Discovering causal relationship using multivariate functional data has received a significant amount of attention very recently. In this article, we introduce a functional linear structural equation model for causal structure learning when the underlying graph involving the multivariate functions may have cycles. To enhance interpretability, our model involves a low-dimensional causal embedded space such that all the relevant causal information in the multivariate functional data is preserved in this lower-dimensional subspace. We prove that the proposed model is causally identifiable under standard assumptions that are often made in the causal discovery literature. To carry out inference of our model, we develop a fully Bayesian framework with suitable prior specifications and uncertainty quantification through posterior summaries. We illustrate the superior performance of our method over existing methods in terms of causal graph estimation through extensive simulation studies. We also demonstrate the proposed method using a brain EEG dataset.

The digital twin concept represents an appealing opportunity to advance condition-based and predictive maintenance paradigms for civil engineering systems, thus allowing reduced lifecycle costs, increased system safety, and increased system availability. This work proposes a predictive digital twin approach to the health monitoring, maintenance, and management planning of civil engineering structures. The asset-twin coupled dynamical system is encoded employing a probabilistic graphical model, which allows all relevant sources of uncertainty to be taken into account. In particular, the time-repeating observations-to-decisions flow is modeled using a dynamic Bayesian network. Real-time structural health diagnostics are provided by assimilating sensed data with deep learning models. The digital twin state is continually updated in a sequential Bayesian inference fashion. This is then exploited to inform the optimal planning of maintenance and management actions within a dynamic decision-making framework. A preliminary offline phase involves the population of training datasets through a reduced-order numerical model and the computation of a health-dependent control policy. The strategy is assessed on two synthetic case studies, involving a cantilever beam and a railway bridge, demonstrating the dynamic decision-making capabilities of health-aware digital twins.

Training data attribution (TDA) techniques find influential training data for the model's prediction on the test data of interest. They approximate the impact of down- or up-weighting a particular training sample. While conceptually useful, they are hardly applicable to deep models in practice, particularly because of their sensitivity to different model initialisation. In this paper, we introduce a Bayesian perspective on the TDA task, where the learned model is treated as a Bayesian posterior and the TDA estimates as random variables. From this novel viewpoint, we observe that the influence of an individual training sample is often overshadowed by the noise stemming from model initialisation and SGD batch composition. Based on this observation, we argue that TDA can only be reliably used for explaining deep model predictions that are consistently influenced by certain training data, independent of other noise factors. Our experiments demonstrate the rarity of such noise-independent training-test data pairs but confirm their existence. We recommend that future researchers and practitioners trust TDA estimates only in such cases. Further, we find a disagreement between ground truth and estimated TDA distributions and encourage future work to study this gap. Code is provided at https://github.com/ElisaNguyen/bayesian-tda.

Imitation learning uses data for training policies to solve complex tasks. However, when the training data is collected from human demonstrators, it often leads to multimodal distributions because of the variability in human actions. Most imitation learning methods rely on a maximum likelihood (ML) objective to learn a parameterized policy, but this can result in suboptimal or unsafe behavior due to the mode-averaging property of the ML objective. In this work, we propose Information Maximizing Curriculum, a curriculum-based approach that assigns a weight to each data point and encourages the model to specialize in the data it can represent, effectively mitigating the mode-averaging problem by allowing the model to ignore data from modes it cannot represent. To cover all modes and thus, enable diverse behavior, we extend our approach to a mixture of experts (MoE) policy, where each mixture component selects its own subset of the training data for learning. A novel, maximum entropy-based objective is proposed to achieve full coverage of the dataset, thereby enabling the policy to encompass all modes within the data distribution. We demonstrate the effectiveness of our approach on complex simulated control tasks using diverse human demonstrations, achieving superior performance compared to state-of-the-art methods.

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on the total number of basis functions $M$. We develop an approach that allows us to use an exponential amount of basis functions without the corresponding exponential computational complexity. The key idea to enable this is using low-rank TNs. We first find a suitable low-dimensional subspace from the data, described by a low-rank TN. In this low-dimensional subspace, we then infer the weights of our model by solving a Bayesian inference problem. Finally, we project the resulting weights back to the original space to make GP predictions. The benefit of our approach comes from the projection to a smaller subspace: It modifies the shape of the basis functions in a way that it sees fit based on the given data, and it allows for efficient computations in the smaller subspace. In an experiment with an 18-dimensional benchmark data set, we show the applicability of our method to an inverse dynamics problem.

Learning curve extrapolation aims to predict model performance in later epochs of training, based on the performance in earlier epochs. In this work, we argue that, while the inherent uncertainty in the extrapolation of learning curves warrants a Bayesian approach, existing methods are (i) overly restrictive, and/or (ii) computationally expensive. We describe the first application of prior-data fitted neural networks (PFNs) in this context. A PFN is a transformer, pre-trained on data generated from a prior, to perform approximate Bayesian inference in a single forward pass. We propose LC-PFN, a PFN trained to extrapolate 10 million artificial right-censored learning curves generated from a parametric prior proposed in prior art using MCMC. We demonstrate that LC-PFN can approximate the posterior predictive distribution more accurately than MCMC, while being over 10 000 times faster. We also show that the same LC-PFN achieves competitive performance extrapolating a total of 20 000 real learning curves from four learning curve benchmarks (LCBench, NAS-Bench-201, Taskset, and PD1) that stem from training a wide range of model architectures (MLPs, CNNs, RNNs, and Transformers) on 53 different datasets with varying input modalities (tabular, image, text, and protein data). Finally, we investigate its potential in the context of model selection and find that a simple LC-PFN based predictive early stopping criterion obtains 2 - 6x speed-ups on 45 of these datasets, at virtually no overhead.

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable invertible transformations. Therefore, once the manifold is properly aligned via a reconstruction loss, the probability density is tractable on the manifold and maximum likelihood can be used to optimize the network parameters. Naturally, the lower-dimensional representation of the data requires an injective-mapping. Recent approaches were able to enforce that the density aligns with the modelled manifold, while efficiently calculating the density volume-change term when embedding to the higher-dimensional space. However, unless the injective-mapping is analytically predefined, the learned manifold is not necessarily an efficient representation of the data. Namely, the latent dimensions of such models frequently learn an entangled intrinsic basis, with degenerate information being stored in each dimension. Alternatively, if a locally orthogonal and/or sparse basis is to be learned, here coined canonical intrinsic basis, it can serve in learning a more compact latent space representation. Toward this end, we propose a canonical manifold learning flow method, where a novel optimization objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. We demonstrate that by minimizing the off-diagonal manifold metric elements $\ell_1$-norm, we can achieve such a basis, which is simultaneously sparse and/or orthogonal. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data, and a better approximation of target distributions than other manifold flow methods in most experiments we conducted, resulting in lower FID scores.

To make reinforcement learning more sample efficient, we need better credit assignment methods that measure an action's influence on future rewards. Building upon Hindsight Credit Assignment (HCA), we introduce Counterfactual Contribution Analysis (COCOA), a new family of model-based credit assignment algorithms. Our algorithms achieve precise credit assignment by measuring the contribution of actions upon obtaining subsequent rewards, by quantifying a counterfactual query: 'Would the agent still have reached this reward if it had taken another action?'. We show that measuring contributions w.r.t. rewarding states, as is done in HCA, results in spurious estimates of contributions, causing HCA to degrade towards the high-variance REINFORCE estimator in many relevant environments. Instead, we measure contributions w.r.t. rewards or learned representations of the rewarding objects, resulting in gradient estimates with lower variance. We run experiments on a suite of problems specifically designed to evaluate long-term credit assignment capabilities. By using dynamic programming, we measure ground-truth policy gradients and show that the improved performance of our new model-based credit assignment methods is due to lower bias and variance compared to HCA and common baselines. Our results demonstrate how modeling action contributions towards rewarding outcomes can be leveraged for credit assignment, opening a new path towards sample-efficient reinforcement learning.

Gibbs samplers [12] are a family of Markov Chain Monte Carlo (MCMC) algorithms [10] commonly used in various scientific fields. In the context of Bayesian Statistics, they are routinely employed to draw samples from posterior distributions of unknown parameters conditional to the observed data [28, 37]. Like most MCMC methods, they are guaranteed to converge to the correct posterior distribution as the number of iterations tends to infinity under mild assumptions [54]. However, understanding how quickly this convergence occurs, for example by quantifying the so-called mixing time of the Markov chain generated by the algorithm, is in general a hard task. In this paper we address this question for Gibbs samplers targeting certain classes of high-dimensional Bayesian hierarchical models. Analysing convergence properties, such as mixing times, is the key technical step needed to rigorously quantify the computational cost of MCMC algorithms.

Optimal topology synthesis is generally resource-intensive and time-consuming to be done in real time for large ad-hoc robot networks. One should only perform topology re-computations if the probability of topology recoverability after the occurrence of any fault surpasses that of its irrecoverability. We formulate this problem as a binary classification problem. Then, we develop a two-pathway data-driven model based on Bayesian Gaussian mixture models that predicts the solution to a typical problem by two different pre-fault and post-fault prediction pathways. The results, obtained by the integration of the predictions of those pathways, clearly indicate the success of our model in solving the topology (ir)recoverability prediction problem compared to the best of current strategies found in the literature.