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.

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.

Data cleaning is crucial but often laborious in most machine learning (ML) applications. However, task-agnostic data cleaning is sometimes unnecessary if certain inconsistencies in the dirty data will not affect the prediction of ML models to the test points. A test point is certifiably robust for an ML classifier if the prediction remains the same regardless of which (among exponentially many) cleaned dataset it is trained on. In this paper, we study certifiable robustness for the Naive Bayes classifier (NBC) on dirty datasets with missing values. We present (i) a linear time algorithm in the number of entries in the dataset that decides whether a test point is certifiably robust for NBC, (ii) an algorithm that counts for each label, the number of cleaned datasets on which the NBC can be trained to predict that label, and (iii) an efficient optimal algorithm that poisons a clean dataset by inserting the minimum number of missing values such that a test point is not certifiably robust for NBC. We prove that (iv) poisoning a clean dataset such that multiple test points become certifiably non-robust is NP-hard for any dataset with at least three features. Our experiments demonstrate that our algorithms for the decision and data poisoning problems achieve up to $19.5\times$ and $3.06\times$ speed-up over the baseline algorithms across different real-world datasets.

Causal representation learning is the task of identifying the underlying causal variables and their relations from high-dimensional observations, such as images. Recent work has shown that one can reconstruct the causal variables from temporal sequences of observations under the assumption that there are no instantaneous causal relations between them. In practical applications, however, our measurement or frame rate might be slower than many of the causal effects. This effectively creates "instantaneous" effects and invalidates previous identifiability results. To address this issue, we propose iCITRIS, a causal representation learning method that allows for instantaneous effects in intervened temporal sequences when intervention targets can be observed, e.g., as actions of an agent. iCITRIS identifies the potentially multidimensional causal variables from temporal observations, while simultaneously using a differentiable causal discovery method to learn their causal graph. In experiments on three datasets of interactive systems, iCITRIS accurately identifies the causal variables and their causal graph.

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.

Recent advances in deep learning have led to a paradigm shift in the field of reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However, non-trivial errors exist in inferences about some out-of-distribution and noisy data. In view of this issue, we propose to consider uncertainty in predictive models based upon a theoretical framework of Bayesian deep learning, thereby creating an adaptive steganographic system. Most modern deep-learning models are regarded as deterministic because they only offer predictions while failing to provide uncertainty measurement. Bayesian neural networks bring a probabilistic perspective to deep learning and can be regarded as self-aware intelligent machinery; that is, a machine that knows its own limitations. To quantify uncertainty, we apply Bayesian statistics to model the predictive distribution and approximate it through Monte Carlo sampling with stochastic forward passes. We further show that predictive uncertainty can be disentangled into aleatoric and epistemic uncertainties and these quantities can be learnt unsupervised. Experimental results demonstrate an improvement delivered by Bayesian uncertainty analysis upon steganographic rate-distortion performance.

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).

How to efficiently explore in reinforcement learning is an open problem. Many exploration algorithms employ the epistemic uncertainty of their own value predictions -- for instance to compute an exploration bonus or upper confidence bound. Unfortunately the required uncertainty is difficult to estimate in general with function approximation. We propose epistemic value estimation (EVE): a recipe that is compatible with sequential decision making and with neural network function approximators. It equips agents with a tractable posterior over all their parameters from which epistemic value uncertainty can be computed efficiently. We use the recipe to derive an epistemic Q-Learning agent and observe competitive performance on a series of benchmarks. Experiments confirm that the EVE recipe facilitates efficient exploration in hard exploration tasks.