Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever observe a single epidemic, and therefore cannot empirically determine aleatoric uncertainty. Here, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching process. Our framework explicitly decomposes aleatoric variance into mechanistic components, quantifying the contribution to uncertainty produced by each factor in the epidemic process, and how these contributions vary over time. The aleatoric variance of an outbreak is itself a renewal equation where past variance affects future variance. We find that, superspreading is not necessary for substantial uncertainty, and profound variation in outbreak size can occur even without overdispersion in the offspring distribution (i.e. the distribution of the number of secondary infections an infected person produces). Aleatoric forecasting uncertainty grows dynamically and rapidly, and so forecasting using only epistemic uncertainty is a significant underestimate. Therefore, failure to account for aleatoric uncertainty will ensure that policymakers are misled about the substantially higher true extent of potential risk. We demonstrate our method, and the extent to which potential risk is underestimated, using two historical examples.
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Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within graph learning processes. This paper therefore addresses this issue by proposing a flexible algorithmic framework for graph learning under low-rank structural constraints on the covariance matrix. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution (a generalization of Gaussian graphical models to possibly heavy-tailed distributions), where the covariance matrix is optionally constrained to be structured as low-rank plus diagonal (low-rank factor model). The resolution of this class of problems is then tackled with Riemannian optimization, where we leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models. Numerical experiments on real-world data sets illustrate the effectiveness of the proposed approach.
Shape completion, i.e., predicting the complete geometry of an object from a partial observation, is highly relevant for several downstream tasks, most notably robotic manipulation. When basing planning or prediction of real grasps on object shape reconstruction, an indication of severe geometric uncertainty is indispensable. In particular, there can be an irreducible uncertainty in extended regions about the presence of entire object parts when given ambiguous object views. To treat this important case, we propose two novel methods for predicting such uncertain regions as straightforward extensions of any method for predicting local spatial occupancy, one through postprocessing occupancy scores, the other through direct prediction of an uncertainty indicator. We compare these methods together with two known approaches to probabilistic shape completion. Moreover, we generate a dataset, derived from ShapeNet, of realistically rendered depth images of object views with ground-truth annotations for the uncertain regions. We train on this dataset and test each method in shape completion and prediction of uncertain regions for known and novel object instances and on synthetic and real data. While direct uncertainty prediction is by far the most accurate in the segmentation of uncertain regions, both novel methods outperform the two baselines in shape completion and uncertain region prediction, and avoiding the predicted uncertain regions increases the quality of grasps for all tested methods. Web: //github.com/DLR-RM/shape-completion
Operating unmanned aerial vehicles (UAVs) in complex environments that feature dynamic obstacles and external disturbances poses significant challenges, primarily due to the inherent uncertainty in such scenarios. Additionally, inaccurate robot localization and modeling errors further exacerbate these challenges. Recent research on UAV motion planning in static environments has been unable to cope with the rapidly changing surroundings, resulting in trajectories that may not be feasible. Moreover, previous approaches that have addressed dynamic obstacles or external disturbances in isolation are insufficient to handle the complexities of such environments. This paper proposes a reliable motion planning framework for UAVs, integrating various uncertainties into a chance constraint that characterizes the uncertainty in a probabilistic manner. The chance constraint provides a probabilistic safety certificate by calculating the collision probability between the robot's Gaussian-distributed forward reachable set and states of obstacles. To reduce the conservatism of the planned trajectory, we propose a tight upper bound of the collision probability and evaluate it both exactly and approximately. The approximated solution is used to generate motion primitives as a reference trajectory, while the exact solution is leveraged to iteratively optimize the trajectory for better results. Our method is thoroughly tested in simulation and real-world experiments, verifying its reliability and effectiveness in uncertain environments.
We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss in estimating a random variable from an observed feature vector and the minimum expected loss in estimating the same random variable from a transformation (statistic) of the feature vector. After characterizing lossless transformations, i.e., transformations for which the excess risk is zero for all loss functions, we construct a partitioning test statistic for the hypothesis that a given transformation is lossless and show that for i.i.d. data the test is strongly consistent. More generally, we develop information-theoretic upper bounds on the excess risk that uniformly hold over fairly general classes of loss functions. Based on these bounds, we introduce the notion of a delta-lossless transformation and give sufficient conditions for a given transformation to be universally delta-lossless. Applications to classification, nonparametric regression, portfolio strategies, information bottleneck, and deep learning, are also surveyed.
Data uncertainties, such as sensor noise or occlusions, can introduce irreducible ambiguities in images, which result in varying, yet plausible, semantic hypotheses. In Machine Learning, this ambiguity is commonly referred to as aleatoric uncertainty. Latent density models can be utilized to address this problem in image segmentation. The most popular approach is the Probabilistic U-Net (PU-Net), which uses latent Normal densities to optimize the conditional data log-likelihood Evidence Lower Bound. In this work, we demonstrate that the PU- Net latent space is severely inhomogenous. As a result, the effectiveness of gradient descent is inhibited and the model becomes extremely sensitive to the localization of the latent space samples, resulting in defective predictions. To address this, we present the Sinkhorn PU-Net (SPU-Net), which uses the Sinkhorn Divergence to promote homogeneity across all latent dimensions, effectively improving gradient-descent updates and model robustness. Our results show that by applying this on public datasets of various clinical segmentation problems, the SPU-Net receives up to 11% performance gains compared against preceding latent variable models for probabilistic segmentation on the Hungarian-Matched metric. The results indicate that by encouraging a homogeneous latent space, one can significantly improve latent density modeling for medical image segmentation.
It is widely believed that a joint factor analysis of item responses and response time (RT) may yield more precise ability scores that are conventionally predicted from responses only. For this purpose, a simple-structure factor model is often preferred as it only requires specifying an additional measurement model for item-level RT while leaving the original item response theory (IRT) model for responses intact. The added speed factor indicated by item-level RT correlates with the ability factor in the IRT model, allowing RT data to carry additional information about respondents' ability. However, parametric simple-structure factor models are often restrictive and fit poorly to empirical data, which prompts under-confidence in the suitablity of a simple factor structure. In the present paper, we analyze the 2015 Programme for International Student Assessment (PISA) mathematics data using a semiparametric simple-structure model. We conclude that a simple factor structure attains a decent fit after further parametric assumptions in the measurement model are sufficiently relaxed. Furthermore, our semiparametric model implies that the association between latent ability and speed/slowness is strong in the population, but the form of association is nonlinear. It follows that scoring based on the fitted model can substantially improve the precision of ability scores.
This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the approximation accuracy and the reducibility (compressibility) in highly nonlinear and singular cases. The proposed XTD method can be a powerful tool for solving nonlinear space-time parametric problems. The method has been successfully applied to parametric elastic-plastic problems and real time additive manufacturing residual stress predictions with uncertainty quantification. Furthermore, a combined XTD-SCA (self-consistent clustering analysis) strategy has been presented for multi-scale material modeling, which enables real time multi-scale multi-parametric simulations. The efficiency of the method is demonstrated with comparison to finite element analysis. The proposed method enables a novel framework for fast manufacturing and material design with uncertainties.
Over the past decade, deep learning technologies have greatly advanced the field of medical image registration. The initial developments, such as ResNet-based and U-Net-based networks, laid the groundwork for deep learning-driven image registration. Subsequent progress has been made in various aspects of deep learning-based registration, including similarity measures, deformation regularizations, and uncertainty estimation. These advancements have not only enriched the field of deformable image registration but have also facilitated its application in a wide range of tasks, including atlas construction, multi-atlas segmentation, motion estimation, and 2D-3D registration. In this paper, we present a comprehensive overview of the most recent advancements in deep learning-based image registration. We begin with a concise introduction to the core concepts of deep learning-based image registration. Then, we delve into innovative network architectures, loss functions specific to registration, and methods for estimating registration uncertainty. Additionally, this paper explores appropriate evaluation metrics for assessing the performance of deep learning models in registration tasks. Finally, we highlight the practical applications of these novel techniques in medical imaging and discuss the future prospects of deep learning-based image registration.
The use of Dynamic Epistemic Logic (DEL) in multi-agent planning has led to a widely adopted action formalism that can handle nondeterminism, partial observability and arbitrary knowledge nesting. As such expressive power comes at the cost of undecidability, several decidable fragments have been isolated, mainly based on syntactic restrictions of the action formalism. In this paper, we pursue a novel semantic approach to achieve decidability. Namely, rather than imposing syntactical constraints, the semantic approach focuses on the axioms of the logic for epistemic planning. Specifically, we augment the logic of knowledge S5$_n$ and with an interaction axiom called (knowledge) commutativity, which controls the ability of agents to unboundedly reason on the knowledge of other agents. We then provide a threefold contribution. First, we show that the resulting epistemic planning problem is decidable. In doing so, we prove that our framework admits a finitary non-fixpoint characterization of common knowledge, which is of independent interest. Second, we study different generalizations of the commutativity axiom, with the goal of obtaining decidability for more expressive fragments of DEL. Finally, we show that two well-known epistemic planning systems based on action templates, when interpreted under the setting of knowledge, conform to the commutativity axiom, hence proving their decidability.
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often refereed to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of hitherto attempts at handling uncertainty in general and formalizing this distinction in particular.
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