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Neural Radiance Fields (NeRF) has become a popular framework for learning implicit 3D representations and addressing different tasks such as novel-view synthesis or depth-map estimation. However, in downstream applications where decisions need to be made based on automatic predictions, it is critical to leverage the confidence associated with the model estimations. Whereas uncertainty quantification is a long-standing problem in Machine Learning, it has been largely overlooked in the recent NeRF literature. In this context, we propose Stochastic Neural Radiance Fields (S-NeRF), a generalization of standard NeRF that learns a probability distribution over all the possible radiance fields modeling the scene. This distribution allows to quantify the uncertainty associated with the scene information provided by the model. S-NeRF optimization is posed as a Bayesian learning problem which is efficiently addressed using the Variational Inference framework. Exhaustive experiments over benchmark datasets demonstrate that S-NeRF is able to provide more reliable predictions and confidence values than generic approaches previously proposed for uncertainty estimation in other domains.

Recent multilingual pre-trained language models have achieved remarkable zero-shot performance, where the model is only finetuned on one source language and directly evaluated on target languages. In this work, we propose a self-learning framework that further utilizes unlabeled data of target languages, combined with uncertainty estimation in the process to select high-quality silver labels. Three different uncertainties are adapted and analyzed specifically for the cross lingual transfer: Language Heteroscedastic/Homoscedastic Uncertainty (LEU/LOU), Evidential Uncertainty (EVI). We evaluate our framework with uncertainties on two cross-lingual tasks including Named Entity Recognition (NER) and Natural Language Inference (NLI) covering 40 languages in total, which outperforms the baselines significantly by 10 F1 on average for NER and 2.5 accuracy score for NLI.

We propose a framework for predictive uncertainty quantification of a neural network that replaces the conventional Bayesian notion of weight probability density function (PDF) with a physics based potential field representation of the model weights in a Gaussian reproducing kernel Hilbert space (RKHS) embedding. This allows us to use perturbation theory from quantum physics to formulate a moment decomposition problem over the model weight-output relationship. The extracted moments reveal successive degrees of regularization of the weight potential field around the local neighborhood of the model output. Such localized moments represent well the PDF tails and provide significantly greater accuracy of the model's predictive uncertainty than the central moments characterized by Bayesian and ensemble methods or their variants. We show that this consequently leads to a better ability to detect false model predictions of test data that has undergone a covariate shift away from the training PDF learned by the model. We evaluate our approach against baseline uncertainty quantification methods on several benchmark datasets that are corrupted using common distortion techniques. Our approach provides fast model predictive uncertainty estimates with much greater precision and calibration.

Methodologies for incorporating the uncertainties characteristic of data-driven object detectors into object tracking algorithms are explored. Object tracking methods rely on measurement error models, typically in the form of measurement noise, false positive rates, and missed detection rates. Each of these quantities, in general, can be dependent on object or measurement location. However, for detections generated from neural-network processed camera inputs, these measurement error statistics are not sufficient to represent the primary source of errors, namely a dissimilarity between run-time sensor input and the training data upon which the detector was trained. To this end, we investigate incorporating data uncertainty into object tracking methods such as to improve the ability to track objects, and particularly those which out-of-distribution w.r.t. training data. The proposed methodologies are validated on an object tracking benchmark as well on experiments with a real autonomous aircraft.

Deep neural networks have significantly contributed to the success in predictive accuracy for classification tasks. However, they tend to make over-confident predictions in real-world settings, where domain shifting and out-of-distribution (OOD) examples exist. Most research on uncertainty estimation focuses on computer vision because it provides visual validation on uncertainty quality. However, few have been presented in the natural language process domain. Unlike Bayesian methods that indirectly infer uncertainty through weight uncertainties, current evidential uncertainty-based methods explicitly model the uncertainty of class probabilities through subjective opinions. They further consider inherent uncertainty in data with different root causes, vacuity (i.e., uncertainty due to a lack of evidence) and dissonance (i.e., uncertainty due to conflicting evidence). In our paper, we firstly apply evidential uncertainty in OOD detection for text classification tasks. We propose an inexpensive framework that adopts both auxiliary outliers and pseudo off-manifold samples to train the model with prior knowledge of a certain class, which has high vacuity for OOD samples. Extensive empirical experiments demonstrate that our model based on evidential uncertainty outperforms other counterparts for detecting OOD examples. Our approach can be easily deployed to traditional recurrent neural networks and fine-tuned pre-trained transformers.

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.

Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.

Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.

Despite the state-of-the-art performance for medical image segmentation, deep convolutional neural networks (CNNs) have rarely provided uncertainty estimations regarding their segmentation outputs, e.g., model (epistemic) and image-based (aleatoric) uncertainties. In this work, we analyze these different types of uncertainties for CNN-based 2D and 3D medical image segmentation tasks. We additionally propose a test-time augmentation-based aleatoric uncertainty to analyze the effect of different transformations of the input image on the segmentation output. Test-time augmentation has been previously used to improve segmentation accuracy, yet not been formulated in a consistent mathematical framework. Hence, we also propose a theoretical formulation of test-time augmentation, where a distribution of the prediction is estimated by Monte Carlo simulation with prior distributions of parameters in an image acquisition model that involves image transformations and noise. We compare and combine our proposed aleatoric uncertainty with model uncertainty. Experiments with segmentation of fetal brains and brain tumors from 2D and 3D Magnetic Resonance Images (MRI) showed that 1) the test-time augmentation-based aleatoric uncertainty provides a better uncertainty estimation than calculating the test-time dropout-based model uncertainty alone and helps to reduce overconfident incorrect predictions, and 2) our test-time augmentation outperforms a single-prediction baseline and dropout-based multiple predictions.