Bayesian Convolutional Neural Networks Research Articles

Expertise-informed Bayesian convolutional neural network for oil production forecasting

This paper presents a novel machine-learning multi-well production forecasting model embedded with expertise, which has strong interpretability and generalization. Expertise is not only reflected in the incorporation of water drive characteristic curves in the model but also in the creation of high-order input features. Furthermore, some parameters of the model loss function are set based on the development experience, which introduces human practical knowledge into the model’s training. These designs enhance the interpretability of the model. In the modeling process, only the production data available on-site are used, which makes the model of practical value. The model is constructed based on Bayesian convolution and fully connected neural networks with regularization effects in structure, which can provide a range of forecasted values that are more in line with practical needs. Simulation results show that the average R-squared (R2) score of the proposed model on the testing set can reach 0.9164. Compared to the scores of typical machine learning models such as XGBoost (0.5170), LSTM (0.6623), and CNN (0.4623), the proposed expertise-informed model has stronger generalization performance. In addition, the experimental results of the proposed model in scenarios containing errors indicate that it has high stability, with the average R2 in the training set and testing set are 0.9439 and 0.9569, respectively.

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

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. 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). 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. 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). 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 theirpolicy.

A single-joint multi-task motor imagery EEG signal recognition method based on Empirical Wavelet and Multi‐Kernel Extreme Learning Machine

BackgroundIn the pursuit of finer Brain-Computer Interface commands, research focus has shifted towards classifying EEG signals for multiple tasks. While single-joint multitasking motor imagery provides support, distinguishing between EEG signals from the same joint remains challenging due to their similar brain spatial distribution. New methodWe designed experiments involving three motor imagery tasks—wrist extension, wrist flexion, and wrist abduction—with six participants. Based on this, a single-joint multi-task motor imagery EEG signal recognition method using Empirical Wavelet Decomposition and Multi-Kernel Extreme Learning Machine is proposed. This method employs Empirical Wavelet Decomposition (EWT) for modal decomposition, screening, and reconstruction of raw EEG signals, feature extraction using Common Spatial Patterns (CSP), and classification using Multi-Kernel Extreme Learning Machine (MKELM). ResultsAfter EWT processing, differences in time and frequency characteristics between EEG signals of different classes were enhanced, with the MKELM model achieving an average recognition accuracy of 91.93 %. Comparison with other methods and conclusionsWe compared EWT with Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), Local Mean Decomposition (LMD), and Wavelet Packet Decomposition (WPD). The results showed that the differences between various types of EEG signals processed by EWT were the most pronounced. The MKELM model outperformed traditional machine learning models such as Extreme Learning Machine (ELM), Support Vector Machine (SVM), K-Nearest Neighbors (KNN), and Linear Discriminant Analysis (LDA) in terms of recognition performance, and also exhibited faster training speeds than deep learning models such as Bayesian Convolutional Neural Network (BCNN) and Attention-based Dual-scale Fusion Convolutional Neural Network (ADFCNN). In summary, the proposed method provides a new approach for achieving finer Brain-Computer Interface commands.

Efficient Bayesian CNN Model Compression using Bayes by Backprop and L1-Norm Regularization

The swift advancement of convolutional neural networks (CNNs) in numerous real-world utilizations urges an elevation in computational cost along with the size of the model. In this context, many researchers steered their focus to eradicate these specific issues by compressing the original CNN models by pruning weights and filters, respectively. As filter pruning has an upper hand over the weight pruning method because filter pruning methods don’t impact sparse connectivity patterns. In this work, we suggested a Bayesian Convolutional Neural Network (BayesCNN) with Variational Inference, which prefaces probability distribution over weights. For the pruning task of Bayesian CNN, we utilized a combined version of L1-norm with capped L1-norm to help epitomize the amount of information that can be extracted through filter and control regularization. In this formation, we pruned unimportant filters directly without any test accuracy loss and achieved a slimmer model with comparative accuracy. The whole process of pruning is iterative and to validate the performance of our proposed work, we utilized several different CNN architectures on the standard classification dataset available. We have compared our results with non-Bayesian CNN models particularly, datasets such as CIFAR-10 on VGG-16, and pruned 75.8% parameters with float-point-operations (FLOPs) reduction of 51.3% without loss of accuracy and has achieved advancement in state-of-art.

Where to model the epistemic uncertainty of Bayesian convolutional neural networks for classification

Modeling the epistemic uncertainty, Bayesian convolutional neural networks (Bayesian-CNNs) place a probability distribution on the kernel of convolutional neural networks (CNNs) to overcome problems of over-fitting and incapability of quantifying the prediction confidence. However, compared with CNNs with point estimates, Bayesian-CNNs have a limited improvement over classification performance. Some experiments show that the closer to the input layer, the larger the variances of the parameters in those layers of Bayesian-CNNs, which means the parameters of the low-level layers are not well-trained. Therefore, it is possibly inappropriate to model the epistemic uncertainty of the parameters in the layers close to the input. In this paper, the question of “where to model the epistemic uncertainty of Bayesian-CNNs” is studied by analyzing the performances by putting randomness over different convolutional groups. For this unique structure by combining certain and uncertain layers, a novel objective function is proposed which consists of KL loss for the uncertain parameters and cross-entropy loss for certain parameters. For the special objective function, a training scheme that updates these two kinds of parameters alternately is proposed. Partial-Bayesian-CNNs (P-Bayesian-CNNs) that model the epistemic uncertainty over the parameters of the last convolutional group are recommended because they bring the highest classification accuracy gain according to the experimental analysis. Compared to the traditional Bayesian-CNNs, P-Bayesian-CNNs increase the accuracy by 3.8% and 3.7% on CIFAR-10 and RAF-DB respectively. Besides, the experimental results by taking Res2Net and Xception as backbones also show performance improvement, which verifies the scalability of the P-Bayesian-CNNs.

BPMB: BayesCNNs with perturbed multi-branch structure for robust facial expression recognition

Wild Facial Expression Recognition (FER) task has been a long-standing challenge due to the various forms of uncertainty exist in expression data. When expression data is fed into a convolutional neural network (CNN), the model's estimated parameters also become uncertain. This uncertainty gives rise to concerns regarding the reliability of the recognition results. To quantify these uncertainties and achieve robust performance in the presence of noisy data, this paper introduces a novel model for Wild Facial Expression Recognition: the Bayesian Convolutional Neural Network with Perturbed Multi-Branch Structure (BPMB). This model aims to address uncertainty issues, enabling the network's decisions to become more deterministic with increasing training accuracy. Specifically, BPMB incorporates variational inference (VI) to introduce a probability distribution for the weights. A variational approximation to the true posterior is derived using Bayes by Backprop, involving two convolution operations: one for classification and another for quantifying uncertainty. Furthermore, an exploration is conducted into a lightweight multi-branch structure that leverages Dropout as a random generator to introduce perturbations during the training process, enhancing the model's robustness while extracting deep features. Extensive experiments validate the superiority of the proposed BPMB algorithm over the majority of existing mainstream algorithms on three widely utilized wild datasets.

Uncertainty quantification and propagation in lithium-ion battery electrodes using bayesian convolutional neural networks

The complex nature of manufacturing processes stipulates electrodes to possess high variability with increased heterogeneity during production. X-ray computed tomography imaging has proved to be critical in visualizing the complicated stochastic particle distribution of as-manufactured electrodes in lithium-ion batteries. However, accurate prediction of their electrochemical performance necessitates precise evaluation of kinetic and transport properties from real electrodes. Image segmentation that characterizes voxels to particle/pore phase is often meticulous and fraught with subjectivity owing to a myriad of unconstrained choices and filter algorithms. We utilize a Bayesian convolutional neural network to tackle segmentation subjectivity and quantify its pertinent uncertainties. Otsu inter-variance and Blind/Referenceless Imaging Spatial Quality Evaluator are used to assess the relative image quality of grayscale tomograms, thus evaluating the uncertainty in the derived microstructural attributes. We analyze how image uncertainty is correlated with the uncertainties and magnitude of kinetic and transport properties of an electrode, further identifying pathways of uncertainty propagation within microstructural attributes. The coupled effect of spatial heterogeneity and microstructural anisotropy on the uncertainty quantification of transport parameters is also understood. This work demonstrates a novel methodology to extract microstructural descriptors from real electrode images through quantification of associated uncertainties and discerning the relative strength of their propagation, thus facilitating feedback to manufacturing processes from accurate image based electrochemical simulations.

Gaussian mixture models for training Bayesian convolutional neural networks

Gaussian mixture models for training Bayesian convolutional neural networks

A Bayesian CNN-based fusion framework of sensor fault diagnosis

Sensors equipped on the high-speed train provide large amounts of data which contributes to its state monitoring. However, it is challenging to distinguish whether the fault originates from the mechanical component or the sensors themselves. The main difficulties lie in the biased amount of normal and fault data as well as the deficiency of multi-source data’s inherent correlation. In this paper, we propose a Bayesian convolutional neural networks (CNN)-based fusion framework to enhance the ability to identify sensor errors. The framework utilizes wavelet time–frequency maps to extract abnormal features, employs a Bayesian CNN to obtain spatial features from a single sensor, integrates multi-source features via bidirectional long short-term memory network and enhances the acquired spatial and temporal features using an attention mechanism. The enhanced information finally generated leads to precise identification of the sensor faults. The proposed feature-level fusion framework and the associated attention mechanism facilitate discovering the inherent correlation and filtering of irrelevant information. Results indicate that our proposed method achieves 95.4% in terms of accuracy, which outperforms methods relying on feature extraction with single-source sensors by 7.8%.

Evaluating the influence of road construction on landslide susceptibility in Saudi Arabia's mountainous terrain: a Bayesian-optimised deep learning approach with attention mechanism and sensitivity analysis.

In the mountainous region of Asir region of Saudi Arabia, road construction activities are closely associated with frequent landslides, posing significant risks to both human life and infrastructural development. This highlights an urgent need for a highly accurate landslide susceptibility map to guide future development and risk mitigation strategies. Therefore, this study aims to (1) develop robust well-optimised deep learning (DL) models for predicting landslide susceptibility and (2) conduct a comprehensive sensitivity analysis to quantify the impact of each parameter influencing landslides. To achieve these aims, three advanced DL models-Deep Neural Networks (DNN), Convolutional Neural Networks (CNN), and Bayesian-optimised CNN with an attention mechanism-were rigorously trained and validated. Model validation included eight matrices, calibration curves, and Receiver Operating Characteristic (ROC) and Precision-Recall curves. Multicollinearity was examined using Variance Inflation Factor (VIF) to ensure variable independence. Additionally, sensitivity analysis was used to interpret the models and explore the influence of parameters on landslide. Results showed that road networks significantly influenced the areas identified as high-risk zones. Specifically, in the 1-km buffer around roadways, CNN_AM identified 10.42% of the area as 'Very High' susceptibility-more than double the 4.04% indicated by DNN. In the extended 2-km buffer zone around roadways, Bayesian CNN_AM continued to flag a larger area as Very High risk (7.46%), in contrast to DNN's 3.07%. In performance metrics, CNN_AM outshined DNN and regular CNN models, achieving near-perfect scores in Area Under the Curve (AUC), precision-recall, and overall accuracy. Sensitivity analysis highlighted 'Soil Texture', 'Geology', 'Distance to Road', and 'Slope' as crucial for landslide prediction. This research offers a robust, high-accuracy model that emphasises the role of road networks in landslide susceptibility, thereby providing valuable insights for planners and policymakers to proactively mitigate landslide risks in vulnerable zones near existing and future road infrastructure.

A Bayesian deep learning framework for reliable fault diagnosis in wind turbine gearboxes under various operating conditions

Vibration-based fault diagnostics combined with deep learning approaches has promising applications in detecting and diagnosing faults in wind turbine gearboxes. Specifically when time series vibration data is transformed to a 2-dimensional cyclic spectral coherence maps, the accuracy of deep neural networks in classifying faults increases. Nevertheless, standard deep learning techniques are vulnerable to inaccurate predictions when tested with new data originating from unseen faults or unusual operating conditions. To address some of these shortcomings in the context of wind turbine gearboxes, this paper investigates fault diagnostics using Bayesian convolutional neural network which provide accurate results with uncertainty bounds reducing wrong overconfident classifications. The performance of Bayesian and standard neural networks is compared using a simulation-based dataset of acceleration signals generated from a multibody dynamic model of a 5 MW wind turbine. The framework proposed in this paper has relevance to fault detection and diagnosis in other rotating machinery applications.

Medicine-Shelf matching strategy based on Bayesian convolutional neural network with fuzzy analytic hierarchy process

In pharmaceutical warehousing operations, a scientific and reasonable medicine and shelf matching strategy can improve medicine shelving efficiency and manual work efficiency. However, the traditional matching strategy has the problems of static matching and low matching efficiency, so this paper proposes the matching algorithm for drugs and shelves based on the fuzzy analytic hierarchy process and Bayesian convolutional neural network (FAHP-BCNN). First, we propose a drug-shelf matching degree model and discuss the influence of the dynamic matching process on the matching results by studying two parts: the attribute matching degree and the dynamic matching influence degree. Secondly, this paper quantitatively assessed the importance of the two matches by means of the fuzzy analytic hierarchy process. Finally, we mapped the massive matching information onto Bayesian convolutional neural network nodes, constructed a dynamic matching network model, and obtained competitive matching strategies and results. The experimental results show that the FAHP-BCNN algorithm exhibits better matching results in all three scenarios with different quantity ratios of drugs and shelf matching. Compared with the fixed cargo matching strategy of the ABC classification method, the FAHP-BCNN algorithm shows excellent performance in both the manual walking distance index and fatigue index. In summary, the drug-shelf matching algorithm based on FAHP-BCNN is effective and can provide theoretical support for pharmaceutical warehousing enterprises to perform drug-shelf matching.

A feature map of frequency response functions based model updating method using the Bayesian convolutional neural network

Combined with the application of deep learning is a hot topic in the current research of finite element (FE) model updating. In this paper, A feature map of frequency response functions (FMFRF) based model updating method using the Bayesian convolutional neural network (BCNN) is proposed. This proposed method is based on frequency response functions (FRFs), which eliminates the steps of modal identification and modal matching and can adjust the structural parameters and damping parameters of the model at the same time, thus improving efficiency. The FRFs of multiple sensors are combined and transformed into the feature map, which is used as the input to the BCNN. The output of BCNN is the vector composed of uncertain model parameters. The FMFRF method solves the model updating problems as positive problems with the help of BCNN, and can accurately build the complex mapping between the FRFs and the model parameters. The BCNN introduces probability distributions over the weights, which helps avoid overfitting when training on small datasets and achieves high accuracy of the network. The benchmark multi-plate structure is used as an example to verify the validity and accuracy of the FMFRF method, and the correlation and sensitivity of the model parameters to the feature maps of FRFs are systematically analyzed. Finally, the robustness of the model updating results is investigated, and it proves that the FMFRF method shows good performance.

A Phenology-guided Bayesian-CNN (PB-CNN) framework for soybean yield estimation and uncertainty analysis

Large-scale crop yield estimation is important for understanding the response of agriculture production to environmental forces and management practices, and plays a critical role in insurance designing, trade decision making, and economic planning. The empirical models (e.g., deep learning models) have been increasingly utilized for estimating crop yields with the ability to take into account a range of yield predictors and complex modeling relationships. Yet empirical estimation of crop yields still faces important challenges, particularly in accommodating spatio-temporal crop phenological development patterns as well as tackling the heterogeneity of a diversity of yield predictors. The different types of uncertainties associated with empirical yield estimations have seldom been explored. The objective of this study is to develop a Phenology-guided Bayesian-Convolutional Neural Network (PB-CNN) framework for county-level crop yield estimation and uncertainty quantification, with soybean in the US Corn Belt as a case study. The PB-CNN framework comprises three key components: Phenology Imagery construction, multi-stream Bayesian-CNN modeling, as well as feature importance (i.e., yield predictor and phenological stage) and predictive uncertainty analysis (i.e., aleatoric and epistemic uncertainty). With the innovative integration of critical crop phenological stages in modeling the crop yield response to a heterogeneous set of yield predictors (i.e., satellite-based, heat-related, water-related, and soil predictors) as well as the associated uncertainties, the developed PB-CNN framework outperforms three advanced benchmark models, achieving an average RMSE of 4.622 bu/ac, an average R2 of 0.709, and an average bias of −2.057 bu/ac in estimating the county-level soybean yield of the US Corn Belt in testing years 2014–2018. Among the yield predictor groups, the satellite-based predictor group is the most critical in soybean yield estimation, followed by the water- and heat-related predictor groups. Throughout the growing season, the soybean blooming to dropping leaves phenological stages play a more crucial role in modeling the soybean yield. The soil predictor group as well as the early growing stages can improve the model estimation accuracy yet potentially brings more uncertainties into the yield estimation. The further uncertainty disentanglement indicates that the dominant uncertainty in yield estimation is the aleatoric uncertainty, mainly stemming from the fluctuations and variations inherent in the modeling input observations. The PB-CNN framework largely enhances our understanding of the complex soybean yield response to varying environmental conditions across crop phenological stages as well as associated uncertainties for more sustainable agricultural development.

Bayesian Convolutional Neural Networks in Medical Imaging Classification: A Promising Solution for Deep Learning Limits in Data Scarcity Scenarios

Deep neural networks (DNNs) have already impacted the field of medicine in data analysis, classification, and image processing. Unfortunately, their performance is drastically reduced when datasets are scarce in nature (e.g., rare diseases or early-research data). In such scenarios, DNNs display poor capacity for generalization and often lead to highly biased estimates and silent failures. Moreover, deterministic systems cannot provide epistemic uncertainty, a key component to asserting the model’s reliability. In this work, we developed a probabilistic system for classification as a framework for addressing the aforementioned criticalities. Specifically, we implemented a Bayesian convolutional neural network (BCNN) for the classification of cardiac amyloidosis (CA) subtypes. We prepared four different CNNs: base-deterministic, dropout-deterministic, dropout-Bayesian, and Bayesian. We then trained them on a dataset of 1107 PET images from 47 CA and control patients (data scarcity scenario). The Bayesian model achieved performances (78.28 (1.99) % test accuracy) comparable to the base-deterministic, dropout-deterministic, and dropout-Bayesian ones, while showing strongly increased “Out of Distribution” input detection (validation-test accuracy mismatch reduction). Additionally, both the dropout-Bayesian and the Bayesian models enriched the classification through confidence estimates, while reducing the criticalities of the dropout-deterministic and base-deterministic approaches. This in turn increased the model’s reliability, also providing much needed insights into the network’s estimates. The obtained results suggest that a Bayesian CNN can be a promising solution for addressing the challenges posed by data scarcity in medical imaging classification tasks.

Automatic identification of crystal structures and interfaces via artificial-intelligence-based electron microscopy

Characterizing crystal structures and interfaces down to the atomic level is an important step for designing advanced materials. Modern electron microscopy routinely achieves atomic resolution and is capable to resolve complex arrangements of atoms with picometer precision. Here, we present AI-STEM, an automatic, artificial-intelligence based method, for accurately identifying key characteristics from atomic-resolution scanning transmission electron microscopy (STEM) images of polycrystalline materials. The method is based on a Bayesian convolutional neural network (BNN) that is trained only on simulated images. AI-STEM automatically and accurately identifies crystal structure, lattice orientation, and location of interface regions in synthetic and experimental images. The model is trained on cubic and hexagonal crystal structures, yielding classifications and uncertainty estimates, while no explicit information on structural patterns at the interfaces is included during training. This work combines principles from probabilistic modeling, deep learning, and information theory, enabling automatic analysis of experimental, atomic-resolution images.

Identification of Underground Artificial Cavities Based on the Bayesian Convolutional Neural Network.

The development of underground artificial cavities plays an important role in the exploitation of urban spatial resources. As the rapidly growing number of underground artificial cavities with different depths and scales increases, the detection and identification of underground artificial cavities has become a key issue in underground engineering studies. Geophysical techniques have been widely used for the construction, management, and maintenance of underground artificial cavities. In this study, we present two identification methods for underground artificial cavities. Apparent resistivity imaging is the most popular technique for quickly identifying underground artificial cavities, using the forward simulation results of a three-dimensional earth model and comparing these with the preset positions of artificial cavities, as demonstrated in the experiment. To further improve the efficiency of underground artificial cavity identification, we developed a fast recognition approach for underground artificial cavities based on the Bayesian convolutional neural network (BCNN). Compared to a traditional convolutional neural network, the performance of the BCNN method was greatly improved in terms of the classification accuracy and efficiency of identifying underground artificial cavities with apparent resistivity image datasets.

Monte Carlo DropBlock for modeling uncertainty in object detection

With the advancements made in deep learning, computer vision problems have seen a great improvement in performance. However, in many real-world applications such as autonomous driving vehicles, the risk associated with incorrect predictions of objects or segmentation of images is very high. Standard deep learning models for object detection and segmentation such as YOLO models are often overconfident in their predictions and do not take into account the uncertainty in predictions on out-of-distribution data. In this work, we propose an efficient and effective approach, Monte-Carlo DropBlock (MC-DropBlock), to model uncertainty in YOLO and convolutional vision Transformers for object detection. The proposed approach applies drop-block during training time and testing time on the convolutional layer of the deep learning models such as YOLO and convolutional transformer. We theoretically show that this leads to a Bayesian convolutional neural network capable of capturing the epistemic uncertainty in the model. Additionally, we capture the aleatoric uncertainty in the data using a Gaussian likelihood. We demonstrate the effectiveness of the proposed approach on modeling uncertainty in object detection and segmentation tasks using out-of-distribution experiments. Experimental results show that MC-DropBlock improves the generalization, calibration, and uncertainty modeling capabilities of YOLO models and convolutional Transformer models for object detection and segmentation.

Optimized Bayesian convolutional neural networks for invasive breast cancer diagnosis system

Deep learning (DL) has depicted unprecedented results in the diagnosis of invasive ductal carcinoma (IDC). However, most DL methods are not able to infer the uncertainty in their predictions, and are often too confident which may cause undesirable consequences. The ability of DL models to express their uncertainty in their predictions is particularly important in diagnosing diseases. Therefore, this paper proposes an uncertainty-aware approach called optimized Bayesian convolutional neural network (OBCNN) for the automated detection of IDC from histopathology images and is capable of estimating and inferring the uncertainty in its predictions. The proposed OBCNN employs an approximate Bayesian version of a pre-trained convolutional neural network (CNN) model named ResNet101V2 that is fine-tuned to the histopathology images of IDC. The Bayesian approximation is performed by adding Monte Carlo dropout (MC-dropout) to ResNet101V2 architecture. Due to the effect of MC-dropout on the obtained posterior predictive distribution (PPD), the value of MC-dropout should be chosen carefully because if the MC-dropout value is too large, the predictive distribution (PD) will be very diverse. Whereas if the MC-dropout value is very small, the PD will be very similar. Therefore, an optimization algorithm known as the slime mould algorithm is utilized to set the optimal value of the MC-dropout. During inference, the proposed OBCNN runs for T forward passes to configure the PPD. The mean, standard deviation (SD) and entropy are then calculated over the obtained PD to estimate the predictive uncertainty (PU) of the OBCNN. The proposed OBCNN achieved an accuracy of 93.83%, a precision of 96.14%, a G-mean of 93.04%, False Negative Rate of 4.72%, and False Positive Rate of 9.96 %. The proposed OBCNN has also been compared with recent related work, the comparison’s results demonstrated that OBCNN performed better in the diagnosis of IDC.

Approximating the uncertainty of deep learning reconstruction predictions in single-pixel imaging

Single-pixel imaging (SPI) has the advantages of high-speed acquisition over a broad wavelength range and system compactness. Deep learning (DL) is a powerful tool that can achieve higher image quality than conventional reconstruction approaches. Here, we propose a Bayesian convolutional neural network (BCNN) to approximate the uncertainty of the DL predictions in SPI. Each pixel in the predicted image represents a probability distribution rather than an image intensity value, indicating the uncertainty of the prediction. We show that the BCNN uncertainty predictions are correlated to the reconstruction errors. When the BCNN is trained and used in practical applications where the ground truths are unknown, the level of the predicted uncertainty can help to determine whether system, data, or network adjustments are needed. Overall, the proposed BCNN can provide a reliable tool to indicate the confidence levels of DL predictions as well as the quality of the model and dataset for many applications of SPI.