A traditional assurance case employs a positive argument in which reasoning steps, grounded on evidence and assumptions, sustain a top claim that has external significance. Human judgement is required to check the evidence, the assumptions, and the narrative justifications for the reasoning steps; if all are assessed good, then the top claim can be accepted. A valid concern about this process is that human judgement is fallible and prone to confirmation bias. The best defense against this concern is vigorous and skeptical debate and discussion in the manner of a dialectic or Socratic dialog. There is merit in recording aspects of this discussion for the benefit of subsequent developers and assessors. Defeaters are a means doing this: they express doubts about aspects of the argument and can be developed into subcases that confirm or refute the doubts, and can record them as documentation to assist future consideration. This report describes how defeaters, and multiple levels of defeaters, should be represented and assessed in Assurance 2.0 and its Clarissa/ASCE tool support. These mechanisms also support eliminative argumentation, which is a contrary approach to assurance, favored by some, that uses a negative argument to refute all reasons why the top claim could be false.
Unlike traditional statistical methods, Conformal Prediction (CP) allows for the determination of valid and accurate confidence levels associated with individual predictions based only on exchangeability of the data. We here introduce a new feature selection method that takes advantage of the CP framework. Our proposal, named Conformal Recursive Feature Elimination (CRFE), identifies and recursively removes features that increase the non-conformity of a dataset. We also present an automatic stopping criterion for CRFE, as well as a new index to measure consistency between subsets of features. CRFE selections are compared to the classical Recursive Feature Elimination (RFE) method on several multiclass datasets by using multiple partitions of the data. The results show that CRFE clearly outperforms RFE in half of the datasets, while achieving similar performance in the rest. The automatic stopping criterion provides subsets of effective and non-redundant features without computing any classification performance.
Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating stringent assumptions regarding data distribution or merely providing asymptotic guarantees. We introduce a novel approach termed CCR, which employs a combination of conformal prediction intervals for the model outputs to establish confidence regions for model parameters. We present coverage guarantees under minimal assumptions on noise and that is valid in finite sample regime. Our approach is applicable to both split conformal predictions and black-box methodologies including full or cross-conformal approaches. In the specific case of linear models, the derived confidence region manifests as the feasible set of a Mixed-Integer Linear Program (MILP), facilitating the deduction of confidence intervals for individual parameters and enabling robust optimization. We empirically compare CCR to recent advancements in challenging settings such as with heteroskedastic and non-Gaussian noise.
Dynamic graphs provide a flexible data abstraction for modelling many sorts of real-world systems, such as transport, trade, and social networks. Graph neural networks (GNNs) are powerful tools allowing for different kinds of prediction and inference on these systems, but getting a handle on uncertainty, especially in dynamic settings, is a challenging problem. In this work we propose to use a dynamic graph representation known in the tensor literature as the unfolding, to achieve valid prediction sets via conformal prediction. This representation, a simple graph, can be input to any standard GNN and does not require any modification to existing GNN architectures or conformal prediction routines. One of our key contributions is a careful mathematical consideration of the different inference scenarios which can arise in a dynamic graph modelling context. For a range of practically relevant cases, we obtain valid prediction sets with almost no assumptions, even dispensing with exchangeability. In a more challenging scenario, which we call the semi-inductive regime, we achieve valid prediction under stronger assumptions, akin to stationarity. We provide real data examples demonstrating validity, showing improved accuracy over baselines, and sign-posting different failure modes which can occur when those assumptions are violated.
While existing depression prediction methods based on deep learning show promise, their practical application is hindered by the lack of trustworthiness, as these deep models are often deployed as black box models, leaving us uncertain on the confidence of their predictions. For high-risk clinical applications like depression prediction, uncertainty quantification is essential in decision-making. In this paper, we introduce conformal depression prediction (CDP), a depression prediction method with uncertainty quantification based on conformal prediction (CP), giving valid confidence intervals with theoretical coverage guarantees for the model predictions. CDP is a plug-and-play module that requires neither model retraining nor an assumption about the depression data distribution. As CDP provides only an average coverage guarantee across all inputs rather than per-input performance guarantee, we further propose CDP-ACC, an improved conformal prediction with approximate conditional coverage. CDP-ACC firstly estimates the prediction distribution through neighborhood relaxation, and then introduces a conformal score function by constructing nested sequences, so as to provide a tighter prediction interval adaptive to specific input. We empirically demonstrate the application of CDP in uncertainty-aware facial depression prediction, as well as the effectiveness and superiority of CDP-ACC on the AVEC 2013 and AVEC 2014 datasets. Our code is publicly available at https://github.com/PushineLee/CDP.
Conformal Prediction (CP) is a popular uncertainty quantification method that provides distribution-free, statistically valid prediction sets, assuming that training and test data are exchangeable. In such a case, CP's prediction sets are guaranteed to cover the (unknown) true test output with a user-specified probability. Nevertheless, this guarantee is violated when the data is subjected to adversarial attacks, which often result in a significant loss of coverage. Recently, several approaches have been put forward to recover CP guarantees in this setting. These approaches leverage variations of randomised smoothing to produce conservative sets which account for the effect of the adversarial perturbations. They are, however, limited in that they only support $\ell^2$-bounded perturbations and classification tasks. This paper introduces VRCP (Verifiably Robust Conformal Prediction), a new framework that leverages recent neural network verification methods to recover coverage guarantees under adversarial attacks. Our VRCP method is the first to support perturbations bounded by arbitrary norms including $\ell^1$, $\ell^2$, and $\ell^\infty$, as well as regression tasks. We evaluate and compare our approach on image classification tasks (CIFAR10, CIFAR100, and TinyImageNet) and regression tasks for deep reinforcement learning environments. In every case, VRCP achieves above nominal coverage and yields significantly more efficient and informative prediction regions than the SotA.
The observed similarities in the behavior of humans and Large Language Models (LLMs) have prompted researchers to consider the potential of using LLMs as models of human cognition. However, several significant challenges must be addressed before LLMs can be legitimately regarded as cognitive models. For instance, LLMs are trained on far more data than humans typically encounter, and may have been directly trained on human data in specific cognitive tasks or aligned with human preferences. Consequently, the origins of these behavioral similarities are not well understood. In this paper, we propose a novel way to enhance the utility of LLMs as cognitive models. This approach involves (i) leveraging computationally equivalent tasks that both an LLM and a rational agent need to master for solving a cognitive problem and (ii) examining the specific task distributions required for an LLM to exhibit human-like behaviors. We apply this approach to decision-making -- specifically risky and intertemporal choice -- where the key computationally equivalent task is the arithmetic of expected value calculations. We show that an LLM pretrained on an ecologically valid arithmetic dataset, which we call Arithmetic-GPT, predicts human behavior better than many traditional cognitive models. Pretraining LLMs on ecologically valid arithmetic datasets is sufficient to produce a strong correspondence between these models and human decision-making. Our results also suggest that LLMs used as cognitive models should be carefully investigated via ablation studies of the pretraining data.
The growing complexity of AI systems has intensified the need for transparency through Explainable AI (XAI). Counterfactual explanations (CFs) offer actionable "what-if" scenarios on three levels: Local CFs providing instance-specific insights, Global CFs addressing broader trends, and Group-wise CFs (GWCFs) striking a balance and revealing patterns within cohesive groups. Despite the availability of methods for each granularity level, the field lacks a unified method that integrates these complementary approaches. We address this limitation by proposing a gradient-based optimization method for differentiable models that generates Local, Global, and Group-wise Counterfactual Explanations in a unified manner. We especially enhance GWCF generation by combining instance grouping and counterfactual generation into a single efficient process, replacing traditional two-step methods. Moreover, to ensure trustworthiness, we innovatively introduce the integration of plausibility criteria into the GWCF domain, making explanations both valid and realistic. Our results demonstrate the method's effectiveness in balancing validity, proximity, and plausibility while optimizing group granularity, with practical utility validated through practical use cases.
We present PPCEF, a novel method for generating probabilistically plausible counterfactual explanations (CFs). PPCEF advances beyond existing methods by combining a probabilistic formulation that leverages the data distribution with the optimization of plausibility within a unified framework. Compared to reference approaches, our method enforces plausibility by directly optimizing the explicit density function without assuming a particular family of parametrized distributions. This ensures CFs are not only valid (i.e., achieve class change) but also align with the underlying data's probability density. For that purpose, our approach leverages normalizing flows as powerful density estimators to capture the complex high-dimensional data distribution. Furthermore, we introduce a novel loss that balances the trade-off between achieving class change and maintaining closeness to the original instance while also incorporating a probabilistic plausibility term. PPCEF's unconstrained formulation allows for efficient gradient-based optimization with batch processing, leading to orders of magnitude faster computation compared to prior methods. Moreover, the unconstrained formulation of PPCEF allows for the seamless integration of future constraints tailored to specific counterfactual properties. Finally, extensive evaluations demonstrate PPCEF's superiority in generating high-quality, probabilistically plausible counterfactual explanations in high-dimensional tabular settings. This makes PPCEF a powerful tool for not only interpreting complex machine learning models but also for improving fairness, accountability, and trust in AI systems.
Machine unlearning (MU) aims to remove the influence of specific data from trained models, addressing privacy concerns and ensuring compliance with regulations such as the "right to be forgotten." Evaluating strong unlearning, where the unlearned model is indistinguishable from one retrained without the forgetting data, remains a significant challenge in deep neural networks (DNNs). Common black-box metrics, such as variants of membership inference attacks and accuracy comparisons, primarily assess model outputs but often fail to capture residual information in intermediate layers. To bridge this gap, we introduce the Information Difference Index (IDI), a novel white-box metric inspired by information theory. IDI quantifies retained information in intermediate features by measuring mutual information between those features and the labels to be forgotten, offering a more comprehensive assessment of unlearning efficacy. Our experiments demonstrate that IDI effectively measures the degree of unlearning across various datasets and architectures, providing a reliable tool for evaluating strong unlearning in DNNs.
Machine learning algorithms have become indispensable in today's world. They support and accelerate the way we make decisions based on the data at hand. This acceleration means that data structures that were valid at one moment could no longer be valid in the future. With these changing data structures, it is necessary to adapt machine learning (ML) systems incrementally to the new data. This is done with the use of online learning or continuous ML technologies. While deep learning technologies have shown exceptional performance on predefined datasets, they have not been widely applied to online, streaming, and continuous learning. In this retrospective of our tutorial titled Opportunities and Challenges of Online Deep Learning held at ECML PKDD 2023, we provide a brief overview of the opportunities but also the potential pitfalls for the application of neural networks in online learning environments using the frameworks River and Deep-River.
Directed acyclic graph (DAG) learning is a central task in structure discovery and causal inference. Although the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to learn a single (point estimate) DAG from data, let alone provide uncertainty quantification. We address the difficult task of quantifying graph uncertainty by developing a Bayesian variational inference framework based on novel, provably valid distributions that have support directly on the space of sparse DAGs. These distributions, which we use to define our prior and variational posterior, are induced by a projection operation that maps an arbitrary continuous distribution onto the space of sparse weighted acyclic adjacency matrices. While this projection is combinatorial, it can be solved efficiently using recent continuous reformulations of acyclicity constraints. We empirically demonstrate that our method, ProDAG, can outperform state-of-the-art alternatives in both accuracy and uncertainty quantification.
Algorithmic stability is a central notion in learning theory that quantifies the sensitivity of an algorithm to small changes in the training data. If a learning algorithm satisfies certain stability properties, this leads to many important downstream implications, such as generalization, robustness, and reliable predictive inference. Verifying that stability holds for a particular algorithm is therefore an important and practical question. However, recent results establish that testing the stability of a black-box algorithm is impossible, given limited data from an unknown distribution, in settings where the data lies in an uncountably infinite space (such as real-valued data). In this work, we extend this question to examine a far broader range of settings, where the data may lie in any space -- for example, categorical data. We develop a unified framework for quantifying the hardness of testing algorithmic stability, which establishes that across all settings, if the available data is limited then exhaustive search is essentially the only universally valid mechanism for certifying algorithmic stability. Since in practice, any test of stability would naturally be subject to computational constraints, exhaustive search is impossible and so this implies fundamental limits on our ability to test the stability property for a black-box algorithm.
This paper introduces a conformal inference method to evaluate uncertainty in classification by generating prediction sets with valid coverage conditional on adaptively chosen features. These features are carefully selected to reflect potential model limitations or biases. This can be useful to find a practical compromise between efficiency -- by providing informative predictions -- and algorithmic fairness -- by ensuring equalized coverage for the most sensitive groups. We demonstrate the validity and effectiveness of this method on simulated and real data sets.
Inventory control is subject to service-level requirements, in which sufficient stock levels must be maintained despite an unknown demand. We propose a data-driven order policy that certifies any prescribed service level under minimal assumptions on the unknown demand process. The policy achieves this using any online learning method along with integral action. We further propose an inference method that is valid in finite samples. The properties and theoretical guarantees of the method are illustrated using both synthetic and real-world data.
We introduce a data-driven approach to computing finite bisimulations for state transition systems with very large, possibly infinite state space. Our novel technique computes stutter-insensitive bisimulations of deterministic systems, which we characterize as the problem of learning a state classifier together with a ranking function for each class. Our procedure learns a candidate state classifier and candidate ranking functions from a finite dataset of sample states; then, it checks whether these generalise to the entire state space using satisfiability modulo theory solving. Upon the affirmative answer, the procedure concludes that the classifier constitutes a valid stutter-insensitive bisimulation of the system. Upon a negative answer, the solver produces a counterexample state for which the classifier violates the claim, adds it to the dataset, and repeats learning and checking in a counterexample-guided inductive synthesis loop until a valid bisimulation is found. We demonstrate on a range of benchmarks from reactive verification and software model checking that our method yields faster verification results than alternative state-of-the-art tools in practice. Our method produces succinct abstractions that enable an effective verification of linear temporal logic without next operator, and are interpretable for system diagnostics.
We study min-max algorithms to solve zero-sum differential games on Riemannian manifold. Based on the notions of differential Stackelberg equilibrium and differential Nash equilibrium on Riemannian manifold, we analyze the local convergence of two representative deterministic simultaneous algorithms $\tau$-GDA and $\tau$-SGA to such equilibria. Sufficient conditions are obtained to establish the linear convergence rate of $\tau$-GDA based on the Ostrowski theorem on manifold and spectral analysis. To avoid strong rotational dynamics in $\tau$-GDA, $\tau$-SGA is extended from the symplectic gradient-adjustment method in Euclidean space. We analyze an asymptotic approximation of $\tau$-SGA when the learning rate ratio $\tau$ is big. In some cases, it can achieve a faster convergence rate to differential Stackelberg equilibrium compared to $\tau$-GDA. We show numerically how the insights obtained from the convergence analysis may improve the training of orthogonal Wasserstein GANs using stochastic $\tau$-GDA and $\tau$-SGA on simple benchmarks.
Leveraging connections between diffusion-based sampling, optimal transport, and stochastic optimal control through their shared links to the Schr\"odinger bridge problem, we propose novel objective functions that can be used to transport $\nu$ to $\mu$, consequently sample from the target $\mu$, via optimally controlled dynamics. We highlight the importance of the pathwise perspective and the role various optimality conditions on the path measure can play for the design of valid training losses, the careful choice of which offer numerical advantages in implementation. Basing the formalism on Schr\"odinger bridge comes with the additional practical capability of baking in inductive bias when it comes to Neural Network training.
Identifying the causal pathways of unfairness is a critical objective for improving policy design and algorithmic decision-making. Prior work in causal fairness analysis often requires knowledge of the causal graph, hindering practical applications in complex or low-knowledge domains. Moreover, global discovery methods that learn causal structure from data can display unstable performance on finite samples, preventing robust fairness conclusions. To mitigate these challenges, we introduce local discovery for direct discrimination (LD3): a method that uncovers structural evidence of direct unfairness by identifying the causal parents of an outcome variable. LD3 performs a linear number of conditional independence tests relative to variable set size, and allows for latent confounding under the sufficient condition that all parents of the outcome are observed. We show that LD3 returns a valid adjustment set (VAS) under a new graphical criterion for the weighted controlled direct effect, a qualitative indicator of direct discrimination. LD3 limits unnecessary adjustment, providing interpretable VAS for assessing unfairness. We use LD3 to analyze causal fairness in two complex decision systems: criminal recidivism prediction and liver transplant allocation. LD3 was more time-efficient and returned more plausible results on real-world data than baselines, which took 46$\times$ to 5870$\times$ longer to execute.
Graph Neural Networks have achieved remarkable accuracy in semi-supervised node classification tasks. However, these results lack reliable uncertainty estimates. Conformal prediction methods provide a theoretical guarantee for node classification tasks, ensuring that the conformal prediction set contains the ground-truth label with a desired probability (e.g., 95%). In this paper, we empirically show that for each node, aggregating the non-conformity scores of nodes with the same label can improve the efficiency of conformal prediction sets while maintaining valid marginal coverage. This observation motivates us to propose a novel algorithm named Similarity-Navigated Adaptive Prediction Sets (SNAPS), which aggregates the non-conformity scores based on feature similarity and structural neighborhood. The key idea behind SNAPS is that nodes with high feature similarity or direct connections tend to have the same label. By incorporating adaptive similar nodes information, SNAPS can generate compact prediction sets and increase the singleton hit ratio (correct prediction sets of size one). Moreover, we theoretically provide a finite-sample coverage guarantee of SNAPS. Extensive experiments demonstrate the superiority of SNAPS, improving the efficiency of prediction sets and singleton hit ratio while maintaining valid coverage.