Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and epistemic uncertainty based on proper scoring rules, which are loss functions with the meaningful property that they incentivize the learner to predict ground-truth (conditional) probabilities. We assume two common representations of (epistemic) uncertainty, namely, in terms of a credal set, i.e. a set of probability distributions, or a second-order distribution, i.e., a distribution over probability distributions. Our framework establishes a natural bridge between these representations. We provide a formal justification of our approach and introduce new measures of epistemic and aleatoric uncertainty as concrete instantiations.

Explaining Bayesian Optimization by Shapley Values Facilitates Human-AI Collaboration

Bayesian optimization (BO) with Gaussian processes (GP) has become an indispensable algorithm for black box optimization problems. Not without a dash of irony, BO is often considered a black box itself, lacking ways to provide reasons as to why certain parameters are proposed to be evaluated. This is particularly relevant in human-in-the-loop applications of BO, such as in robotics. We address this issue by proposing ShapleyBO, a framework for interpreting BO's proposals by game-theoretic Shapley values.They quantify each parameter's contribution to BO's acquisition function. Exploiting the linearity of Shapley values, we are further able to identify how strongly each parameter drives BO's exploration and exploitation for additive acquisition functions like the confidence bound. We also show that ShapleyBO can disentangle the contributions to exploration into those that explore aleatoric and epistemic uncertainty. Moreover, our method gives rise to a ShapleyBO-assisted human machine interface (HMI), allowing users to interfere with BO in case proposals do not align with human reasoning. We demonstrate this HMI's benefits for the use case of personalizing wearable robotic devices (assistive back exosuits) by human-in-the-loop BO. Results suggest human-BO teams with access to ShapleyBO can achieve lower regret than teams without.

Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?

Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative approaches, such as evidential deep learning methods, have become popular in recent years. The latter group of methods in essence extends empirical risk minimization (ERM) for predicting second-order probability distributions over outcomes, from which measures of epistemic (and aleatoric) uncertainty can be extracted. This paper presents novel theoretical insights of evidential deep learning, highlighting the difficulties in optimizing second-order loss functions and interpreting the resulting epistemic uncertainty measures. With a systematic setup that covers a wide range of approaches for classification, regression and counts, it provides novel insights into issues of identifiability and convergence in second-order loss minimization, and the relative (rather than absolute) nature of epistemic uncertainty measures.

Conformalized Credal Set Predictors

Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty representation, in particular due to their ability to represent both the aleatoric and epistemic uncertainty in a prediction. However, the design of methods for learning credal set predictors remains a challenging problem. In this paper, we make use of conformal prediction for this purpose. More specifically, we propose a method for predicting credal sets in the classification task, given training data labeled by probability distributions. Since our method inherits the coverage guarantees of conformal prediction, our conformal credal sets are guaranteed to be valid with high probability (without any assumptions on model or distribution). We demonstrate the applicability of our method to natural language inference, a highly ambiguous natural language task where it is common to obtain multiple annotations per example.

Information Leakage Detection through Approximate Bayes-optimal Prediction

In today's data-driven world, the proliferation of publicly available information intensifies the challenge of information leakage (IL), raising security concerns. IL involves unintentionally exposing secret (sensitive) information to unauthorized parties via systems' observable information. Conventional statistical approaches, which estimate mutual information (MI) between observable and secret information for detecting IL, face challenges such as the curse of dimensionality, convergence, computational complexity, and MI misestimation. Furthermore, emerging supervised machine learning (ML) methods, though effective, are limited to binary system-sensitive information and lack a comprehensive theoretical framework. To address these limitations, we establish a theoretical framework using statistical learning theory and information theory to accurately quantify and detect IL. We demonstrate that MI can be accurately estimated by approximating the log-loss and accuracy of the Bayes predictor. As the Bayes predictor is typically unknown in practice, we propose to approximate it with the help of automated machine learning (AutoML). First, we compare our MI estimation approaches against current baselines, using synthetic data sets generated using the multivariate normal (MVN) distribution with known MI. Second, we introduce a cut-off technique using one-sided statistical tests to detect IL, employing the Holm-Bonferroni correction to increase confidence in detection decisions. Our study evaluates IL detection performance on real-world data sets, highlighting the effectiveness of the Bayes predictor's log-loss estimation, and finds our proposed method to effectively estimate MI on synthetic data sets and thus detect ILs accurately.

Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles

While shallow decision trees may be interpretable, larger ensemble models like gradient-boosted trees, which often set the state of the art in machine learning problems involving tabular data, still remain black box models. As a remedy, the Shapley value (SV) is a well-known concept in explainable artificial intelligence (XAI) research for quantifying additive feature attributions of predictions. The model-specific TreeSHAP methodology solves the exponential complexity for retrieving exact SVs from tree-based models. Expanding beyond individual feature attribution, Shapley interactions reveal the impact of intricate feature interactions of any order. In this work, we present TreeSHAP-IQ, an efficient method to compute any-order additive Shapley interactions for predictions of tree-based models. TreeSHAP-IQ is supported by a mathematical framework that exploits polynomial arithmetic to compute the interaction scores in a single recursive traversal of the tree, akin to Linear TreeSHAP. We apply TreeSHAP-IQ on state-of-the-art tree ensembles and explore interactions on well-established benchmark datasets.

Second-Order Uncertainty Quantification: Variance-Based Measures

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way to use variance-based measures to quantify uncertainty on the basis of second-order distributions in classification problems. A distinctive feature of the measures is the ability to reason about uncertainties on a class-based level, which is useful in situations where nuanced decision-making is required. Recalling some properties from the literature, we highlight that the variance-based measures satisfy important (axiomatic) properties. In addition to this axiomatic approach, we present empirical results showing the measures to be effective and competitive to commonly used entropy-based measures.

A Survey of Reinforcement Learning from Human Feedback

Reinforcement learning from human feedback (RLHF) is a variant of reinforcement learning (RL) that learns from human feedback instead of relying on an engineered reward function. Building on prior work on the related setting of preference-based reinforcement learning (PbRL), it stands at the intersection of artificial intelligence and human-computer interaction. This positioning offers a promising avenue to enhance the performance and adaptability of intelligent systems while also improving the alignment of their objectives with human values. The training of Large Language Models (LLMs) has impressively demonstrated this potential in recent years, where RLHF played a decisive role in targeting the model's capabilities toward human objectives. This article provides a comprehensive overview of the fundamentals of RLHF, exploring the intricate dynamics between machine agents and human input. While recent focus has been on RLHF for LLMs, our survey adopts a broader perspective, examining the diverse applications and wide-ranging impact of the technique. We delve into the core principles that underpin RLHF, shedding light on the symbiotic relationship between algorithms and human feedback, and discuss the main research trends in the field. By synthesizing the current landscape of RLHF research, this article aims to provide researchers as well as practitioners with a comprehensive understanding of this rapidly growing field of research.

Second-Order Uncertainty Quantification: A Distance-Based Approach

In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order probability distributions, i.e., predictions in the form of distributions on probability distributions. A completely conclusive solution has not yet been found, however, as shown by recent criticisms of commonly used uncertainty measures associated with second-order distributions, identifying undesirable theoretical properties of these measures. In light of these criticisms, we propose a set of formal criteria that meaningful uncertainty measures for predictive uncertainty based on second-order distributions should obey. Moreover, we provide a general framework for developing uncertainty measures to account for these criteria, and offer an instantiation based on the Wasserstein distance, for which we prove that all criteria are satisfied.