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A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges

Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U Rajendra Acharya, Vladimir Makarenkov, Saeid Nahavandi

arXiv:2011.06225v4cs.LGcs.AIcs.CV

TL;DR

Deep learning models often produce overconfident predictions, making reliable uncertainty quantification important for real-world decisions. This review synthesizes UQ methods, applications, reinforcement-learning uses, research gaps, and future directions, providing a comparative overview of current approaches.

  • Problem

    Deep neural networks can achieve competitive accuracy while producing poorly quantified, overconfident uncertainty estimates that are difficult to evaluate reliably.

  • Method

    The paper reviews and comparatively analyzes state-of-the-art uncertainty-quantification approaches across machine learning, deep learning, applications, and reinforcement learning.

  • Results

    The review provides a comprehensive description and comparative analysis of current UQ approaches, applications, research gaps, and future directions.

  • Takeaways & Limitations

    UQ research spans diverse applications, while self-supervised learning and attention mechanisms remain identified gaps for further investigation.

  • Takeaways & Limitations

    Comparing ensembling methods remains challenging because performance metrics vary across models and datasets and lack interpretable baselines.

Abstract

from arXiv · show

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.

1 INTRODUCTION

Uncertainty quantification is important for trustworthy AI decision making because deep-learning predictions can reflect noisy data, incorrect inference, and incomplete knowledge. This review examines UQ methods in machine and deep learning, their applications, research gaps, and future directions.

  • Motivation: Trustworthy AI systems should represent uncertainty because model predictions are vulnerable to noise, wrong inference, and inherent inductive assumptions.Evaluating AI-system efficacy before deployment is described as important for reliable use.
  • Uncertainty sources: Aleatoric uncertainty is irreducible uncertainty inherent in the data distribution, whereas epistemic uncertainty arises from inadequate knowledge and data.Aleatoric uncertainty is also called data uncertainty; epistemic uncertainty is also called knowledge uncertainty.
  • Motivation: Uncertainty must be quantified across deep-learning workflows, including training-data selection, data completeness and accuracy, and model limitations and performance bounds.These sources arise during the learning process as parameters are optimized for satisfactory performance.
  • Review contributions: The paper presents what it identifies as the first comprehensive review of UQ methods used in machine and deep learning.It also reviews newly proposed UQ methods and aims to cover relevant articles from journals, conferences, and high-quality preprints.
  • Review contributions: The review lists important UQ applications, identifies research gaps, and discusses future research directions.These contributions extend beyond method coverage to applications and the field’s remaining challenges.

2 PRELIMINARIES

This section introduces feed-forward neural-network modeling and Bayesian formulations for deep-learning uncertainty. It distinguishes epistemic and aleatoric uncertainty and describes variational inference for approximating Bayesian predictions.

  • Neural-network structure: A feed-forward network transforms inputs through a linear map, bias, nonlinear activation, and subsequent linear mapping to produce outputs.The hidden-layer activation may use functions such as ReLU, and multiple layers can extend the single-hidden-layer structure.
  • Prediction and losses: Classification uses softmax-normalized scores and softmax loss, whereas regression can use Euclidean loss.The softmax computes label probabilities from the model output.
  • Uncertainty types: Predictive uncertainty comprises epistemic uncertainty from the model and aleatoric uncertainty from the data.Aleatoric uncertainty is categorized as homoscedastic or heteroscedastic.
  • Bayesian modeling: Bayesian modeling represents epistemic uncertainty with a distribution over model parameters, defines likelihoods, and derives a posterior using Bayes’ theorem.Softmax likelihood is used for classification, while Gaussian likelihood can be assumed for regression.
  • Variational inference: Because the posterior is analytically intractable, variational inference approximates it with qθ(ω) by minimizing KL divergence or maximizing the ELBO.Dropout VI is presented as a common approximation for inference in complex models.
  • Data-dependent uncertainty: Data-dependent uncertainty models precision as a function of the input by combining predictive mean and model-precision functions in the likelihood.The predictive variance is then obtained from this formulation.

3 UNCERTAINTY QUANTIFICATION USING BAYESIAN TECHNIQUES · 3.1 Bayesian Deep Learning/Bayesian Neural Networks

Bayesian deep learning and Bayesian neural networks address standard deep learning’s inability to report prediction reliability by interpreting model parameters, while remaining robust to overfitting and usable with small or large datasets.

  • 3.1 Bayesian Deep Learning/Bayesian Neural Networks: Bayesian deep learning and Bayesian neural networks interpret model parameters to provide information about prediction reliability.They are presented as an approach to address a limitation of standard deep learning methods.
  • 3.1 Bayesian Deep Learning/Bayesian Neural Networks: BNNs and BDL are robust to overfitting and can be trained on both small and big datasets.The passage identifies dataset size flexibility alongside robustness to overfitting.

3.2 Monte Carlo (MC) dropout

MC dropout approximates posterior inference by using dropout as a regularizer to estimate predictive uncertainty, avoiding the slow and computationally expensive integration of standard Monte Carlo methods into deep architectures. Studies apply it across uncertainty estimation tasks and compare it with alternative Bayesian and ensemble approaches.

  • Method: MC dropout uses dropout as a regularization term to compute prediction uncertainty while approximating otherwise difficult posterior inference.Standard Monte Carlo is described as slow and computationally expensive when integrated into deep architectures.
  • Method: Dropout samples binary variables for inputs and hidden units in each layer, with layer-specific probability p_i, and reuses the sampled values during backpropagation.The output layer is excluded from dropout, and units with sampled value 0 are dropped for a given input.
  • Applications: MC dropout estimates epistemic and aleatoric uncertainty in medical image segmentation by sampling output-segmentation distributions and augmenting test images to estimate transformation uncertainty.Wang et al. analyzed uncertainty at both pixel and structure levels using deep CNN-based segmentation.
  • Applications: Element-wise and spatial Bernoulli dropout have been used to estimate model uncertainty for end-to-end autonomous vehicle control.Sampling weights with Bernoulli or Gaussian distributions was reported as potentially more accurate than sampling units, although either approach may depict uncertainty.
  • Comparative studies: MC dropout has been compared with mean-field Gaussian VI and BBB, while mean-field Gaussian VI was unable to approximate deep-BNN posteriors adequately for uncertainty estimation.Both MC dropout and mean-field Gaussian VI could express uncertainty well in shallow Bayesian neural networks.

3.3 Markov chain Monte Carlo (MCMC)

MCMC approximates posterior inference by repeatedly applying stochastic transitions from an initial random draw, with the resulting distribution converging toward the exact posterior. Its unknown convergence requirements and long runtime motivate variants such as SG-MCMC and accelerated approaches, alongside applications to predictive distributions and generative models.

  • Core mechanism: MCMC begins with a random draw from q(z0) or q(z0|x) and repeatedly applies a stochastic transition to approximate inference.The transition is applied for T iterations.
  • Core mechanism: After T repetitions, the random outcome converges in distribution to the exact posterior, and MCMC has been used to approximate movie-rating predictive distributions.The sufficient number of iterations is unknown, and convergence requires substantial time.
  • Extensions: Several approaches address conventional MCMC limitations, including auxiliary-variable expansions that interpret stochastic Markov chains as variational approximations.Salimans et al. expanded the sampling space into auxiliary random variables.
  • Extensions: SG-MCMC trains DNNs using gradient estimates from small mini-batches and can converge to the true posterior by decreasing step sizes.Amortized inference was combined with SG-MCMC to improve generalization ability, while accelerated SG-MCMC targeted faster computation.
  • Applications: MCMC has also been integrated with generative methods, including GAN-based stochastic object models and a VAE-MCMC visual tracking system.These applications used MCMC to approximate an ideal observer or support visual tracking.

3.4 Variational Inference (VI)

Variational inference (VI) approximates posterior distributions over Bayesian neural network weights by framing Bayesian inference as an optimization problem trained with stochastic gradient descent. The reviewed methods range from factorized Gaussian approximations to approaches modeling parameter correlations, model and parameter uncertainty, and spatial–temporal posterior distributions.

  • 3.4 Variational Inference (VI): VI approximates posterior distributions over Bayesian neural network weights by converting Bayesian inference into an optimization problem trained with stochastic gradient descent.The loss formulation is used to approximate the posterior distribution over network weights.
  • 3.4 Variational Inference (VI): Variational distributions have progressed from diagonal-covariance Gaussian products to traditional covariance matrices that allow network parameters to correlate.The diagonal-covariance formulation represents posterior uncertainty for each network layer.
  • 3.4 Variational Inference (VI): MOPED combines deterministic weights derived through transfer learning and empirical Bayes with variational inference.The passage introduces MOPED as an approach inspired by transfer learning and empirical Bayes.
  • 3.4 Variational Inference (VI): Stochastic variational inference methods estimate weight posteriors while extending Bayesian neural networks to jointly model model and parameter uncertainties.One approach introduces latent binary variables to include or exclude selected model weights.
  • 3.4 Variational Inference (VI): Variational inference has also been integrated into spatial–temporal neural networks to approximate posterior parameter distributions and estimate probabilities.The passage reports this integration as a method for posterior approximation in spatial–temporal neural networks.

3.5 Bayesian Active Learning (BAL)

Bayesian active learning integrates Bayesian deep-learning uncertainty estimates with acquisition functions to select informative unlabeled samples, addressing active learning’s difficulty with high-dimensional data. Reviewed approaches include disagreement-based batch selection, MC dropout, Bayesian batch inference, crowdsourcing, and generative sampling.

  • Challenges and motivation: Active learning queries an oracle for unlabeled samples, but selecting the right acquisition function and scaling to high-dimensional data remain central challenges.Bayesian approaches represent uncertainty within deep-learning models and use acquisition functions to probe uncertain samples.
  • Bayesian acquisition methods: DBAL combines active learning with Bayesian deep learning for high-dimensional image data, selecting the top n samples by BALD disagreement scores.MOPED priors use BALD for uncertainty evaluation, while MC dropout estimates model uncertainty; BatchBALD later applies greedy batch selection.
  • Application-specific methods: MC dropout and Bayesian architectures support uncertainty-guided selection in human action recognition and biomedical image segmentation.ActiveHARNet links Bayesian neural networks with Gaussian processes, while biomedical segmentation uses the posterior-probability standard deviation across MC samples.
  • Scalable and crowdsourced active learning: Bayesian batch active learning selects sample batches at each iteration to perform posterior inference over model parameters for large-scale problems.Bayesian active user training addresses complex, high-dimensional classification and models annotator confusion-matrix uncertainty.
  • Generative active learning: Generative Bayesian active-learning frameworks combine uncertainty-based sample selection with deep generative models for semi-supervised learning and image classification.BGADL uses DBAL to select informative samples and VAE-ACGAN to generate new samples from them.

3.6 Bayes by Backprop (BBB)

Bayes by Backprop (BBB) quantifies neural-network weight uncertainty by learning a probability distribution while minimizing variational free energy. Extensions apply BBB to Bayesian recurrent networks and uncertainty-guided continual learning, while MC dropout and BBB perform similarly for cardiac MRI segmentation.

  • 3.6 Bayes by Backprop (BBB): BBB learns a distribution over neural-network weights to quantify uncertainty and minimizes the variational free energy, or expected lower bound of marginal likelihood.The algorithm uses a cost function based on compression cost minimization.
  • 3.6 Bayes by Backprop (BBB): BBB uses unbiased gradient estimates of its cost function to learn weight distributions in neural networks.Fortunato et al. adapted truncated back-propagation through time to develop Bayesian recurrent neural networks using BBB.
  • 3.6 Bayes by Backprop (BBB): UCB uses posterior predictive uncertainty to modify important parameters through hard-threshold and soft mechanisms during Bayesian continual learning.The approach aims to learn new tasks while retaining previously acquired knowledge.
  • 3.6 Bayes by Backprop (BBB): MC dropout and BBB demonstrated almost similar performance for cardiac MRI medical image segmentation on a U-Net model.Ng et al. compared the two uncertainty methods in a medical image segmentation task.

3.7 Variational Autoencoders

Variational autoencoders model high-dimensional data distributions through latent variables and variational inference, supporting uncertainty quantification across hashing, inverse problems, medical imaging, simulations, and sequence modeling. Because standard VAEs encode finite-dimensional priors, πVAE extends them as a stochastic process that learns distributions over functions.

  • VAE foundations: VAEs map high-dimensional inputs to low-dimensional latent variables and decode them back to reconstruct the original samples under a prior distribution.They model posterior distributions for high-dimensional data representations.
  • VAE foundations: Variational inference models the evidence lower bound, with qφ(z|x) and pθ(x|z) serving as encoder and decoder models.φ and θ denote the encoder and decoder parameters, respectively.
  • Applications: A discrete VAE with Bernoulli latent variables and pairwise supervised hashing maximizes the ELBO with weighted KL regularization to learn informative binary codes.Its pairwise loss rewards within-class similarity and between-class dissimilarity.
  • Applications: VAE-based uncertainty quantification has been applied to linear inverse problems, magnetic resonance image recovery, reservoir simulations, cosmic microwave background restoration, and action sequences.Examples include mean-field Gaussian posteriors, VAE-GAN recovery, variational U-Nets, Cosmo VAE, and action point process VAE.
  • Limitations and extensions: Because standard VAEs are not stochastic processes, they are limited to finite-dimensional priors; πVAE addresses this by learning distributions over functions.πVAE transforms locations into a high-dimensional feature space and uses a linear mapping to link features to outputs.

4 OTHER METHODS

This section surveys additional uncertainty-quantification methods for deep learning, including deep Gaussian processes, stochastic embeddings, perturbation-based methods, Gaussian models, stochastic normalization, and Laplace approximations. These approaches model uncertainty through hierarchical Gaussian processes, posterior approximations, sampling, weight perturbations, or probabilistic output distributions.

  • Deep Gaussian processes: Deep Gaussian processes extend Gaussian processes into multi-layer hierarchies and can accurately model uncertainty in decision-making models.Gaussian processes are non-parametric Bayesian models that encode sample similarity with kernel functions and represent latent-variable distributions as Gaussian distributions.
  • Posterior approximation: Variational approximations use inducing samples and approximated distributions, while SGHMC has been applied to deep Gaussian processes to approximate posterior distributions.The passage defines Z as the location of inducing samples and q(fx) as the variational approximation to the distribution of fx.
  • Stochastic embeddings: Hedged instance embedding models ambiguity by extending matching probabilities to stochastic embeddings and representing uncertainty with a mixture of C Gaussians.Monte Carlo sampling is used to approximate the stochastic embedding.
  • Weight perturbation: Flipout samples pseudo-independent weight perturbations for each input, reducing gradient variance and training time under multiplicative Gaussian perturbations.It addresses the high variance caused by sharing one perturbation across all samples in a mini-batch.
  • Gaussian predictive models: Probabilistic Gaussian models estimate uncertainty for adversarial examples and object-detection localization by modeling bounding-box coordinates with means and variances.A hybrid GP-DNN addresses adversarial-example uncertainty, while a single Gaussian model predicts YOLOv3 bounding-box uncertainty.
  • Stochastic normalization: Stochastic normalization layers provide approximate uncertainty inference, defend against adversarial attacks, and support exploration in reinforcement-learning tasks.The stochastic batch-normalization approach was proposed because exact inference was computationally inefficient.

5 UNCERTAINTY QUANTIFICATION IN REINFORCEMENT LEARNING

Uncertainty quantification is important for decision performance in reinforcement learning, where Bayesian methods have been widely investigated. Research includes Bayes-Adaptive Markov Decision Processes, Bayesian Policy Optimization for partially observable settings, and uncertainty propagation through Bellman equations.

  • Uncertainty plays a key role in reinforcement-learning decision performance, motivating broad investigation of different uncertainty-quantification methods.
  • Lee et al. formulated model uncertainty as a Bayes-Adaptive Markov Decision Process defined over observable states, latent variables, actions, transitions, rewards, initial beliefs, and discounting.
  • Bayesian Policy Optimization applies to partially observable Markov decision processes as a Bayes filter for computing beliefs over hidden states.
  • The uncertainty Bellman equation quantifies uncertainty by propagating variance relationships associated with Bayesian posterior distributions.
  • Prior reinforcement-learning studies have used Bayesian approaches to handle parameter uncertainty, alongside uncertainty-aware models for controlling mobile robots.

6 ENSEMBLE TECHNIQUES

Ensemble techniques address overconfident neural-network predictions by improving predictive performance and estimating model uncertainty. The section describes uncertainty decomposition, Bayesian interpretations of deep ensembles, and challenges in comparing ensemble methods.

  • Motivation: Neural networks can achieve competitive accuracy while producing poor uncertainty estimates and harmful overconfident predictions, motivating proper uncertainty quantification.Evaluating predictive uncertainty is challenging because empirical uncertainty estimates are generally unavailable.
  • Uncertainty decomposition: Ensembles estimate total uncertainty through predictive entropy and knowledge uncertainty through model disagreement, with mutual information decomposing these components.High predictive entropy indicates uncertainty, while disagreement between models reflects knowledge uncertainty, including in out-of-domain or class-overlap regions.
  • Bayesian interpretation: Wilson and Izmailov reported that deep ensembles can better approximate the Bayesian model average than standard Bayesian methods such as BBB.Their analysis also linked multi-basin marginalization with improved induced correlations, feature generation, structured-data support, and performance over standard training.
  • Challenges and implications: Comparing ensembling methods remains difficult because performance metrics vary across models and datasets and their gains are difficult to interpret.Probability UQ can nevertheless guide model construction by addressing ambiguous DNN generalization behaviors, including random-label fitting, double descent, and overparameterization.
  • Deep ensembles: Deep ensembles provide independent samples from different loss modes and can improve predictions while producing model-uncertainty estimates.They are also described as a powerful fixed-test-time-budget baseline for evaluating other ensembling methods.

7 FURTHER STUDIES OF UQ METHODS

This section surveys additional uncertainty-quantification methods for deep learning, including architecture search, prediction intervals, uncertainty estimation, adversarial detection, physics-informed models, and scalable Bayesian inference. It also identifies ongoing challenges involving convergence, model selection, computational complexity, and limited theoretical foundations.

  • Architecture and prediction-interval methods: NADS searches for suitable distributions of neural architectures and recognizes common blocks across uncertainty-aware architectures to address out-of-distribution errors.The architecture is introduced for cases where training and test data have different distributions.
  • Architecture and prediction-interval methods: SQR estimates conditional quantiles for aleatoric uncertainty, while Orthonormal Certificates estimate epistemic uncertainty and enable well-calibrated prediction intervals.The certificates map training samples to zero, and the resulting quantiles support prediction-interval construction.
  • Applications and empirical findings: Uncertainty-aware methods improved uncertainty estimation, prediction accuracy, certainty estimates, and attention maps correlated with human attention regions across visual question-answering benchmarks.The enhanced attention maps consistently improved different visual question-answering techniques.
  • Applications and empirical findings: Uncertainty modeling was applied to imbalanced classification, where rare-class boundaries are broadened and samples are represented with multivariate Gaussian distributions to improve generalization.The approach addresses concentrated representations and overfitting in rare classes.
  • Additional UQ techniques and challenges: Other approaches include physics-informed latent-variable models, hidden-layer sampling for adversarial detection without additional training, and SLANG for scalable variational inference in large deep models.SLANG uses a stochastic, low-rank, approximate natural-gradient technique to address Gaussian-process approximation complexity.
  • Additional UQ techniques and challenges: Further methods use shrinkage priors for Bayesian neural-network model selection, robust variational-Bayes inference, discriminative jackknife procedures, and analyses of batch-normalization randomness.The review also highlights challenges from node-number selection, computational and theoretical limitations, and the absence of sound underlying theory.

8 APPLICATIONS

This section reviews applications of uncertainty quantification across image processing, computer vision, medical image analysis, natural language processing, and other machine- and deep-learning domains. The surveyed studies show that modeling predictive uncertainty can improve analysis, sampling, calibration, and safety-related decisions.

  • Image Processing and Computer Vision: UQ methods are applied across image processing and computer vision tasks including object detection, semantic segmentation, scene understanding, motion prediction, and recognition.The review introduces these applications before discussing medical image analysis and NLP.
  • Image Processing and Computer Vision: Computer vision systems should quantify predictive uncertainty because incomplete data, sensor noise, and inaccurate mappings can produce harmful misidentifications.The review cites a case in which two African Americans were incorrectly identified as gorillas, leading to racial discrimination.
  • Medical Image Analysis: Proper uncertainty estimation improved medical image analysis, with UMCT outperforming other methods on the same datasets and uncertainty-enhanced prostate cancer segmentation producing better outcomes.These findings support using uncertainty methods to improve medical image analysis performance and segmentation results.
  • Natural Language Processing: NLP applications use UQ to recognize linguistic uncertainty, which is important when languages express uncertainty differently and when classifying clinical reports by disease probability.The reviewed NLP applications include uncertainty in natural-language texts and machine translation.
  • Natural Language Processing: In NLP studies, uncertainty sampling performed best in area under the learning curve, while most diversity-based techniques outperformed random sampling.The passage reports these comparisons using the ALC score.
  • Other Applications: Other UQ applications include Bayesian active learning, flight-trajectory safety assessment, autonomous navigation, and mapping under uncertain obstacle-distance estimates.Bayesian CNN active learning required 35-60% fewer labelled galaxies, while navigation sensors faced incomplete occupancy measurements and transparent surfaces.

9 LITERATURE GAPS AND OPEN ISSUES

The review identifies broad UQ gaps across learning paradigms, model types, and techniques, including limited work on semisupervised, self-supervised, continual, transfer, attention-based, ensemble, and Bayesian optimization methods. It also proposes future directions spanning fusion, decision theories, computer vision, medical imaging, NLP, reinforcement learning, and other domains.

  • Learning paradigms: UQ research is concentrated in supervised and unsupervised learning, leaving semisupervised learning comparatively underexplored.The review identifies this imbalance as an important gap for future work.
  • Model coverage: Most UQ methods target neural and deep learning models, while uncertainty in other machine-learning methods remains insufficiently investigated.The review attributes this focus partly to the strong state-of-the-art performance of deep learning across multiple fields.
  • Methods and decision making: Fusion-based methods and decision-making theories, including three-way decisions and Info-Gap decision theory, show potential for addressing uncertainty but warrant broader use.The review also highlights ensemble methods as effective yet insufficiently used in recent studies.
  • Emerging learning settings: Important open issues include uncertainty in transfer learning, self-supervised learning, attention mechanisms, continual learning, and Bayesian optimization.The review reports few studies in several of these areas and calls for new UQ methods, while uncertainty quantification in Bayesian optimization remains open.
  • Computer vision and image processing: Future computer-vision and image-processing work should simplify UQ integration, address dynamic and multimodal restoration, and combine UQ with advanced inversion approaches.The review also notes that ensemble methods remain important in these applications.
  • Medical image analysis: Medical-image UQ would benefit from larger datasets, closer medical–AI collaboration, specialist review of incorrect predictions, and fusion methods for segmentation uncertainty.The review also recommends improving loss functions beyond standard medical-segmentation losses.

10 CONCLUSION

The conclusion emphasizes uncertainty quantification as central to decision making and increasingly integral to traditional machine learning and deep learning. It summarizes the study’s comprehensive review and comparative analysis of important UQ methods used in these fields.

  • Uncertainty quantification supports decision making and is increasingly used to evaluate uncertainty in real-life applications.
  • The study comprehensively reviews important UQ methods applied in traditional machine learning and deep learning.

TABLE 6 – Continued from previous page

The table surveys UQ methods applied across computer vision and image-processing tasks from 2018 to 2020, spanning perception, prediction, segmentation, restoration, and recognition. It includes Bayesian, dropout, probabilistic, ensemble, and uncertainty-aware approaches across diverse datasets and safety-critical applications.

  • Computer vision and image processing: Several methods explicitly model aleatoric or input-dependent uncertainty, including heteroscedastic dropout, uncertainty-gated propagation, and probabilistic residual learning.The table also reports triplet-loss extensions modeling data uncertainty for each input and local embedding-space noise.
  • Computer vision and image processing: UQ methods covered safety-critical perception tasks including object detection, depth estimation, scene reconstruction, and 3D localization.Examples include KITTI object detection, depth estimation for 3D scene reconstruction, and 3D pedestrian localization.
  • Computer vision and image processing: Applications extend to semantic segmentation, image restoration, optical flow, face recognition, person re-identification, and image-caption retrieval.The table lists land-cover and video segmentation, single-image de-raining, video-based face recognition, person re-identification, and image-caption embedding and retrieval.
  • Computer vision and image processing: The surveyed approaches include Bayesian inference, MC dropout, probabilistic CNNs, Gaussian models, and model averaging.Specific methods include Bayesian inference with MC, MC dropout during training and inference, lightweight probabilistic CNNs, multivariate Gaussian modeling, and posterior model averaging.
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