Uncertainty quantification in multi-class image classification using chest X-ray images of COVID-19 and pneumonia.

This paper investigates uncertainty quantification (UQ) techniques in multi-class classification of chest X-ray images (COVID-19, Pneumonia, and Normal). We evaluate Bayesian Neural Networks (BNN) and the Deep Neural Network with UQ (DNN with UQ) techniques, including Monte Carlo dropout, Ensemble Bayesian Neural Network (EBNN), Ensemble Monte Carlo (EMC) dropout, across different evaluation metrics. Our analysis reveals that DNN with UQ, especially EBNN and EMC dropout, consistently outperform BNNs. For example, in Class 0 vs. All, EBNN achieved a UAcc of 92.6%, UAUC-ROC of 95.0%, and a Brier Score of 0.157, significantly surpassing BNN's performance. Similarly, EMC Dropout excelled in Class 1 vs. All with a UAcc of 83.5%, UAUC-ROC of 95.8%, and a Brier Score of 0.165. These advanced models demonstrated higher accuracy, better discriaminative capability, and more accurate probabilistic predictions. Our findings highlight the efficacy of DNN with UQ in enhancing model reliability and interpretability, making them highly suitable for critical healthcare applications like chest X-ray imageQ6 classification.

A Bayesian convolutional neural network-based generalized linear model.

Convolutional neural networks (CNNs) provide flexible function approximations for a wide variety of applications when the input variables are in the form of images or spatial data. Although CNNs often outperform traditional statistical models in prediction accuracy, statistical inference, such as estimating the effects of covariates and quantifying the prediction uncertainty, is not trivial due to the highly complicated model structure and overparameterization. To address this challenge, we propose a new Bayesian approach by embedding CNNs within the generalized linear models (GLMs) framework. We use extracted nodes from the last hidden layer of CNN with Monte Carlo (MC) dropout as informative covariates in GLM. This improves accuracy in prediction and regression coefficient inference, allowing for the interpretation of coefficients and uncertainty quantification. By fitting ensemble GLMs across multiple realizations from MC dropout, we can account for uncertainties in extracting the features. We apply our methods to biological and epidemiological problems, which have both high-dimensional correlated inputs and vector covariates. Specifically, we consider malaria incidence data, brain tumor image data, and fMRI data. By extracting information from correlated inputs, the proposed method can provide an interpretable Bayesian analysis. The algorithm can be broadly applicable to image regressions or correlated data analysis by enabling accurate Bayesian inference quickly.

Uncertainty quantification in multi-class segmentation: Comparison between Bayesian and non-Bayesian approaches in a clinical perspective.

BACKGROUND: Automatic segmentation techniques based on Convolutional Neural Networks (CNNs) are widely adopted to automatically identify any structure of interest from a medical image, as they are not time consuming and not subject to high intra- and inter-operator variability. However, the adoption of these approaches in clinical practice is slowed down by some factors, such as the difficulty in providing an accurate quantification of their uncertainty. PURPOSE: This work aims to evaluate the uncertainty quantification provided by two Bayesian and two non-Bayesian approaches for a multi-class segmentation problem, and to compare the risk propensity among these approaches, considering CT images of patients affected by renal cancer (RC). METHODS: Four uncertainty quantification approaches were implemented in this work, based on a benchmark CNN currently employed in medical image segmentation: two Bayesian CNNs with different regularizations (Dropout and DropConnect), named BDR and BDC, an ensemble method (Ens) and a test-time augmentation (TTA) method. They were compared in terms of segmentation accuracy, using the Dice score, uncertainty quantification, using the ratio of correct-certain pixels (RCC) and incorrect-uncertain pixels (RIU), and with respect to inter-observer variability in manual segmentation. They were trained with the Kidney and Kidney Tumor Segmentation Challenge launched in 2021 (Kits21), for which multi-class segmentations of kidney, RC, and cyst on 300 CT volumes are available. Moreover, they were tested considering this and other two public renal CT datasets. RESULTS: Accuracy results achieved large differences across the structures of interest for all approaches, with an average Dice score of 0.92, 0.58, and 0.21 for kidney, tumor, and cyst, respectively. In terms of uncertainties, TTA provided the highest uncertainty, followed by Ens and BDC, whereas BDR provided the lowest, and minimized the number of incorrect certain pixels worse than the other approaches. Again, large differences were seen across the three structures in terms of RCC and RIU. These metrics were associated with different risk propensity, as BDR was the most risk-taking approach, able to provide higher accuracy in its prediction, but failing to assign uncertainty on incorrect segmentation in every case. The other three approaches were more conservative, providing large uncertainty regions, with the drawback of giving alert also on correct areas. Finally, the analysis of the inter-observer segmentation variability showed a significant variation among the four approaches on the external dataset, with BDR reporting the lowest agreement (Dice = 0.82), and TTA obtaining the highest score (Dice = 0.94). CONCLUSIONS: Our outcomes highlight the importance of quantifying the segmentation uncertainty and that decision-makers can choose the approach most in line with the risk propensity degree required by the application and their policy.

Optimisation and Calibration of Bayesian Neural Network for Probabilistic Prediction of Biogas Performance in an Anaerobic Lagoon.

This study aims to enhance diagnostic capabilities for optimising the performance of the anaerobic sewage treatment lagoon at Melbourne Water's Western Treatment Plant (WTP) through a novel machine learning (ML)-based monitoring strategy. This strategy employs ML to make accurate probabilistic predictions of biogas performance by leveraging diverse real-life operational and inspection sensor and other measurement data for asset management, decision making, and structural health monitoring (SHM). The paper commences with data analysis and preprocessing of complex irregular datasets to facilitate efficient learning in an artificial neural network. Subsequently, a Bayesian mixture density neural network model incorporating an attention-based mechanism in bidirectional long short-term memory (BiLSTM) was developed. This probabilistic approach uses a distribution output layer based on the Gaussian mixture model and Monte Carlo (MC) dropout technique in estimating data and model uncertainties, respectively. Furthermore, systematic hyperparameter optimisation revealed that the optimised model achieved a negative log-likelihood (NLL) of 0.074, significantly outperforming other configurations. It achieved an accuracy approximately 9 times greater than the average model performance (NLL = 0.753) and 22 times greater than the worst performing model (NLL = 1.677). Key factors influencing the model's accuracy, such as the input window size and the number of hidden units in the BiLSTM layer, were identified, while the number of neurons in the fully connected layer was found to have no significant impact on accuracy. Moreover, model calibration using the expected calibration error was performed to correct the model's predictive uncertainty. The findings suggest that the inherent data significantly contribute to the overall uncertainty of the model, highlighting the need for more high-quality data to enhance learning. This study lays the groundwork for applying ML in transforming high-value assets into intelligent structures and has broader implications for ML in asset management, SHM applications, and renewable energy sectors.

Clinical assessment of deep learning-based uncertainty maps in lung cancer segmentation.

Objective. Prior to radiation therapy planning, accurate delineation of gross tumour volume (GTVs) and organs at risk (OARs) is crucial. In the current clinical practice, tumour delineation is performed manually by radiation oncologists, which is time-consuming and prone to large inter-observer variability. With the advent of deep learning (DL) models, automated contouring has become possible, speeding up procedures and assisting clinicians. However, these tools are currently used in the clinic mostly for contouring OARs, since these systems are not reliable yet for contouring GTVs. To improve the reliability of these systems, researchers have started exploring the topic of probabilistic neural networks. However, there is still limited knowledge of the practical implementation of such networks in real clinical settings.Approach. In this work, we developed a 3D probabilistic system that generates DL-based uncertainty maps for lung cancer CT segmentations. We employed the Monte Carlo (MC) dropout technique to generate probabilistic and uncertainty maps, while the model calibration was evaluated by using reliability diagrams. A clinical validation was conducted in collaboration with a radiation oncologist to qualitatively assess the value of the uncertainty estimates. We also proposed two novel metrics, namely mean uncertainty (MU) and relative uncertainty volume (RUV), as potential indicators for clinicians to assess the need for independent visual checks of the DL-based segmentation. Main results. Our study showed that uncertainty mapping effectively identified cases of under or over-contouring. Although the overconfidence of the model, a strong correlation was observed between the clinical opinion and MU metric. Moreover, both MU and RUV revealed high AUC values in discretising between low and high uncertainty cases.Significance. Our study is one of the first attempts to clinically validate uncertainty estimates in DL-based contouring. The two proposed metrics exhibited promising potential as indicators for clinicians to independently assess the quality of tumour delineation.

Uncertainty Evaluation of a Gas Turbine Model Based on a Nonlinear Autoregressive Exogenous Model and Monte Carlo Dropout.

Gas turbines are thermoelectric plants with various applications, such as large-scale electricity production, petrochemical industry, and steam generation. In order to optimize the operation of a gas turbine, it is necessary to develop system identification models that allow for the development of studies and analyses to increase the system's reliability. Current strategies for modeling complex and non-linear systems can be based on artificial intelligence techniques, using autoregressive neural networks of the NARX and LSTM type. In this context, this work aims to develop a model of a gas turbine capable of estimating the rotation speed of the turbine and simultaneously estimating the uncertainty associated with the estimation. These methodologies are based on artificial neural networks and the Monte Carlo dropout simulation method. The results were obtained from experimental data from a 215 MW gas turbine, getting the best model with a MAPE of 0.02% and an uncertainty associated with the turbine rotation speed of 2.2 RPM.

Towards greater neuroimaging classification transparency via the integration of explainability methods and confidence estimation approaches.

The field of neuroimaging has increasingly sought to develop artificial intelligence-based models for neurological and neuropsychiatric disorder automated diagnosis and clinical decision support. However, if these models are to be implemented in a clinical setting, transparency will be vital. Two aspects of transparency are (1) confidence estimation and (2) explainability. Confidence estimation approaches indicate confidence in individual predictions. Explainability methods give insight into the importance of features to model predictions. In this study, we integrate confidence estimation and explainability approaches for the first time. We demonstrate their viability for schizophrenia diagnosis using resting state functional magnetic resonance imaging (rs-fMRI) dynamic functional network connectivity (dFNC) data. We compare two confidence estimation approaches: Monte Carlo dropout (MCD) and MC batch normalization (MCBN). We combine them with two gradient-based explainability approaches, saliency and layer-wise relevance propagation (LRP), and examine their effects upon explanations. We find that MCD often adversely affects model gradients, making it ill-suited for integration with gradient-based explainability methods. In contrast, MCBN does not affect model gradients. Additionally, we find many participant-level differences between regular explanations and the distributions of explanations for combined explainability and confidence estimation approaches. This suggests that a similar confidence estimation approach used in a clinical context with explanations only output for the regular model would likely not yield adequate explanations. We hope that our findings will provide a starting point for the integration of the two fields, provide useful guidance for future studies, and accelerate the development of transparent neuroimaging clinical decision support systems.

A Hybrid Method for Performance Degradation Probability Prediction of Proton Exchange Membrane Fuel Cell.

The proton exchange membrane fuel cell (PEMFC) is a promising power source, but the short lifespan and high maintenance cost restrict its development and widespread application. Performance degradation prediction is an effective technique to extend the lifespan and reduce the maintenance cost of PEMFC. This paper proposed a novel hybrid method for the performance degradation prediction of PEMFC. Firstly, considering the randomness of PEMFC degradation, a Wiener process model is established to describe the degradation of the aging factor. Secondly, the unscented Kalman filter algorithm is used to estimate the degradation state of the aging factor from monitoring voltage. Then, in order to predict the degradation state of PEMFC, the transformer structure is used to capture the data characteristics and fluctuations of the aging factor. To quantify the uncertainty of the predicted results, we also add the Monte Carlo dropout technology to the transformer to obtain the confidence interval of the predicted result. Finally, the effectiveness and superiority of the proposed method are verified on the experimental datasets.

Active learning for data efficient semantic segmentation of canine bones in radiographs.

X-ray bone semantic segmentation is one crucial task in medical imaging. Due to deep learning's emergence, it was possible to build high-precision models. However, these models require a large quantity of annotated data. Furthermore, semantic segmentation requires pixel-wise labeling, thus being a highly time-consuming task. In the case of hip joints, there is still a need for increased anatomic knowledge due to the intrinsic nature of the femur and acetabulum. Active learning aims to maximize the model's performance with the least possible amount of data. In this work, we propose and compare the use of different queries, including uncertainty and diversity-based queries. Our results show that the proposed methods permit state-of-the-art performance using only 81.02% of the data, with O ( 1 ) time complexity.

Exploring uncertainty measures in convolutional neural network for semantic segmentation of oral cancer images.

Significance: Oral cancer is one of the most prevalent cancers, especially in middle- and low-income countries such as India. Automatic segmentation of oral cancer images can improve the diagnostic workflow, which is a significant task in oral cancer image analysis. Despite the remarkable success of deep-learning networks in medical segmentation, they rarely provide uncertainty quantification for their output. Aim: We aim to estimate uncertainty in a deep-learning approach to semantic segmentation of oral cancer images and to improve the accuracy and reliability of predictions. Approach: This work introduced a UNet-based Bayesian deep-learning (BDL) model to segment potentially malignant and malignant lesion areas in the oral cavity. The model can quantify uncertainty in predictions. We also developed an efficient model that increased the inference speed, which is almost six times smaller and two times faster (inference speed) than the original UNet. The dataset in this study was collected using our customized screening platform and was annotated by oral oncology specialists. Results: The proposed approach achieved good segmentation performance as well as good uncertainty estimation performance. In the experiments, we observed an improvement in pixel accuracy and mean intersection over union by removing uncertain pixels. This result reflects that the model provided less accurate predictions in uncertain areas that may need more attention and further inspection. The experiments also showed that with some performance compromises, the efficient model reduced computation time and model size, which expands the potential for implementation on portable devices used in resource-limited settings. Conclusions: Our study demonstrates the UNet-based BDL model not only can perform potentially malignant and malignant oral lesion segmentation, but also can provide informative pixel-level uncertainty estimation. With this extra uncertainty information, the accuracy and reliability of the model's prediction can be improved.

Uncertainty Quantification in Segmenting Tuberculosis-Consistent Findings in Frontal Chest X-rays.

Deep learning (DL) methods have demonstrated superior performance in medical image segmentation tasks. However, selecting a loss function that conforms to the data characteristics is critical for optimal performance. Further, the direct use of traditional DL models does not provide a measure of uncertainty in predictions. Even high-quality automated predictions for medical diagnostic applications demand uncertainty quantification to gain user trust. In this study, we aim to investigate the benefits of (i) selecting an appropriate loss function and (ii) quantifying uncertainty in predictions using a VGG16-based-U-Net model with the Monto-Carlo (MCD) Dropout method for segmenting Tuberculosis (TB)-consistent findings in frontal chest X-rays (CXRs). We determine an optimal uncertainty threshold based on several uncertainty-related metrics. This threshold is used to select and refer highly uncertain cases to an expert. Experimental results demonstrate that (i) the model trained with a modified Focal Tversky loss function delivered superior segmentation performance (mean average precision (mAP): 0.5710, 95% confidence interval (CI): (0.4021,0.7399)), (ii) the model with 30 MC forward passes during inference further improved and stabilized performance (mAP: 0.5721, 95% CI: (0.4032,0.7410), and (iii) an uncertainty threshold of 0.7 is observed to be optimal to refer highly uncertain cases.

Bayesian deep learning-based 1 H-MRS of the brain: Metabolite quantification with uncertainty estimation using Monte Carlo dropout.

PURPOSE: To develop a Bayesian convolutional neural network (BCNN) with Monte Carlo dropout sampling for metabolite quantification with simultaneous uncertainty estimation in deep learning-based proton MRS of the brain. METHODS: Human brain spectra were simulated using basis spectra for 17 metabolites and macromolecules (N = 100 000) at 3.0 Tesla. In addition, actual in vivo spectra (N = 5) were modified by adjusting SNR and linewidth with increasing severity of spectral degradation (N = 50). A BCNN was trained on the simulated spectra to generate a noise-free, line-narrowed, macromolecule signal-removed, metabolite-only spectrum from a typical human brain spectrum. At inference, each input spectrum was Monte Carlo dropout sampled (50 times), and the resulting mean spectrum and variance spectrum were used for metabolite quantification and uncertainty estimation, respectively. RESULTS: Using the simulated spectra, the mean absolute percent errors of the BCNN-predicted metabolite content were < 10% for Cr, Glu, Gln, mI, NAA, and Tau (< 5% for Glu, NAA, and mI). For all metabolites, the correlations (r's) between the ground-truth error and BCNN-predicted uncertainty ranged 0.72-0.94 (0.83 ± 0.06; p < 0.001). Using the modified in vivo spectra, the extent of variation in the estimated metabolite content against the increasing severity of spectral degradation tended to be smaller with BCNN than with linear combination of model spectra (LCModel). Overall, the variation in metabolite content tended to be more highly correlated with the uncertainty from BCNN than with the Cramér-Rao lower-bounds from LCModel (0.938 ± 0.019 vs. 0.881 ± 0.057 [p = 0.115]). CONCLUSION: The BCNN with Monte Carlo dropout sampling may be used in deep learning-based MRS for the estimation of uncertainty in the machine-predicted metabolite content, which is important in the clinical application of deep learning-based MRS.

Automatic brain segmentation in preterm infants with post-hemorrhagic hydrocephalus using 3D Bayesian U-Net.

Post-hemorrhagic hydrocephalus (PHH) is a severe complication of intraventricular hemorrhage (IVH) in very preterm infants. PHH monitoring and treatment decisions rely heavily on manual and subjective two-dimensional measurements of the ventricles. Automatic and reliable three-dimensional (3D) measurements of the ventricles may provide a more accurate assessment of PHH, and lead to improved monitoring and treatment decisions. To accurately and efficiently obtain these 3D measurements, automatic segmentation of the ventricles can be explored. However, this segmentation is challenging due to the large ventricular anatomical shape variability in preterm infants diagnosed with PHH. This study aims to (a) propose a Bayesian U-Net method using 3D spatial concrete dropout for automatic brain segmentation (with uncertainty assessment) of preterm infants with PHH; and (b) compare the Bayesian method to three reference methods: DenseNet, U-Net, and ensemble learning using DenseNets and U-Nets. A total of 41 T2 -weighted MRIs from 27 preterm infants were manually segmented into lateral ventricles, external CSF, white and cortical gray matter, brainstem, and cerebellum. These segmentations were used as ground truth for model evaluation. All methods were trained and evaluated using 4-fold cross-validation and segmentation endpoints, with additional uncertainty endpoints for the Bayesian method. In the lateral ventricles, segmentation endpoint values for the DenseNet, U-Net, ensemble learning, and Bayesian U-Net methods were mean Dice score = 0.814 ± 0.213, 0.944 ± 0.041, 0.942 ± 0.042, and 0.948 ± 0.034 respectively. Uncertainty endpoint values for the Bayesian U-Net were mean recall = 0.953 ± 0.037, mean  negative predictive value = 0.998 ± 0.005, mean accuracy = 0.906 ± 0.032, and mean AUC = 0.949 ± 0.031. To conclude, the Bayesian U-Net showed the best segmentation results across all methods and provided accurate uncertainty maps. This method may be used in clinical practice for automatic brain segmentation of preterm infants with PHH, and lead to better PHH monitoring and more informed treatment decisions.

Towards targeted ultrasound-guided prostate biopsy by incorporating model and label uncertainty in cancer detection.

PURPOSE: Systematic prostate biopsy is widely used for cancer diagnosis. The procedure is blind to underlying prostate tissue micro-structure; hence, it can lead to a high rate of false negatives. Development of a machine-learning model that can reliably identify suspicious cancer regions is highly desirable. However, the models proposed to-date do not consider the uncertainty present in their output or the data to benefit clinical decision making for targeting biopsy. METHODS: We propose a deep network for improved detection of prostate cancer in systematic biopsy considering both the label and model uncertainty. The architecture of our model is based on U-Net, trained with temporal enhanced ultrasound (TeUS) data. We estimate cancer detection uncertainty using test-time augmentation and test-time dropout. We then use uncertainty metrics to report the cancer probability for regions with high confidence to help the clinical decision making during the biopsy procedure. RESULTS: Experiments for prostate cancer classification includes data from 183 prostate biopsy cores of 41 patients. We achieve an area under the curve, sensitivity, specificity and balanced accuracy of 0.79, 0.78, 0.71 and 0.75, respectively. CONCLUSION: Our key contribution is to automatically estimate model and label uncertainty towards enabling targeted ultrasound-guided prostate biopsy. We anticipate that such information about uncertainty can decrease the number of unnecessary biopsy with a higher rate of cancer yield.

Monte Carlo Dropout for Uncertainty Estimation and Motor Imagery Classification.

Motor Imagery (MI)-based Brain-Computer Interfaces (BCIs) have been widely used as an alternative communication channel to patients with severe motor disabilities, achieving high classification accuracy through machine learning techniques. Recently, deep learning techniques have spotlighted the state-of-the-art of MI-based BCIs. These techniques still lack strategies to quantify predictive uncertainty and may produce overconfident predictions. In this work, methods to enhance the performance of existing MI-based BCIs are proposed in order to obtain a more reliable system for real application scenarios. First, the Monte Carlo dropout (MCD) method is proposed on MI deep neural models to improve classification and provide uncertainty estimation. This approach was implemented using Shallow Convolutional Neural Network (SCNN-MCD) and with an ensemble model (E-SCNN-MCD). As another contribution, to discriminate MI task predictions of high uncertainty, a threshold approach is introduced and tested for both SCNN-MCD and E-SCNN-MCD approaches. The BCI Competition IV Databases 2a and 2b were used to evaluate the proposed methods for both subject-specific and non-subject-specific strategies, obtaining encouraging results for MI recognition.

Uncertainty-aware convolutional neural network for COVID-19 X-ray images classification.

Deep learning (DL) has shown great success in the field of medical image analysis. In the wake of the current pandemic situation of SARS-CoV-2, a few pioneering works based on DL have made significant progress in automated screening of COVID-19 disease from the chest X-ray (CXR) images. But these DL models have no inherent way of expressing uncertainty associated with the model's prediction, which is very important in medical image analysis. Therefore, in this paper, we develop an uncertainty-aware convolutional neural network model, named UA-ConvNet, for the automated detection of COVID-19 disease from CXR images, with an estimation of associated uncertainty in the model's predictions. The proposed approach utilizes the EfficientNet-B3 model and Monte Carlo (MC) dropout, where an EfficientNet-B3 model has been fine-tuned on the CXR images. During inference, MC dropout has been applied for M forward passes to obtain the posterior predictive distribution. After that mean and entropy have been calculated on the obtained predictive distribution to get the mean prediction and model uncertainty. The proposed method is evaluated on the three different datasets of chest X-ray images, namely the COVID19CXr, X-ray image, and Kaggle datasets. The proposed UA-ConvNet model achieves a G-mean of 98.02% (with a Confidence Interval (CI) of 97.99-98.07) and sensitivity of 98.15% for the multi-class classification task on the COVID19CXr dataset. For binary classification, the proposed model achieves a G-mean of 99.16% (with a CI of 98.81-99.19) and a sensitivity of 99.30% on the X-ray Image dataset. Our proposed approach shows its superiority over the existing methods for diagnosing the COVID-19 cases from the CXR images.

Uncertainty quantification in skin cancer classification using three-way decision-based Bayesian deep learning.

Accurate automated medical image recognition, including classification and segmentation, is one of the most challenging tasks in medical image analysis. Recently, deep learning methods have achieved remarkable success in medical image classification and segmentation, clearly becoming the state-of-the-art methods. However, most of these methods are unable to provide uncertainty quantification (UQ) for their output, often being overconfident, which can lead to disastrous consequences. Bayesian Deep Learning (BDL) methods can be used to quantify uncertainty of traditional deep learning methods, and thus address this issue. We apply three uncertainty quantification methods to deal with uncertainty during skin cancer image classification. They are as follows: Monte Carlo (MC) dropout, Ensemble MC (EMC) dropout and Deep Ensemble (DE). To further resolve the remaining uncertainty after applying the MC, EMC and DE methods, we describe a novel hybrid dynamic BDL model, taking into account uncertainty, based on the Three-Way Decision (TWD) theory. The proposed dynamic model enables us to use different UQ methods and different deep neural networks in distinct classification phases. So, the elements of each phase can be adjusted according to the dataset under consideration. In this study, two best UQ methods (i.e., DE and EMC) are applied in two classification phases (the first and second phases) to analyze two well-known skin cancer datasets, preventing one from making overconfident decisions when it comes to diagnosing the disease. The accuracy and the F1-score of our final solution are, respectively, 88.95% and 89.00% for the first dataset, and 90.96% and 91.00% for the second dataset. Our results suggest that the proposed TWDBDL model can be used effectively at different stages of medical image analysis.

A generative adversarial network approach to (ensemble) weather prediction.

We use a conditional deep convolutional generative adversarial network to predict the geopotential height of the 500 hPa pressure level, the two-meter temperature and the total precipitation for the next 24 h over Europe. The proposed models are trained on 4 years of ERA5 reanalysis data from with the goal to predict the associated meteorological fields in 2019. The forecasts show a good qualitative and quantitative agreement with the true reanalysis data for the geopotential height and two-meter temperature, while failing for total precipitation, thus indicating that weather forecasts based on data alone may be possible for specific meteorological parameters. We further use Monte-Carlo dropout to develop an ensemble weather prediction system based purely on deep learning strategies, which is computationally cheap and further improves the skill of the forecasting model, by allowing to quantify the uncertainty in the current weather forecast as learned by the model.

Compensating for visibility artefacts in photoacoustic imaging with a deep learning approach providing prediction uncertainties.

Conventional photoacoustic imaging may suffer from the limited view and bandwidth of ultrasound transducers. A deep learning approach is proposed to handle these problems and is demonstrated both in simulations and in experiments on a multi-scale model of leaf skeleton. We employed an experimental approach to build the training and the test sets using photographs of the samples as ground truth images. Reconstructions produced by the neural network show a greatly improved image quality as compared to conventional approaches. In addition, this work aimed at quantifying the reliability of the neural network predictions. To achieve this, the dropout Monte-Carlo procedure is applied to estimate a pixel-wise degree of confidence on each predicted picture. Last, we address the possibility to use transfer learning with simulated data in order to drastically limit the size of the experimental dataset.

Left ventricle quantification with sample-level confidence estimation via Bayesian neural network.

Quantification of cardiac left ventricle has become a hot topic due to its great significance in clinical practice. Many efforts have been devoted to LV quantification and obtained promising performance with the help of various deep neural networks when validated on a group of samples. However, none of them can provide sample-level confidence of the results, i.e., how reliable is the prediction result for one single sample, which would help clinicians make decisions of whether or not to accept the automatic results. In this paper, we achieve this by introducing the uncertainty analysis theory into our LV quantification network. Two types of uncertainty, Model Uncertainty, and Data Uncertainty are analyzed for the quantification performance and contribute to the sample-level confidence. Experiments with data of 145 subjects validate that our method not only improved the quantification performance with an uncertainty-weighted regression loss but also is capable of providing for each sample the confidence level of the estimation results for clinicians' further consideration.