Counterfactual explanation (CE) is a core technique in explainable artificial intelligence (XAI), widely used to interpret model decisions and suggest actionable alternatives. This work presents a structure-aware and robustness-oriented counterfactual search method based on the conditional Gaussian network classifier (CGNC). The CGNC has a generative structure that encodes conditional dependencies and potential causal relations among features through a directed acyclic graph (DAG). This structure naturally embeds feature relationships into the search process, eliminating the need for additional constraints to ensure consistency with the model's structural assumptions. We adopt a convergence-guaranteed cutting-set procedure as an adversarial optimization framework, which iteratively approximates solutions that satisfy global robustness conditions. To address the nonconvex quadratic structure induced by feature dependencies, we apply piecewise McCormick relaxation to reformulate the problem as a mixed-integer linear program (MILP), ensuring global optimality. Experimental results show that our method achieves strong robustness, with direct global optimization of the original formulation providing especially stable and efficient results. The proposed framework is extensible to more complex constraint settings, laying the groundwork for future advances in counterfactual reasoning under nonconvex quadratic formulations.
HyConEx: Hypernetwork classifier with counterfactual explanations for tabular data
Faculty of Mathematics and Computer Science, Jagiellonian University（数学与计算机科学学院，杰兹维日大学）；Wrocław University of Science and Technology（沃拉什大学技术学院）；IDEAS Research Institute（IDEAS研究所）
While machine learning models are usually assumed to always output a prediction, there also exist extensions in the form of reject options which allow the model to reject inputs where only a prediction with an unacceptably low certainty would be possible. With the ongoing rise of eXplainable AI, a lot of methods for explaining model predictions have been developed. However, understanding why a given input was rejected, instead of being classified by the model, is also of interest. Surprisingly, explanations of rejects have not been considered so far. We propose to use counterfactual explanatio…
We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more generally, theory-of-mind reasoning systems) should be at least as expressive as first-order (quantified) modal logic (QML) to be well-behaved. While existing work on moral reasoning has focused on counterfactual-free QML moral reasoning, we present a fully specified and implemented formal system that includes counterfactual conditionals. We validate our model with t…
We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in this context through simple arithmetical operations that allow us to capture the intuition that certain antecedents can not be validated by any number of observations. We frame our approach as a form of finite belief improvement, and we propose a model of conditional belief revision in which only the "right" hypothetical levels of implausibility are revised.
In this paper titled A Symbolic Approach for Counterfactual Explanations we propose a novel symbolic approach to provide counterfactual explanations for a classifier predictions. Contrary to most explanation approaches where the goal is to understand which and to what extent parts of the data helped to give a prediction, counterfactual explanations indicate which features must be changed in the data in order to change this classifier prediction. Our approach is symbolic in the sense that it is based on encoding the decision function of a classifier in an equivalent CNF formula. In this approac…
UC San Diego（加州大学圣地亚哥分校）；Stanford University（斯坦福大学）
Despite their high accuracies, modern complex image classifiers cannot be trusted for sensitive tasks due to their unknown decision-making process and potential biases. Counterfactual explanations are very effective in providing transparency for these black-box algorithms. Nevertheless, generating counterfactuals that can have a consistent impact on classifier outputs and yet expose interpretable feature changes is a very challenging task. We introduce a novel method to generate causal and yet interpretable counterfactual explanations for image classifiers using pretrained generative models wi…
We study abductive, causal, and non-causal conditionals in indicative and counterfactual formulations using probabilistic truth table tasks under incomplete probabilistic knowledge (N = 80). We frame the task as a probability-logical inference problem. The most frequently observed response type across all conditions was a class of conditional event interpretations of conditionals; it was followed by conjunction interpretations. An interesting minority of participants neglected some of the relevant imprecision involved in the premises when inferring lower or upper probability bounds on the targ…
We propose a novel method for explaining the predictions of any classifier. In our approach, local explanations are expected to explain both the outcome of a prediction and how that prediction would change if 'things had been different'. Furthermore, we argue that satisfactory explanations cannot be dissociated from a notion and measure of fidelity, as advocated in the early days of neural networks' knowledge extraction. We introduce a definition of fidelity to the underlying classifier for local explanation models which is based on distances to a target decision boundary. A system called CLEA…
In this paper we study selected argument forms involving counterfactuals and indicative conditionals under uncertainty. We selected argument forms to explore whether people with an Eastern cultural background reason differently about conditionals compared to Westerners, because of the differences in the location of negations. In a 2x2 between-participants design, 63 Japanese university students were allocated to four groups, crossing indicative conditionals and counterfactuals, and each presented in two random task orders. The data show close agreement between the responses of Easterners and W…
The elegant Stalnaker/Lewis semantics for counterfactual conditonals works with distances between models. But human beings certainly have no tables of models and distances in their head. We begin here an investigation using a more realistic picture, based on findings in neuroscience. We call it a pre-semantics, as its meaning is not a description of the world, but of the brain, whose structure is (partly) determined by the world it reasons about. In the final section, we reconsider the components, and postulate that there are no atomic pictures, we can always look inside.
As AI-based systems increasingly impact many areas of our lives, auditing these systems for fairness is an increasingly high-stakes problem. Traditional group fairness metrics can miss discrimination against individuals and are difficult to apply after deployment. Counterfactual fairness describes an individualized notion of fairness but is even more challenging to evaluate after deployment. We present prediction sensitivity, an approach for continual audit of counterfactual fairness in deployed classifiers. Prediction sensitivity helps answer the question: would this prediction have been diff…
There exists an apparent negative correlation between performance and interpretability of deep learning models. In an effort to reduce this negative correlation, we propose a Born Identity Network (BIN), which is a post-hoc approach for producing multi-way counterfactual maps. A counterfactual map transforms an input sample to be conditioned and classified as a target label, which is similar to how humans process knowledge through counterfactual thinking. For example, a counterfactual map can localize hypothetical abnormalities from a normal brain image that may cause it to be diagnosed with a…
A principle behind dozens of attribution methods is to take the prediction difference between before-and-after an input feature (here, a token) is removed as its attribution. A popular Input Marginalization (IM) method (Kim et al., 2020) uses BERT to replace a token, yielding more plausible counterfactuals. While Kim et al. (2020) reported that IM is effective, we find this conclusion not convincing as the DeletionBERT metric used in their paper is biased towards IM. Importantly, this bias exists in Deletion-based metrics, including Insertion, Sufficiency, and Comprehensiveness. Furthermore, o…
Counterfactual MRI Data Augmentation using Conditional Denoising Diffusion Generative Models
Instituto Superior Técnico（高等技术学院）；Universidade de Lisboa（里斯本大学）；Digital Surgery LAB（数字外科实验室）；Champalimaud Foundation（尚帕利莫基金会）；Faculdade de Medicina, Universidade de Lisboa（里斯本大学医学院）；Instituto de Telecomunicações（电信研究所）
Accenture Labs（埃森哲实验室）；Accenture The Dock（埃森哲The Dock）；Inria（法国国家信息与自动化研究所）
We predict credit applications with off-the-shelf, interchangeable black-box classifiers and we explain single predictions with counterfactual explanations. Counterfactual explanations expose the minimal changes required on the input data to obtain a different result e.g., approved vs rejected application. Despite their effectiveness, counterfactuals are mainly designed for changing an undesired outcome of a prediction i.e. loan rejected. Counterfactuals, however, can be difficult to interpret, especially when a high number of features are involved in the explanation. Our contribution is two-f…
Microsoft Research（微软研究院）；University of Colorado Boulder（科罗拉多大学博尔德分校）
To construct interpretable explanations that are consistent with the original ML model, counterfactual examples---showing how the model's output changes with small perturbations to the input---have been proposed. This paper extends the work in counterfactual explanations by addressing the challenge of feasibility of such examples. For explanations of ML models in critical domains such as healthcare and finance, counterfactual examples are useful for an end-user only to the extent that perturbation of feature inputs is feasible in the real world. We formulate the problem of feasibility as prese…
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；AXA（安盛）；Polish Academy of Science（波兰科学院）
Counterfactual post-hoc interpretability approaches have been proven to be useful tools to generate explanations for the predictions of a trained blackbox classifier. However, the assumptions they make about the data and the classifier make them unreliable in many contexts. In this paper, we discuss three desirable properties and approaches to quantify them: proximity, connectedness and stability. In addition, we illustrate that there is a risk for post-hoc counterfactual approaches to not satisfy these properties.
The paper proposes summarized attribution-based post-hoc explanations for the detection and identification of bias in data. A global explanation is proposed, and a step-by-step framework on how to detect and test bias is introduced. Since removing unwanted bias is often a complicated and tremendous task, it is automatically inserted, instead. Then, the bias is evaluated with the proposed counterfactual approach. The obtained results are validated on a sample skin lesion dataset. Using the proposed method, a number of possible bias causing artifacts are successfully identified and confirmed in …
Otto-von-Guericke University Magdeburg（马格德堡奥托·冯·格里克大学）；Jagiellonian University（雅盖隆大学）；Halmstad University（哈尔姆斯塔德大学）；Center for Applied Intelligence Systems Research（应用智能系统研究中心）
With the ongoing rise of machine learning, the need for methods for explaining decisions made by artificial intelligence systems is becoming a more and more important topic. Especially for image classification tasks, many state-of-the-art tools to explain such classifiers rely on visual highlighting of important areas of the input data. Contrary, counterfactual explanation systems try to enable a counterfactual reasoning by modifying the input image in a way such that the classifier would have made a different prediction. By doing so, the users of counterfactual explanation systems are equippe…
IMFACT: Counterfactual Explanations for Time Series via Intrinsic Mode Function Substitution
LMU Munich（慕尼黑大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；TU Graz（格拉茨工业大学）；BOKU University Vienna（维也纳农业大学）；TECNALIA（泰克纳利亚）；University of the Basque Country (EHU)（巴斯克大学）
The same method that creates adversarial examples (AEs) to fool image-classifiers can be used to generate counterfactual explanations (CEs) that explain algorithmic decisions. This observation has led researchers to consider CEs as AEs by another name. We argue that the relationship to the true label and the tolerance with respect to proximity are two properties that formally distinguish CEs and AEs. Based on these arguments, we introduce CEs, AEs, and related concepts mathematically in a common framework. Furthermore, we show connections between current methods for generating CEs and AEs, and…
The increasing use of machine learning in practice and legal regulations like EU's GDPR cause the necessity to be able to explain the prediction and behavior of machine learning models. A prominent example of particularly intuitive explanations of AI models in the context of decision making are counterfactual explanations. Yet, it is still an open research problem how to efficiently compute counterfactual explanations for many models. We investigate how to efficiently compute counterfactual explanations for an important class of models, prototype-based classifiers such as learning vector quant…
Counterfactual explanations for machine learning models are used to find minimal interventions to the feature values such that the model changes the prediction to a different output or a target output. A valid counterfactual explanation should have likely feature values. Here, we address the challenge of generating counterfactual explanations that lie in the same data distribution as that of the training data and more importantly, they belong to the target class distribution. This requirement has been addressed through the incorporation of auto-encoder reconstruction loss in the counterfactual…
Automated computer vision systems have been applied in many domains including security, law enforcement, and personal devices, but recent reports suggest that these systems may produce biased results, discriminating against people in certain demographic groups. Diagnosing and understanding the underlying true causes of model biases, however, are challenging tasks because modern computer vision systems rely on complex black-box models whose behaviors are hard to decode. We propose to use an encoder-decoder network developed for image attribute manipulation to synthesize facial images varying in…
The semantically disentangled latent subspace in GAN provides rich interpretable controls in image generation. This paper includes two contributions on semantic latent subspace analysis in the scenario of face generation using StyleGAN2. First, we propose a novel approach to disentangle latent subspace semantics by exploiting existing face analysis models, e.g., face parsers and face landmark detectors. These models provide the flexibility to construct various criterions with very concrete and interpretable semantic meanings (e.g., change face shape or change skin color) to restrict latent sub…
Huazhong University of Science and Technology（华中科技大学）
The fully convolutional network (FCN) has achieved tremendous success in dense visual recognition tasks, such as scene segmentation. The last layer of FCN is typically a global classifier (1x1 convolution) to recognize each pixel to a semantic label. We empirically show that this global classifier, ignoring the intra-class distinction, may lead to sub-optimal results. In this work, we present a conditional classifier to replace the traditional global classifier, where the kernels of the classifier are generated dynamically conditioned on the input. The main advantages of the new classifier con…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
In this work, we propose an introspection technique for deep neural networks that relies on a generative model to instigate salient editing of the input image for model interpretation. Such modification provides the fundamental interventional operation that allows us to obtain answers to counterfactual inquiries, i.e., what meaningful change can be made to the input image in order to alter the prediction. We demonstrate how to reveal interesting properties of the given classifiers by utilizing the proposed introspection approach on both the MNIST and the CelebA dataset.
