Monitoring the Covid19 pandemic constitutes a critical societal stake that received considerable research efforts. The intensity of the pandemic on a given territory is efficiently measured by the reproduction number, quantifying the rate of growth of daily new infections. Recently, estimates for the time evolution of the reproduction number were produced using an inverse problem formulation with a nonsmooth functional minimization. While it was designed to be robust to the limited quality of the Covid19 data (outliers, missing counts), the procedure lacks the ability to output credibility interval based estimates. This remains a severe limitation for practical use in actual pandemic monitoring by epidemiologists that the present work aims to overcome by use of Monte Carlo sampling. After interpretation of the nonsmooth functional into a Bayesian framework, several sampling schemes are tailored to adjust the nonsmooth nature of the resulting posterior distribution. The originality of the devised algorithms stems from combining a Langevin Monte Carlo sampling scheme with Proximal operators. Performance of the new algorithms in producing relevant credibility intervals for the reproduction number estimates and denoised counts are compared. Assessment is conducted on real daily new infection counts made available by the Johns Hopkins University. The interest of the devised monitoring tools are illustrated on Covid19 data from several different countries.

Normalizing flows are tractable density models that can approximate complicated target distributions, e.g. Boltzmann distributions of physical systems. However, current methods for training flows either suffer from mode-seeking behavior, use samples from the target generated beforehand by expensive MCMC methods, or use stochastic losses that have high variance. To avoid these problems, we augment flows with annealed importance sampling (AIS) and minimize the mass-covering $\alpha$-divergence with $\alpha=2$, which minimizes importance weight variance. Our method, Flow AIS Bootstrap (FAB), uses AIS to generate samples in regions where the flow is a poor approximation of the target, facilitating the discovery of new modes. We apply FAB to multimodal targets and show that we can approximate them very accurately where previous methods fail. To the best of our knowledge, we are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the unnormalized target density, without access to samples generated via Molecular Dynamics (MD) simulations: FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations. After reweighting the samples, we obtain unbiased histograms of dihedral angles that are almost identical to the ground truth.

We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. In particular, we focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation, but the over-approximation may result in inefficient exploration. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values and explicitly characterizes the gap in previous work. Moreover, our uncertainty quantification technique is easily integrated into common exploration strategies and scales naturally beyond the tabular setting by using standard deep reinforcement learning architectures. Experiments in difficult exploration tasks, both in tabular and continuous control settings, show that our sharper uncertainty estimates improve sample-efficiency.

This paper investigates when the importance weighting (IW) correction is needed to address covariate shift, a common situation in supervised learning where the input distributions of training and test data differ. Classic results show that the IW correction is needed when the model is parametric and misspecified. In contrast, recent results indicate that the IW correction may not be necessary when the model is nonparametric and well-specified. We examine the missing case in the literature where the model is nonparametric and misspecified, and show that the IW correction is needed for obtaining the best approximation of the true unknown function for the test distribution. We do this by analyzing IW-corrected kernel ridge regression, covering a variety of settings, including parametric and nonparametric models, well-specified and misspecified settings, and arbitrary weighting functions.

We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and column-wise interpretations and contain structural information that can be lost with naive vectorization approaches. To address this, we propose a method called principal support matrix machine (PSMM) for the matrix sufficient dimension reduction. The PSMM converts the sufficient dimension reduction problem into a series of classification problems by dividing the response variables into slices. It effectively utilizes the matrix structure by finding hyperplanes with rank-1 normal matrix that optimally separate the sliced responses. Additionally, we extend our approach to the higher-order tensor case. Our numerical analysis demonstrates that the PSMM outperforms existing methods and has strong interpretability in real data applications.

Federated learning (FL) is a promising framework that models distributed machine learning while protecting the privacy of clients. However, FL suffers performance degradation from heterogeneous and limited data. To alleviate the degradation, we present a novel personalized Bayesian FL approach named pFedBayes. By using the trained global distribution from the server as the prior distribution of each client, each client adjusts its own distribution by minimizing the sum of the reconstruction error over its personalized data and the KL divergence with the downloaded global distribution. Then, we propose a sparse personalized Bayesian FL approach named sFedBayes. To overcome the extreme heterogeneity in non-i.i.d. data, we propose a clustered Bayesian FL model named cFedbayes by learning different prior distributions for different clients. Theoretical analysis gives the generalization error bound of three approaches and shows that the generalization error convergence rates of the proposed approaches achieve minimax optimality up to a logarithmic factor. Moreover, the analysis presents that cFedbayes has a tighter generalization error rate than pFedBayes. Numerous experiments are provided to demonstrate that the proposed approaches have better performance than other advanced personalized methods on private models in the presence of heterogeneous and limited data.

The complexity of the operating environment and required technologies for highly automated driving is unprecedented. A different type of threat to safe operation besides the fault-error-failure model by Laprie et al. arises in the form of performance limitations. We propose a system theoretic approach to handle these and derive a taxonomy based on uncertainty, i.e. lack of knowledge, as a root cause. Uncertainty is a threat to the dependability of a system, as it limits our ability to assess its dependability properties. We distinguish uncertainties by aleatory (inherent to probabilistic models), epistemic (lack of model parameter knowledge) and ontological (incompleteness of models) in order to determine strategies and methods to cope with them. Analogous to the taxonomy of Laprie et al. we cluster methods into uncertainty prevention (use of elements with well-known behavior, avoiding architectures prone to emergent behavior, restriction of operational design domain, etc.), uncertainty removal (during design time by design of experiment, etc. and after release by field observation, continuous updates, etc.), uncertainty tolerance (use of redundant architectures with diverse uncertainties, uncertainty aware deep learning, etc.) and uncertainty forecasting (estimation of residual uncertainty, etc.).

This report documents the programme and the outcomes of Dagstuhl Seminar 22382 "Machine Learning for Science: Bridging Data-Driven and Mechanistic Modelling". Today's scientific challenges are characterised by complexity. Interconnected natural, technological, and human systems are influenced by forces acting across time- and spatial-scales, resulting in complex interactions and emergent behaviours. Understanding these phenomena -- and leveraging scientific advances to deliver innovative solutions to improve society's health, wealth, and well-being -- requires new ways of analysing complex systems. The transformative potential of AI stems from its widespread applicability across disciplines, and will only be achieved through integration across research domains. AI for science is a rendezvous point. It brings together expertise from $\mathrm{AI}$ and application domains; combines modelling knowledge with engineering know-how; and relies on collaboration across disciplines and between humans and machines. Alongside technical advances, the next wave of progress in the field will come from building a community of machine learning researchers, domain experts, citizen scientists, and engineers working together to design and deploy effective AI tools. This report summarises the discussions from the seminar and provides a roadmap to suggest how different communities can collaborate to deliver a new wave of progress in AI and its application for scientific discovery.

Adopting reasonable strategies is challenging but crucial for an intelligent agent with limited resources working in hazardous, unstructured, and dynamic environments to improve the system's utility, decrease the overall cost, and increase mission success probability. This paper proposes a novel hierarchical strategy decomposition approach based on the Bayesian chain rule to separate an intricate policy into several simple sub-policies and organize their relationships as Bayesian strategy networks (BSN). We integrate this approach into the state-of-the-art DRL method -- soft actor-critic (SAC) and build the corresponding Bayesian soft actor-critic (BSAC) model by organizing several sub-policies as a joint policy. We compare the proposed BSAC method with the SAC and other state-of-the-art approaches such as TD3, DDPG, and PPO on the standard continuous control benchmarks -- Hopper-v2, Walker2d-v2, and Humanoid-v2 -- in MuJoCo with the OpenAI Gym environment. The results demonstrate that the promising potential of the BSAC method significantly improves training efficiency.

Successful machine learning methods require a trade-off between memorization and generalization. Too much memorization and the model cannot generalize to unobserved examples. Too much over-generalization and we risk under-fitting the data. While we commonly measure their performance through cross validation and accuracy metrics, how should these algorithms cope in domains that are extremely under-determined where accuracy is always unsatisfactory? We present a novel probabilistic graphical model structure learning approach that can learn, generalize and explain in these elusive domains by operating at the random variable instantiation level. Using Minimum Description Length (MDL) analysis, we propose a new decomposition of the learning problem over all training exemplars, fusing together minimal entropy inferences to construct a final knowledge base. By leveraging Bayesian Knowledge Bases (BKBs), a framework that operates at the instantiation level and inherently subsumes Bayesian Networks (BNs), we develop both a theoretical MDL score and associated structure learning algorithm that demonstrates significant improvements over learned BNs on 40 benchmark datasets. Further, our algorithm incorporates recent off-the-shelf DAG learning techniques enabling tractable results even on large problems. We then demonstrate the utility of our approach in a significantly under-determined domain by learning gene regulatory networks on breast cancer gene mutational data available from The Cancer Genome Atlas (TCGA).