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.

Robotic Exploration has evolved rapidly in the past two decades as new and more complex techniques have been created to explore unknown regions efficiently. Exciting advancements in exploration, autonomous navigation, and sensor technology have created opportunities for robots to be utilized in new environments and for new objectives ranging from mapping of abandon mines and deep oceans to the efficient creation of indoor models for navigation and search. In this paper we present and discuss a number of examples in research literature of these recent advancements, specifically focusing on robotic exploration algorithms for unmanned vehicles.

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.

Purpose: Navigation guidance is a key requirement for a multitude of lung interventions using video bronchoscopy. State-of-the-art solutions focus on lung biopsies using electromagnetic tracking and intraoperative image registration w.r.t. preoperative CT scans for guidance. The requirement of patient-specific CT scans hampers the utilisation of navigation guidance for other applications such as intensive care units. Methods: This paper addresses navigation guidance solely incorporating bronchosopy video data. In contrast to state-of-the-art approaches we entirely omit the use of electromagnetic tracking and patient-specific CT scans. Guidance is enabled by means of topological bronchoscope localization w.r.t. an interpatient airway model. Particularly, we take maximally advantage of anatomical constraints of airway trees being sequentially traversed. This is realized by incorporating sequences of CNN-based airway likelihoods into a Hidden Markov Model. Results: Our approach is evaluated based on multiple experiments inside a lung phantom model. With the consideration of temporal context and use of anatomical knowledge for regularization, we are able to improve the accuracy up to to 0.98 compared to 0.81 (weighted F1: 0.98 compared to 0.81) for a classification based on individual frames. Conclusion: We combine CNN-based single image classification of airway segments with anatomical constraints and temporal HMM-based inference for the first time. Our approach renders vision-only guidance for bronchoscopy interventions in the absence of electromagnetic tracking and patient-specific CT scans possible.

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.

We consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of Markov chain Monte Carlo (MCMC) procedures. Given any Markov chain corresponding to a target probability distribution, we design a self-repellent random walk (SRRW) which is less likely to transition to nodes that were highly visited in the past, and more likely to transition to seldom visited nodes. For a class of SRRWs parameterized by a positive real {\alpha}, we prove that the empirical distribution of the process converges almost surely to the the target (stationary) distribution of the underlying Markov chain kernel. We then provide a central limit theorem and derive the exact form of the arising asymptotic co-variance matrix, which allows us to show that the SRRW with a stronger repellence (larger {\alpha}) always achieves a smaller asymptotic covariance, in the sense of Loewner ordering of co-variance matrices. Especially for SRRW-driven MCMC algorithms, we show that the decrease in the asymptotic sampling variance is of the order O(1/{\alpha}), eventually going down to zero. Finally, we provide numerical simulations complimentary to our theoretical results, also empirically testing a version of SRRW with {\alpha} increasing in time to combine the benefits of smaller asymptotic variance due to large {\alpha}, with empirically observed faster mixing properties of SRRW with smaller {\alpha}.

Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal discovery are often unable to uncover causal links, between random variables in a dynamic setting, that manifest only when the variables first experience low-probability realizations. To address this issue, we introduce a novel statistical independence test on data collected from time-invariant dynamical systems in which rare but consequential events occur. In particular, we exploit the time-invariance of the underlying data to construct a superimposed dataset of the system state before rare events happen at different timesteps. We then design a conditional independence test on the reorganized data. We provide non-asymptotic sample complexity bounds for the consistency of our method, and validate its performance across various simulated and real-world datasets, including incident data collected from the Caltrans Performance Measurement System (PeMS). Code containing the datasets and experiments is publicly available.