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Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product between a divergence function and the posterior. Current methods such as Deep Ensembles or MC dropout underperform at estimating the epistemic uncertainty, since they primarily consider the posterior when sampling models. We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to better estimate the epistemic uncertainty. QUAM identifies regions where the whole product under the integral is large, not just the posterior. Consequently, QUAM has lower approximation error of the epistemic uncertainty compared to previous methods. Models for which the product is large correspond to adversarial models (not adversarial examples!). Adversarial models have both a high posterior as well as a high divergence between their predictions and that of a reference model. Our experiments show that QUAM excels in capturing epistemic uncertainty for deep learning models and outperforms previous methods on challenging tasks in the vision domain.

In the past years, deep learning has seen an increase in usage in the domain of histopathological applications. However, while these approaches have shown great potential, in high-risk environments deep learning models need to be able to judge their uncertainty and be able to reject inputs when there is a significant chance of misclassification. In this work, we conduct a rigorous evaluation of the most commonly used uncertainty and robustness methods for the classification of Whole Slide Images, with a focus on the task of selective classification, where the model should reject the classification in situations in which it is uncertain. We conduct our experiments on tile-level under the aspects of domain shift and label noise, as well as on slide-level. In our experiments, we compare Deep Ensembles, Monte-Carlo Dropout, Stochastic Variational Inference, Test-Time Data Augmentation as well as ensembles of the latter approaches. We observe that ensembles of methods generally lead to better uncertainty estimates as well as an increased robustness towards domain shifts and label noise, while contrary to results from classical computer vision benchmarks no systematic gain of the other methods can be shown. Across methods, a rejection of the most uncertain samples reliably leads to a significant increase in classification accuracy on both in-distribution as well as out-of-distribution data. Furthermore, we conduct experiments comparing these methods under varying conditions of label noise. Lastly, we publish our code framework to facilitate further research on uncertainty estimation on histopathological data.

Uncertainty sampling is a prevalent active learning algorithm that queries sequentially the annotations of data samples which the current prediction model is uncertain about. However, the usage of uncertainty sampling has been largely heuristic: (i) There is no consensus on the proper definition of "uncertainty" for a specific task under a specific loss; (ii) There is no theoretical guarantee that prescribes a standard protocol to implement the algorithm, for example, how to handle the sequentially arrived annotated data under the framework of optimization algorithms such as stochastic gradient descent. In this work, we systematically examine uncertainty sampling algorithms under both stream-based and pool-based active learning. We propose a notion of equivalent loss which depends on the used uncertainty measure and the original loss function and establish that an uncertainty sampling algorithm essentially optimizes against such an equivalent loss. The perspective verifies the properness of existing uncertainty measures from two aspects: surrogate property and loss convexity. Furthermore, we propose a new notion for designing uncertainty measures called \textit{loss as uncertainty}. The idea is to use the conditional expected loss given the features as the uncertainty measure. Such an uncertainty measure has nice analytical properties and generality to cover both classification and regression problems, which enable us to provide the first generalization bound for uncertainty sampling algorithms under both stream-based and pool-based settings, in the full generality of the underlying model and problem. Lastly, we establish connections between certain variants of the uncertainty sampling algorithms with risk-sensitive objectives and distributional robustness, which can partly explain the advantage of uncertainty sampling algorithms when the sample size is small.

Causal inference for extreme events has many potential applications in fields such as climate science, medicine and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real data set to estimate the extremal quantile treatment effect of college education on wage.

We present an end-to-end procedure for embodied exploration based on two biologically inspired computations: predictive coding and uncertainty minimization. The procedure can be applied to any exploration setting in a task-independent and intrinsically driven manner. We first demonstrate our approach in a maze navigation task and show that our model is capable of discovering the underlying transition distribution and reconstructing the spatial features of the environment. Second, we apply our model to the more complex task of active vision, where an agent must actively sample its visual environment to gather information. We show that our model is able to build unsupervised representations that allow it to actively sample and efficiently categorize sensory scenes. We further show that using these representations as input for downstream classification leads to superior data efficiency and learning speed compared to other baselines, while also maintaining lower parameter complexity. Finally, the modularity of our model allows us to analyze its internal mechanisms and to draw insight into the interactions between perception and action during exploratory behavior.

As sequential neural architectures become deeper and more complex, uncertainty estimation is more and more challenging. Efforts in quantifying uncertainty often rely on specific training procedures, and bear additional computational costs due to the dimensionality of such models. In this paper, we propose to decompose a classification or regression task in two steps: a representation learning stage to learn low-dimensional states, and a state space model for uncertainty estimation. This approach allows to separate representation learning and design of generative models. We demonstrate how predictive distributions can be estimated on top of an existing and trained neural network, by adding a state space-based last layer whose parameters are estimated with Sequential Monte Carlo methods. We apply our proposed methodology to the hourly estimation of Electricity Transformer Oil temperature, a publicly benchmarked dataset. Our model accounts for the noisy data structure, due to unknown or unavailable variables, and is able to provide confidence intervals on predictions.

Although Large Language Models (LLMs) have shown great potential in Natural Language Generation, it is still challenging to characterize the uncertainty of model generations, i.e., when users could trust model outputs. Our research is derived from the heuristic facts that tokens are created unequally in reflecting the meaning of generations by auto-regressive LLMs, i.e., some tokens are more relevant (or representative) than others, yet all the tokens are equally valued when estimating uncertainty. It is because of the linguistic redundancy where mostly a few keywords are sufficient to convey the meaning of a long sentence. We name these inequalities as generative inequalities and investigate how they affect uncertainty estimation. Our results reveal that considerable tokens and sentences containing limited semantics are weighted equally or even heavily when estimating uncertainty. To tackle these biases posed by generative inequalities, we propose to jointly Shifting Attention to more Relevant (SAR) components from both the token level and the sentence level while estimating uncertainty. We conduct experiments over popular "off-the-shelf" LLMs (e.g., OPT, LLaMA) with model sizes up to 30B and powerful commercial LLMs (e.g., Davinci from OpenAI), across various free-form question-answering tasks. Experimental results and detailed demographic analysis indicate the superior performance of SAR. Code is available at //github.com/jinhaoduan/shifting-attention-to-relevance.

We explore the use of uncertainty estimation in the maritime domain, showing the efficacy on toy datasets (CIFAR10) and proving it on an in-house dataset, SHIPS. We present a method joining the intra-class uncertainty achieved using Monte Carlo Dropout, with recent discoveries in the field of outlier detection, to gain more holistic uncertainty measures. We explore the relationship between the introduced uncertainty measures and examine how well they work on CIFAR10 and in a real-life setting. Our work improves the FPR95 by 8% compared to the current highest-performing work when the models are trained without out-of-distribution data. We increase the performance by 77% compared to a vanilla implementation of the Wide ResNet. We release the SHIPS dataset and show the effectiveness of our method by improving the FPR95 by 44.2% with respect to the baseline. Our approach is model agnostic, easy to implement, and often does not require model retraining.

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.

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.