This paper introduces an efficient sub-model ensemble framework aimed at enhancing the interpretability of medical deep learning models, thus increasing their clinical applicability. By generating uncertainty maps, this framework enables end-users to evaluate the reliability of model outputs. We developed a strategy to develop diverse models from a single well-trained checkpoint, facilitating the training of a model family. This involves producing multiple outputs from a single input, fusing them into a final output, and estimating uncertainty based on output disagreements. Implemented using U-Net and UNETR models for segmentation and synthesis tasks, this approach was tested on CT body segmentation and MR-CT synthesis datasets. It achieved a mean Dice coefficient of 0.814 in segmentation and a Mean Absolute Error of 88.17 HU in synthesis, improved from 89.43 HU by pruning. Additionally, the framework was evaluated under corruption and undersampling, maintaining correlation between uncertainty and error, which highlights its robustness. These results suggest that the proposed approach not only maintains the performance of well-trained models but also enhances interpretability through effective uncertainty estimation, applicable to both convolutional and transformer models in a range of imaging tasks.

We consider the problem of estimating the transition dynamics $T^*$ from near-optimal expert trajectories in the context of offline model-based reinforcement learning. We develop a novel constraint-based method, Inverse Transition Learning, that treats the limited coverage of the expert trajectories as a \emph{feature}: we use the fact that the expert is near-optimal to inform our estimate of $T^*$. We integrate our constraints into a Bayesian approach. Across both synthetic environments and real healthcare scenarios like Intensive Care Unit (ICU) patient management in hypotension, we demonstrate not only significant improvements in decision-making, but that our posterior can inform when transfer will be successful.

An improved bilinear fuzzy genetic algorithm (BFGA) is introduced in this chapter for the design optimization of steel structures with semi-rigid connections. Semi-rigid connections provide a compromise between the stiffness of fully rigid connections and the flexibility of fully pinned connections. However, designing such structures is challenging due to the non-linear behavior of semi-rigid connections. The BFGA is a robust optimization method that combines the strengths of fuzzy logic and genetic algorithm to handle the complexity and uncertainties of structural design problems. The BFGA, compared to standard GA, demonstrated to generate highquality solutions in a reasonable time. The application of the BFGA is demonstrated through the optimization of steel structures with semi-rigid connections, considering the weight, and performance criteria. The results show that the proposed BFGA is capable of finding optimal designs that satisfy all the design requirements and constraints. The proposed approach provides a promising solution for the optimization of complex structures with non-linear behavior.

Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios, only output-level data are available to learn the input model parameters, which is challenging due to the often intractable likelihood of the stochastic simulation model. Moreover, stochastic simulation models are frequently inexact, with discrepancies between the model and the target system. No existing methods can effectively learn and quantify the uncertainties of input parameters using only output-level data. In this paper, we propose to learn differentiable input parameters of stochastic simulation models using output-level data via kernel score minimization with stochastic gradient descent. We quantify the uncertainties of the learned input parameters using a frequentist confidence set procedure based on a new asymptotic normality result that accounts for model inexactness. The proposed method is evaluated on exact and inexact G/G/1 queueing models.

Grasp learning in noisy environments, such as occlusions, sensor noise, and out-of-distribution (OOD) objects, poses significant challenges. Recent learning-based approaches focus primarily on capturing aleatoric uncertainty from inherent data noise. The epistemic uncertainty, which represents the OOD recognition, is often addressed by ensembles with multiple forward paths, limiting real-time application. In this paper, we propose an uncertainty-aware approach for 6-DoF grasp detection using evidential learning to comprehensively capture both uncertainties in real-world robotic grasping. As a key contribution, we introduce vMF-Contact, a novel architecture for learning hierarchical contact grasp representations with probabilistic modeling of directional uncertainty as von Mises-Fisher (vMF) distribution. To achieve this, we derive and analyze the theoretical formulation of the second-order objective on the posterior parametrization, providing formal guarantees for the model's ability to quantify uncertainty and improve grasp prediction performance. Moreover, we enhance feature expressiveness by applying partial point reconstructions as an auxiliary task, improving the comprehension of uncertainty quantification as well as the generalization to unseen objects. In the real-world experiments, our method demonstrates a significant improvement by 39% in the overall clearance rate compared to the baselines. Video is under https://www.youtube.com/watch?v=4aQsrDgdV8Y&t=12s

For the retrieval of large-scale vegetation biophysical parameters, the inversion of radiative transfer models (RTMs) is the most commonly used approach. In recent years, Artificial Neural Network (ANN)-based methods have become the mainstream for inverting RTMs due to their high accuracy and computational efficiency. It has been widely used in the retrieval of biophysical variables (BV). However, due to the lack of the Bayesian inversion theory interpretation, it faces challenges in quantifying the retrieval uncertainty, a crucial metric for product quality validation and downstream applications such as data assimilation or ecosystem carbon cycling modeling. This study proved that the ANN trained with squared loss outputs the posterior mean, providing a rigorous foundation for its uncertainty quantification, regularization, and incorporation of prior information. A Bayesian theoretical framework was subsequently proposed for ANN-based methods. Using this framework, we derived a new algorithm called Uncertainty Prediction Neural Network (UpNet), which enables the simultaneous training of two ANNs to retrieve BV and provide retrieval uncertainty. To validate our method, we compared UpNet with the standard Bayesian inference method, i.e., Markov Chain Monte Carlo (MCMC), in the inversion of a widely used RTM called ProSAIL for retrieving BVs and estimating uncertainty. The results demonstrated that the BVs retrieved and the uncertainties estimated by UpNet were highly consistent with those from MCMC, achieving over a million-fold acceleration. These results indicated that UpNet has significant potential for fast retrieval and uncertainty quantification of BVs or other parameters with medium and high-resolution remote sensing data. Our Python implementation is available at: https://github.com/Dash-RSer/UpNet.

An open question in \emph{Imprecise Probabilistic Machine Learning} is how to empirically derive a credal region (i.e., a closed and convex family of probabilities on the output space) from the available data, without any prior knowledge or assumption. In classification problems, credal regions are a tool that is able to provide provable guarantees under realistic assumptions by characterizing the uncertainty about the distribution of the labels. Building on previous work, we show that credal regions can be directly constructed using conformal methods. This allows us to provide a novel extension of classical conformal prediction to problems with ambiguous ground truth, that is, when the exact labels for given inputs are not exactly known. The resulting construction enjoys desirable practical and theoretical properties: (i) conformal coverage guarantees, (ii) smaller prediction sets (compared to classical conformal prediction regions) and (iii) disentanglement of uncertainty sources (epistemic, aleatoric). We empirically verify our findings on both synthetic and real datasets.

Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random effects. Such matrices are typically sparse; however, the sparsity pattern resembles a multi partite random graph, which does not lend itself well to default sparse linear algebra techniques. Notably, we show that, for typical GLMMs, the Cholesky factor is dense even when the original precision is sparse. We thus turn to approximate iterative techniques, in particular to the conjugate gradient (CG) method. We combine a detailed analysis of the spectrum of said precision matrices with results from random graph theory to show that CG-based methods applied to high-dimensional GLMMs typically achieve a fixed approximation error with a total cost that scales linearly with the number of parameters and observations. Numerical illustrations with both real and simulated data confirm the theoretical findings, while at the same time illustrating situations, such as nested structures, where CG-based methods struggle.

Recent advances in large language models (LLMs) show the potential of using LLMs as evaluators for assessing the quality of text generations from LLMs. However, applying LLM evaluators naively to compare or judge between different systems can lead to unreliable results due to the intrinsic win rate estimation bias of LLM evaluators. In order to mitigate this problem, we propose two calibration methods, Bayesian Win Rate Sampling (BWRS) and Bayesian Dawid-Skene, both of which leverage Bayesian inference to more accurately infer the true win rate of generative language models. We empirically validate our methods on six datasets covering story generation, summarization, and instruction following tasks. We show that both our methods are effective in improving the accuracy of win rate estimation using LLMs as evaluators, offering a promising direction for reliable automatic text quality evaluation.

Neural networks are traditionally trained under the assumption that data come from a stationary distribution. However, settings which violate this assumption are becoming more popular; examples include supervised learning under distributional shifts, reinforcement learning, continual learning and non-stationary contextual bandits. In this work we introduce a novel learning approach that automatically models and adapts to non-stationarity, via an Ornstein-Uhlenbeck process with an adaptive drift parameter. The adaptive drift tends to draw the parameters towards the initialisation distribution, so the approach can be understood as a form of soft parameter reset. We show empirically that our approach performs well in non-stationary supervised and off-policy reinforcement learning settings.