Reinforcement Learning (RL) Sutton and Barto [2018] and Probabilistic planning Puterman [2014] are two research branches that address stochastic problems, often under the Markov assumption for state dynamics. The planning approach requires a given model, while the learning approach improves through repeated interaction with an environment, which can be viewed as a black box. Thus, the tools and the benchmarks for these two branches have grown apart. Learning agents do not require to be able to simulate model-based transitions, and thus frameworks such as OpenAI Gym Brockman et al. [2016] have become a standard, serving also as an interface for third-party benchmarks such as Todorov et al. [2012], Bellemare et al. [2013] and more. As the model is not necessary for solving the learning problem, the environments are hard-coded in a programming language. This has several downsides; if one does wish to see the model describing the environment, it has to be reverse-engineered from the environment framework, complex problems can result in a significant development period, code bugs may make their way into the environment and finally, there is no clean way to verify the model or reuse it directly. Thus, the creation of a verified acceptable benchmark is a challenging task. Planning agents on the other hand can interact with an environment Sanner [2010a], but in many cases simulate the model within the planning agent in order to solve the problem Keller and Eyerich [2012]. The planning community has also come up with formal description languages for various types of problems; these include the Planning Domain Definition Language (PDDL) Aeronautiques et al. [1998] for classical planning problems, PDDL2.1 Fox and Long [2003] for problems involving time and continuous variables, PPDDL Bryce and Buet [2008] for classical planning problems with action probabilistic effects and rewards, and Relational Dynamic Influence Diagram Language (RDDL)

In the context of digital twins, structural health monitoring (SHM) constitutes the backbone of condition-based maintenance, facilitating the interconnection between virtual and physical assets. Guided wave propagation (GWP) is commonly employed for the inspection of structures in SHM. However, GWP is sensitive to variations in the material properties of the structure, leading to false alarms. In this direction, uncertainty quantification (UQ) is regularly applied to improve the reliability of predictions. Computational mechanics is a useful tool for the simulation of GWP, and is often applied for UQ. Even so, the application of UQ methods requires numerous simulations, while large-scale, transient numerical GWP solutions increase the computational cost. Reduced order models (ROMs) are commonly employed to provide numerical results in a limited amount of time. In this paper, we propose a machine learning (ML)-based ROM, mentioned as BO-ML-ROM, to decrease the computational time related to the simulation of the GWP. The ROM is integrated with a Bayesian optimization (BO) framework, to adaptively sample the parameters for the ROM training. The finite element method is used for the simulation of the high-fidelity models. The formulated ROM is used for forward UQ of the GWP in an aluminum plate with varying material properties. To determine the influence of each parameter perturbation, a global, variance-based sensitivity analysis is implemented based on Sobol' indices. It is shown that Bayesian optimization outperforms one-shot sampling methods, both in terms of accuracy and speed-up. The predicted results reveal the efficiency of BO-ML-ROM for GWP and demonstrate its value for UQ.

In recent years, word embeddings have been widely used to measure biases in texts. Even if they have proven to be effective in detecting a wide variety of biases, metrics based on word embeddings lack transparency and interpretability. We analyze an alternative PMI-based metric to quantify biases in texts. It can be expressed as a function of conditional probabilities, which provides a simple interpretation in terms of word co-occurrences. We also prove that it can be approximated by an odds ratio, which allows estimating confidence intervals and statistical significance of textual biases. This approach produces similar results to metrics based on word embeddings when capturing gender gaps of the real world embedded in large corpora.

Algorithmic and data-driven decisions and recommendations are commonly used in high-stakes decision-making settings such as criminal justice, medicine, and public policy. We investigate whether it would have been possible to improve a security assessment algorithm employed during the Vietnam War, using outcomes measured immediately after its introduction in late 1969. This empirical application raises several methodological challenges that frequently arise in high-stakes algorithmic decision-making. First, before implementing a new algorithm, it is essential to characterize and control the risk of yielding worse outcomes than the existing algorithm. Second, the existing algorithm is deterministic, and learning a new algorithm requires transparent extrapolation. Third, the existing algorithm involves discrete decision tables that are common but difficult to optimize over. To address these challenges, we introduce the Average Conditional Risk (ACRisk), which first quantifies the risk that a new algorithmic policy leads to worse outcomes for subgroups of individual units and then averages this over the distribution of subgroups. We also propose a Bayesian policy learning framework that maximizes the posterior expected value while controlling the posterior expected ACRisk. This framework separates the estimation of heterogeneous treatment effects from policy optimization, enabling flexible estimation of effects and optimization over complex policy classes. We characterize the resulting chance-constrained optimization problem as a constrained linear programming problem. Our analysis shows that compared to the actual algorithm used during the Vietnam War, the learned algorithm assesses most regions as more secure and emphasizes economic and political factors over military factors.

Stellar ages are critical building blocks of evolutionary models, but challenging to measure for low mass main sequence stars. An unexplored solution in this regime is the application of probabilistic machine learning methods to gyrochronology, a stellar dating technique that is uniquely well suited for these stars. While accurate analytical gyrochronological models have proven challenging to develop, here we apply conditional normalizing flows to photometric data from open star clusters, and demonstrate that a data-driven approach can constrain gyrochronological ages with a precision comparable to other standard techniques. We evaluate the flow results in the context of a Bayesian framework, and show that our inferred ages recover literature values well. This work demonstrates the potential of a probabilistic data-driven solution to widen the applicability of gyrochronological stellar dating.

Flow matching is a recent framework to train generative models that exhibits impressive empirical performance while being relatively easier to train compared with diffusion-based models. Despite its advantageous properties, prior methods still face the challenges of expensive computing and a large number of function evaluations of off-the-shelf solvers in the pixel space. Furthermore, although latent-based generative methods have shown great success in recent years, this particular model type remains underexplored in this area. In this work, we propose to apply flow matching in the latent spaces of pretrained autoencoders, which offers improved computational efficiency and scalability for high-resolution image synthesis. This enables flow-matching training on constrained computational resources while maintaining their quality and flexibility. Additionally, our work stands as a pioneering contribution in the integration of various conditions into flow matching for conditional generation tasks, including label-conditioned image generation, image inpainting, and semantic-to-image generation. Through extensive experiments, our approach demonstrates its effectiveness in both quantitative and qualitative results on various datasets, such as CelebA-HQ, FFHQ, LSUN Church & Bedroom, and ImageNet. We also provide a theoretical control of the Wasserstein-2 distance between the reconstructed latent flow distribution and true data distribution, showing it is upper-bounded by the latent flow matching objective. Our code will be available at https://github.com/VinAIResearch/LFM.git.

Corruption is frequently observed in collected data and has been extensively studied in machine learning under different corruption models. Despite this, there remains a limited understanding of how these models relate such that a unified view of corruptions and their consequences on learning is still lacking. In this work, we formally analyze corruption models at the distribution level through a general, exhaustive framework based on Markov kernels. We highlight the existence of intricate joint and dependent corruptions on both labels and attributes, which are rarely touched by existing research. Further, we show how these corruptions affect standard supervised learning by analyzing the resulting changes in Bayes Risk. Our findings offer qualitative insights into the consequences of "more complex" corruptions on the learning problem, and provide a foundation for future quantitative comparisons. Applications of the framework include corruption-corrected learning, a subcase of which we study in this paper by theoretically analyzing loss correction with respect to different corruption instances.

Supervised learning in Neural Machine Translation (NMT) typically follows a teacher forcing paradigm where reference tokens constitute the conditioning context in the model's prediction, instead of its own previous predictions. In order to alleviate this lack of exploration in the space of translations, we present a simple extension of standard maximum likelihood estimation by a contrastive marking objective. The additional training signals are extracted automatically from reference translations by comparing the system hypothesis against the reference, and used for up/down-weighting correct/incorrect tokens. The proposed new training procedure requires one additional translation pass over the training set per epoch, and does not alter the standard inference setup. We show that training with contrastive markings yields improvements on top of supervised learning, and is especially useful when learning from postedits where contrastive markings indicate human error corrections to the original hypotheses. Code is publicly released.

Combining complex mathematical models with observational data is an extremely challenging yet ubiquitous problem in the field of modern applied mathematics and data science. Inverse problems, where one is interested in learning inputs to a mathematical model such as physical parameters and initial conditions given partial and noisy observation of model outputs, are hence of frequent interest. Adopting a Bayesian approach[15, 32], we incorporate our prior knowledge on the inputs into a probability distribution, the prior distribution, and obtain a more accurate representation of the model inputs in the posterior distribution, which results from conditioning the prior distribution on the observed data. The posterior distribution contains all the necessary information about the characteristics of our inputs.

Gaussian Processes (GPs) offer an attractive method for regression over small, structured and correlated datasets. However, their deployment is hindered by computational costs and limited guidelines on how to apply GPs beyond simple low-dimensional datasets. We propose a framework to identify the suitability of GPs to a given problem and how to set up a robust and well-specified GP model. The guidelines formalise the decisions of experienced GP practitioners, with an emphasis on kernel design and options for computational scalability. The framework is then applied to a case study of glacier elevation change yielding more accurate results at test time.