Uncertainty Estimation in Unsupervised MR-CT Synthesis of Scoliotic Spines.

Uncertainty estimations through approximate Bayesian inference provide interesting insights to deep neural networks' behavior. In unsupervised learning tasks, where expert labels are unavailable, it becomes ever more important to critique the model through uncertainties. This paper presents a proof-of-concept for generalizing the aleatoric and epistemic uncertainties in unsupervised MR-CT synthesis of scoliotic spines. A novel adaptation of the cycle-consistency constraint in CycleGAN is proposed such that the model predicts the aleatoric uncertainty maps in addition to the standard volume-to-volume translation between Magnetic Resonance (MR) and Computed Tomography (CT) data. Ablation experiments were performed to understand uncertainty estimation as an implicit regularizer and a measure of the model's confidence. The aleatoric uncertainty helps in distinguishing between the bone and soft-tissue regions in CT and MR data during translation, while the epistemic uncertainty provides interpretable information to the user for downstream tasks.

Hybrid representation-enhanced sampling for Bayesian active learning in musculoskeletal segmentation of lower extremities.

PURPOSE: Manual annotations for training deep learning models in auto-segmentation are time-intensive. This study introduces a hybrid representation-enhanced sampling strategy that integrates both density and diversity criteria within an uncertainty-based Bayesian active learning (BAL) framework to reduce annotation efforts by selecting the most informative training samples. METHODS: The experiments are performed on two lower extremity datasets of MRI and CT images, focusing on the segmentation of the femur, pelvis, sacrum, quadriceps femoris, hamstrings, adductors, sartorius, and iliopsoas, utilizing a U-net-based BAL framework. Our method selects uncertain samples with high density and diversity for manual revision, optimizing for maximal similarity to unlabeled instances and minimal similarity to existing training data. We assess the accuracy and efficiency using dice and a proposed metric called reduced annotation cost (RAC), respectively. We further evaluate the impact of various acquisition rules on BAL performance and design an ablation study for effectiveness estimation. RESULTS: In MRI and CT datasets, our method was superior or comparable to existing ones, achieving a 0.8% dice and 1.0% RAC increase in CT (statistically significant), and a 0.8% dice and 1.1% RAC increase in MRI (not statistically significant) in volume-wise acquisition. Our ablation study indicates that combining density and diversity criteria enhances the efficiency of BAL in musculoskeletal segmentation compared to using either criterion alone. CONCLUSION: Our sampling method is proven efficient in reducing annotation costs in image segmentation tasks. The combination of the proposed method and our BAL framework provides a semi-automatic way for efficient annotation of medical image datasets.

Advanced error modeling and Bayesian uncertainty quantification in mechanistic liquid chromatography modeling.

Current mechanistic chromatography process modeling methods lack the ability to account for the impact of experimental errors beyond detector noise (e.g. pump delays and variable feed composition) on the uncertainty in calibrated model parameters and the resulting model-predicted chromatograms. This paper presents an uncertainty quantification method that addresses this limitation by determining the probability distribution of parameters in calibrated models, taking into consideration multiple realistic sources of experimental error. The method, which is based on Bayes' theorem and utilizes Markov chain Monte Carlo with an ensemble sampler, is demonstrated to be robust and extensible using synthetic and industrial data. The corresponding software is freely available as open-source code at https://github.com/modsim/CADET-Match.

Approximating the Operating Characteristics of Bayesian Uncertainty Directed Trial Designs.

Bayesian response adaptive clinical trials are currently evaluating experimental therapies for several diseases. Adaptive decisions, such as pre-planned variations of the randomization probabilities, attempt to accelerate the development of new treatments. The design of response adaptive trials, in most cases, requires time consuming simulation studies to describe operating characteristics, such as type I/II error rates, across plausible scenarios. We investigate large sample approximations of pivotal operating characteristics in Bayesian Uncertainty directed trial Designs (BUDs). A BUD trial utilizes an explicit metric u to quantify the information accrued during the study on parameters of interest, for example the treatment effects. The randomization probabilities vary during time to minimize the uncertainty summary u at completion of the study. We provide an asymptotic analysis (i) of the allocation of patients to treatment arms and (ii) of the randomization probabilities. For BUDs with outcome distributions belonging to the natural exponential family with quadratic variance function, we illustrate the asymptotic normality of the number of patients assigned to each arm and of the randomization probabilities. We use these results to approximate relevant operating characteristics such as the power of the BUD. We evaluate the accuracy of the approximations through simulations under several scenarios for binary, time-to-event and continuous outcome models.

QSAR modeling without descriptors using graph convolutional neural networks: the case of mutagenicity prediction.

Deep neural networks are effective in learning directly from low-level encoded data without the need of feature extraction. This paper shows how QSAR models can be constructed from 2D molecular graphs without computing chemical descriptors. Two graph convolutional neural network-based models are presented with and without a Bayesian estimation of the prediction uncertainty. The property under investigation is mutagenicity: Models developed here predict the output of the Ames test. These models take the SMILES representation of the molecules as input to produce molecular graphs in terms of adjacency matrices and subsequently use attention mechanisms to weight the role of their subgraphs in producing the output. The results positively compare with current state-of-the-art models. Furthermore, our proposed model interpretation can be enhanced by the automatic extraction of the substructures most important in driving the prediction, as well as by uncertainty estimations.

A data-centric approach to generative modelling for 3D-printed steel.

The emergence of additive manufacture (AM) for metallic material enables components of near arbitrary complexity to be produced. This has potential to disrupt traditional engineering approaches. However, metallic AM components exhibit greater levels of variation in their geometric and mechanical properties compared to standard components, which is not yet well understood. This uncertainty poses a fundamental barrier to potential users of the material, since extensive post-manufacture testing is currently required to ensure safety standards are met. Taking an interdisciplinary approach that combines probabilistic mechanics and uncertainty quantification, we demonstrate that intrinsic variation in AM steel can be well described by a generative statistical model that enables the quality of a design to be predicted before manufacture. Specifically, the geometric variation in the material can be described by an anisotropic spatial random field with oscillatory covariance structure, and the mechanical behaviour by a stochastic anisotropic elasto-plastic material model. The fitted generative model is validated on a held-out experimental dataset and our results underscore the need to combine both statistical and physics-based modelling in the characterization of new AM steel products.

Optimization of rain gauge sampling density for river discharge prediction using Bayesian calibration.

River discharges are often predicted based on a calibrated rainfall-runoff model. The major sources of uncertainty, namely input, parameter and model structural uncertainty must all be taken into account to obtain realistic estimates of the accuracy of discharge predictions. Over the past years, Bayesian calibration has emerged as a suitable method for quantifying uncertainty in model parameters and model structure, where the latter is usually modelled by an additive or multiplicative stochastic term. Recently, much work has also been done to include input uncertainty in the Bayesian framework. However, the use of geostatistical methods for characterizing the prior distribution of the catchment rainfall is underexplored, particularly in combination with assessments of the influence of increasing or decreasing rain gauge network density on discharge prediction accuracy. In this article we integrate geostatistics and Bayesian calibration to analyze the effect of rain gauge density on river discharge prediction accuracy. We calibrated the HBV hydrological model while accounting for input, initial state, model parameter and model structural uncertainty, and also taking uncertainties in the discharge measurements into account. Results for the Thur basin in Switzerland showed that model parameter uncertainty was the main contributor to the joint posterior uncertainty. We also showed that a low rain gauge density is enough for the Bayesian calibration, and that increasing the number of rain gauges improved model prediction until reaching a density of one gauge per 340 km2. While the optimal rain gauge density is case-study specific, we make recommendations on how to handle input uncertainty in Bayesian calibration for river discharge prediction and present the methodology that may be used to carry out such experiments.

Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching.

A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10-7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.

Benchmarking inference methods for water quality monitoring and status classification.

River water quality monitoring at limited temporal resolution can lead to imprecise and inaccurate classification of physicochemical status due to sampling error. Bayesian inference allows for the quantification of this uncertainty, which can assist decision-making. However, implicit assumptions of Bayesian methods can cause further uncertainty in the uncertainty quantification, so-called second-order uncertainty. In this study, and for the first time, we rigorously assessed this second-order uncertainty for inference of common water quality statistics (mean and 95th percentile) based on sub-sampling high-frequency (hourly) total reactive phosphorus (TRP) concentration data from three watersheds. The statistics were inferred with the low-resolution sub-samples using the Bayesian lognormal distribution and bootstrap, frequentist t test, and face-value approach and were compared with those of the high-frequency data as benchmarks. The t test exhibited a high risk of bias in estimating the water quality statistics of interest and corresponding physicochemical status (up to 99% of sub-samples). The Bayesian lognormal model provided a good fit to the high-frequency TRP concentration data and the least biased classification of physicochemical status (< 5% of sub-samples). Our results suggest wide applicability of Bayesian inference for water quality status classification, a new approach for regulatory practice that provides uncertainty information about water quality monitoring and regulatory classification with reduced bias compared to frequentist approaches. Furthermore, the study elucidates sizeable second-order uncertainty due to the choice of statistical model, which could be quantified based on the high-frequency data.

Explore a Multivariate Bayesian Uncertainty Processor driven by artificial neural networks for probabilistic PM2.5 forecasting.

Quantifying predictive uncertainty inherent in the nonlinear multivariate dependence structure of multi-step-ahead PM2.5 forecasts is challenging. This study integrates a Multivariate Bayesian Uncertainty Processor (MBUP) and an artificial neural network (ANN) to make accurate probabilistic PM2.5 forecasts. The contributions of the proposed approach are two-fold. First, the MBUP can capture the nonlinear multivariate dependence structure between observed and forecasted data. Second, the MBUP can alleviate predictive uncertainty encountered in PM2.5 forecast models that are configured by ANNs. The reliability of the proposed approach was assessed by a case study on air quality in Taipei City of Taiwan. We consider forecasts of PM2.5 concentrations as a function of meteorological and air quality factors based on long-term (2010-2018) hourly observational datasets. Firstly, the Back Propagation Neural Network (BPNN) and the Adaptive Neural Fuzzy Inference System (ANFIS) were investigated to produce deterministic forecasts. Results revealed that the ANFIS model could learn different air pollutant emission mechanisms (i.e. primary, secondary and natural processes) from the clustering-based fuzzy inference system and produce more accurate deterministic forecasts than the BPNN. The ANFIS model then provided inputs (i.e. point estimates) to probabilistic forecast models. Next, two post-processing techniques (MBUP and the Univariate Bayesian Uncertainty Processor (UBUP)) were separately employed to produce probabilistic forecasts. The Bayesian Uncertainty Processors (BUPs) can model the dependence structure (i.e. posterior density function) between observed and forecasted data using a prior density function and a likelihood density function. Here in BUPs, the Monte Carlo simulation was introduced to create a probabilistic predictive interval of PM2.5 concentrations. The results demonstrated that the MBUP not only outperformed the UBUP but also suitably characterized the complex nonlinear multivariate dependence structure between observations and forecasts. Consequently, the proposed approach could reduce predictive uncertainty while significantly improving model reliability and PM2.5 forecast accuracy for future horizons.

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions.

BACKGROUND: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. METHODS: Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. RESULTS: The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model's structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described. CONCLUSIONS: Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.