Normalizing flows (NFs) provide uncorrelated samples from complex distributions, making them an appealing tool for parameter estimation. However, the practical utility of NFs remains limited by their tendency to collapse to a single mode of a multimodal distribution. In this study, we show that annealing with an adaptive schedule based on the effective sample size (ESS) can mitigate mode collapse. We demonstrate that our approach can converge the marginal likelihood for a biochemical oscillator model fit to time-series data in ten-fold less computation time than a widely used ensemble Markov chain Monte Carlo (MCMC) method. We show that the ESS can also be used to reduce variance by pruning the samples. We expect these developments to be of general use for sampling with NFs and discuss potential opportunities for further improvements.

Data derived from remote sensing or numerical simulations often have a regular gridded structure and are large in volume, making it challenging to find accurate spatial models that can fill in missing grid cells or simulate the process effectively, especially in the presence of spatial heterogeneity and heavy-tailed marginal distributions. To overcome this issue, we present a spatial autoregressive modeling framework, which maps observations at a location and its neighbors to independent random variables. This is a highly flexible modeling approach and well-suited for non-Gaussian fields, providing simpler interpretability. In particular, we consider the SAR model with Generalized Extreme Value distribution innovations to combine the observation at a central grid location with its neighbors, capturing extreme spatial behavior based on the heavy-tailed innovations. While these models are fast to simulate by exploiting the sparsity of the key matrices in the computations, the maximum likelihood estimation of the parameters is prohibitive due to the intractability of the likelihood, making optimization challenging. To overcome this, we train a convolutional neural network on a large training set that covers a useful parameter space, and then use the trained network for fast parameter estimation. Finally, we apply this model to analyze annual maximum precipitation data from ERA-Interim-driven Weather Research and Forecasting (WRF) simulations, allowing us to explore its spatial extreme behavior across North America.

We propose a novel nonparametric approach for linking covariates to Continuous Time Markov Chains (CTMCs) using the mathematical framework of Reproducing Kernel Hilbert Spaces (RKHS). CTMCs provide a robust framework for modeling transitions across clinical or behavioral states, but traditional multistate models often rely on linear relationships. In contrast, we use a generalized Representer Theorem to enable tractable inference in functional space. For the Frequen-tist version, we apply normed square penalties, while for the Bayesian version, we explore sparsity inducing spike and slab priors. Due to the computational challenges posed by high-dimensional spaces, we successfully adapt the Expectation Maximization Variable Selection (EMVS) algorithm to efficiently identify the posterior mode. We demonstrate the effectiveness of our method through extensive simulation studies and an application to follicular cell lymphoma data. Our performance metrics include the normalized difference between estimated and true nonlinear transition functions, as well as the difference in the probability of getting absorbed in one the final states, capturing the ability of our approach to predict long-term behaviors.

Distributionally Robust Optimisation (DRO) protects risk-averse decision-makers by considering the worst-case risk within an ambiguity set of distributions based on the empirical distribution or a model. To further guard against finite, noisy data, model-based approaches admit Bayesian formulations that propagate uncertainty from the posterior to the decision-making problem. However, when the model is misspecified, the decision maker must stretch the ambiguity set to contain the data-generating process (DGP), leading to overly conservative decisions. We address this challenge by introducing DRO with Robust, to model misspecification, Bayesian Ambiguity Sets (DRO-RoBAS). These are Maximum Mean Discrepancy ambiguity sets centred at a robust posterior predictive distribution that incorporates beliefs about the DGP. We show that the resulting optimisation problem obtains a dual formulation in the Reproducing Kernel Hilbert Space and we give probabilistic guarantees on the tolerance level of the ambiguity set. Our method outperforms other Bayesian and empirical DRO approaches in out-of-sample performance on the Newsvendor and Portfolio problems with various cases of model misspecification.

Bioprocess mechanistic modeling is essential for advancing intelligent digital twin representation of biomanufacturing, yet challenges persist due to complex intracellular regulation, stochastic system behavior, and limited experimental data. This paper introduces a symbolic and statistical learning framework to identify key regulatory mechanisms and quantify model uncertainty. Bioprocess dynamics is formulated with stochastic differential equations characterizing intrinsic process variability, with a predefined set of candidate regulatory mechanisms constructed from biological knowledge. A Bayesian learning approach is developed, which is based on a joint learning of kinetic parameters and regulatory structure through a formulation of the mixture model. To enhance computational efficiency, a Metropolis-adjusted Langevin algorithm with adjoint sensitivity analysis is developed for posterior exploration. Compared to state-of-the-art Bayesian inference approaches, the proposed framework achieves improved sample efficiency and robust model selection. An empirical study demonstrates its ability to recover missing regulatory mechanisms and improve model fidelity under data-limited conditions.

Handling missing values at test time is challenging for machine learning models, especially when aiming for both high accuracy and interpretability. Established approaches often add bias through imputation or excessive model complexity via missingness indicators. Moreover, either method can obscure interpretability, making it harder to understand how the model utilizes the observed variables in predictions. We propose missingness-avoiding (MA) machine learning, a general framework for training models to rarely require the values of missing (or imputed) features at test time. We create tailored MA learning algorithms for decision trees, tree ensembles, and sparse linear models by incorporating classifier-specific regularization terms in their learning objectives. The tree-based models leverage contextual missingness by reducing reliance on missing values based on the observed context. Experiments on real-world datasets demonstrate that MA-DT, MA-LASSO, MA-RF, and MA-GBT effectively reduce the reliance on features with missing values while maintaining predictive performance competitive with their unregularized counterparts. This shows that our framework gives practitioners a powerful tool to maintain interpretability in predictions with test-time missing values.

Uncertainty Quantification (UQ) is pivotal in enhancing the robustness, reliability, and interpretability of Machine Learning (ML) systems for healthcare, optimizing resources and improving patient care. Despite the emergence of ML-based clinical decision support tools, the lack of principled quantification of uncertainty in ML models remains a major challenge. Current reviews have a narrow focus on analyzing the state-of-the-art UQ in specific healthcare domains without systematically evaluating method efficacy across different stages of model development, and despite a growing body of research, its implementation in healthcare applications remains limited. Therefore, in this survey, we provide a comprehensive analysis of current UQ in healthcare, offering an informed framework that highlights how different methods can be integrated into each stage of the ML pipeline including data processing, training and evaluation. We also highlight the most popular methods used in healthcare and novel approaches from other domains that hold potential for future adoption in the medical context. We expect this study will provide a clear overview of the challenges and opportunities of implementing UQ in the ML pipeline for healthcare, guiding researchers and practitioners in selecting suitable techniques to enhance the reliability, safety and trust from patients and clinicians on ML-driven healthcare solutions.

Meta-reasoning Using Attention Maps and Its Applications in Cloud Robotics Adrian Lendinez 1, Renxi Qiu 1, Lanfranco Zanzi 2 and Dayou Li 1, Abstract -- Meta-reasoning, a branch of AI, focuses on reasoning about reasons. It has the potential to enhance robots' decision-making processes in unexpected situations. However, the concept has largely been confined to theoretical discussions and case-by-case investigations, lacking general and practical solutions when the V alue of Computation (V oC) is undefined, which is common in unexpected situations. In this work, we propose a revised meta-reasoning framework that significantly improves the scalability of the original approach in unexpected situations. This is achieved by incorporating semantic attention maps and unsupervised "attention" updates into the meta-reasoning processes. T o accommodate environmental dynamics, "lines of thought" are used to bridge context-specific objects with abstracted attentions, while meta-information is monitored and controlled at the meta-level for effective reasoning. The practicality of the proposed approach is demonstrated through cloud robots deployed in real-world scenarios, showing improved performance and robustness. I NTRODUCTION Significant progress has been made in probabilistic robotics to improve the adaptability and robustness of robot operations [1]. By integrating probabilistic models and statistical methods into perception and decision-making processes, robots can address structured uncertainty and randomness. However, to remain robust in unexpected situations, autonomous systems must also manage their reasoning processes, such as effectively handling uncertainties at the ground level and adapting objects at the conceptual level. This capability, known as meta-reasoning, facilitates reasoning about reasons [2].

Policy gradient (PG) methods have played an essential role in the empirical successes of reinforcement learning. In order to handle large state-action spaces, PG methods are typically used with function approximation. In this setting, the approximation error in modeling problem-dependent quantities is a key notion for characterizing the global convergence of PG methods. We focus on Softmax PG with linear function approximation (referred to as $\texttt{Lin-SPG}$) and demonstrate that the approximation error is irrelevant to the algorithm's global convergence even for the stochastic bandit setting. Consequently, we first identify the necessary and sufficient conditions on the feature representation that can guarantee the asymptotic global convergence of $\texttt{Lin-SPG}$. Under these feature conditions, we prove that $T$ iterations of $\texttt{Lin-SPG}$ with a problem-specific learning rate result in an $O(1/T)$ convergence to the optimal policy. Furthermore, we prove that $\texttt{Lin-SPG}$ with any arbitrary constant learning rate can ensure asymptotic global convergence to the optimal policy.

Cooperative transportation by multi-aerial robots has the potential to support various payloads and improve failsafe against dropping. Furthermore, changing the attachment positions of robots according payload characteristics increases the stability of transportation. However, there are almost no transportation systems capable of scaling to the payload weight and size and changing the optimal attachment positions. To address this issue, we propose a cooperative transportation system comprising autonomously executable software and suitable hardware, covering the entire process, from pre-takeoff setting to controlled flight. The proposed system decides the formation of the attachment positions by prioritizing controllability based on the center of gravity obtained from Bayesian estimations with robot pairs. We investigated the cooperative transportation of an unknown payload larger than that of whole carrier robots through numerical simulations. Furthermore, we performed cooperative transportation of an unknown payload (with a weight of about 3.2 kg and maximum length of 1.76 m) using eight robots. The proposed system was found to be versatile with regard to handling unknown payloads with different shapes and center-of-gravity positions.