL.

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method of choice. Indeed, kernel distribution regression is both computationally favorable, and supported by a recent learning theory. This theory also tackles the two-stage sampling setting, where only samples from the input distributions are available. In this paper, we improve the learning theory of kernel distribution regression. We address kernels based on Hilbertian embeddings, that encompass most, if not all, of the existing approaches. We introduce the novel near-unbiased condition on the Hilbertian embeddings, that enables us to provide new error bounds on the effect of the two-stage sampling, thanks to a new analysis. We show that this near-unbiased condition holds for three important classes of kernels, based on optimal transport and mean embedding. As a consequence, we strictly improve the existing convergence rates for these kernels. Our setting and results are illustrated by numerical experiments.

In images collected by astronomical surveys, stars and galaxies often overlap visually. Deblending is the task of distinguishing and characterizing individual light sources in survey images. We propose StarNet, a Bayesian method to deblend sources in astronomical images of crowded star fields. StarNet leverages recent advances in variational inference, including amortized variational distributions and an optimization objective targeting an expectation of the forward KL divergence. In our experiments with SDSS images of the M2 globular cluster, StarNet is substantially more accurate than two competing methods: Probabilistic Cataloging (PCAT), a method that uses MCMC for inference, and DAOPHOT, a software pipeline employed by SDSS for deblending. In addition, the amortized approach to inference gives StarNet the scaling characteristics necessary to perform Bayesian inference on modern astronomical surveys.

We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. We discuss and prove some results on maximum likelihood estimation of parameters of Taylor kernels. The proposed framework is a special case of Gaussian process regression based on data that is orthogonal in the reproducing kernel Hilbert space of the covariance kernel.

This paper presents alternative techniques for inference on classical Bayesian networks in which all probabilities are fixed, and for synthesis problems when conditional probability tables (CPTs) in such networks contain symbolic parameters rather than concrete probabilities. The key idea is to exploit probabilistic model checking as well as its recent extension to parameter synthesis techniques for parametric Markov chains. To enable this, the Bayesian networks are transformed into Markov chains and their objectives are mapped onto probabilistic temporal logic formulas. For exact inference, we compare probabilistic model checking to weighted model counting on various Bayesian network benchmarks. We contrast symbolic model checking using multi-terminal binary (aka: algebraic) decision diagrams to symbolic inference using proba- bilistic sentential decision diagrams, symbolic data structures that are tailored to Bayesian networks. For the parametric setting, we describe how our techniques can be used for various synthesis problems such as computing sensitivity functions (and values), simple and difference parameter tuning and ratio parameter tuning. Our parameter synthesis techniques are applicable to arbitrarily many, possibly dependent, parameters that may occur in multiple CPTs. This lifts restrictions, e.g., on the number of parametrized CPTs, or on parameter dependencies between several CPTs, that exist in the literature. Experiments on several benchmarks show that our parameter synthesis techniques can treat parameter synthesis for Bayesian networks (with hundreds of unknown parameters) that are out of reach for existing techniques.

We present a new transport-based approach to efficiently perform sequential Bayesian inference of static model parameters. The strategy is based on the extraction of conditional distribution from the joint distribution of parameters and data, via the estimation of structured (e.g., block triangular) transport maps. This gives explicit surrogate models for the likelihood functions and their gradients. This allow gradient-based characterizations of posterior density via transport maps in a model-free, online phase. This framework is well suited for parameter estimation in case of complex noise models including nuisance parameters and when the forward model is only known as a black box. The numerical application of this method is performed in the context of characterization of ice thickness with conductivity measurements.

The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In statistics the many applications of sparse modeling span regression, classification tasks, graphical model selection, sparse M-estimators and sparse dimensionality reduction. It is also particularly effective in many statistical and machine learning areas where the primary goal is to discover predictive patterns from data which would enhance our understanding and control of underlying physical, biological, and other natural processes, beyond just building accurate outcome black-box predictors. Common examples include selecting biomarkers in biological procedures, finding relevant brain activity locations which are predictive about brain states and processes based on fMRI data, and identifying network bottlenecks best explaining end-to-end performance. Moreover, the research and applications of efficient recovery of high-dimensional sparse signals from a relatively small number of observations, which is the main focus of compressed sensing or compressive sensing, have rapidly grown and became an extremely intense area of study beyond classical signal processing. Likewise interestingly, sparse modeling is directly related to various artificial vision tasks, such as image denoising, segmentation, restoration and superresolution, object or face detection and recognition in visual scenes, and action recognition. In this manuscript, we provide a brief introduction of the basic theory underlying sparse representation and compressive sensing, and then discuss some methods for recovering sparse solutions to optimization problems in effective way, together with some applications of sparse recovery in a machine learning problem known as sparse dictionary learning.