We argue that current definitions of machine unlearning are underspecified for second-order optimizers. We compare first-order and second-order learners for their ability to handle the data deletion task with varying degrees of eigendecomposition to mimic the loss model memory. While both first and second-order methods realign with the ideal counterfactul in terms of performance and gradient, the second-order optimizer shows significant volatility in the optimizer state. This indicates residual information, supposedly deleted, that isn't detectable by first-order analysis. Various eigendecay treatments show that stability and information loss is regained only under controlled state pertubation where geometric information (or memory) is erased.

Decision-makers are faced with the challenge of estimating what is likely to happen when they take an action. For instance, if I choose not to treat this patient, are they likely to die? Practitioners commonly use supervised learning algorithms to fit predictive models that help decision-makers reason about likely future outcomes, but we show that this approach is unreliable, and sometimes even dangerous. The key issue is that supervised learning algorithms are highly sensitive to the policy used to choose actions in the training data, which causes the model to capture relationships that do not generalize. We propose using a different learning objective that predicts counterfactuals instead of predicting outcomes under an existing action policy as in supervised learning. To support decision-making in temporal settings, we introduce the Counterfactual Gaussian Process (CGP) to predict the counterfactual future progression of continuous-time trajectories under sequences of future actions. We demonstrate the benefits of the CGP on two important decision-support tasks: risk prediction and "what if?" reasoning for individualized treatment planning.

One use of such an estimate is to evaluate risk; e.g. is this patient likely to die if I do not

Counterfactual reasoning aims at answering contrary-to-fact questions like "Would have Alice recovered had she taken aspirin?" and corresponds to the most fine-grained layer of causation. Critically, while many counterfactual statements cannot be falsified--even by randomized experiments--they underpin fundamental concepts like individual-wise fairness. Therefore, providing models to formalize and implement counterfactual beliefs remains a fundamental scientific problem. In the Markovian setting of Pearl's causal framework, we propose an alternative approach to structural causal models to represent counterfactuals compatible with a given causal graphical model. More precisely, we introduce counterfactual models, also called canonical representations of structural causal models. They enable analysts to choose a counterfactual assumption via random-process probability distributions with preassigned marginals and characterize the counterfactual equivalence class of structural causal models. Using these representations, we present a normalization procedure to disentangle the (arbitrary and unfalsifiable) counterfactual choice from the (typically testable) interventional constraints. In contrast to structural causal models, this allows to implement many counterfactual assumptions while preserving interventional knowledge, and does not require any estimation step at the individual-counterfactual layer: only to make a choice. Finally, we illustrate the specific role of counterfactuals in causality and the benefits of our approach on theoretical and numerical examples.

Wearable sensor data offer opportunities for personalized health monitoring, yet deriving actionable insights from their complex, longitudinal data streams is challenging. This paper introduces a framework to learn personalized counterfactual models from multivariate wearable data. This enables exploring what-if scenarios to understand potential individual-specific outcomes of lifestyle choices. Our approach first augments individual datasets with data from similar patients via multi-modal similarity analysis. We then use a temporal PC (Peter-Clark) algorithm adaptation to discover predictive relationships, modeling how variables at time t-1 influence physiological changes at time t. Gradient Boosting Machines are trained on these discovered relationships to quantify individual-specific effects. These models drive a counterfactual engine projecting physiological trajectories under hypothetical interventions (e.g., activity or sleep changes). We evaluate the framework via one-step-ahead predictive validation and by assessing the plausibility and impact of interventions. Evaluation showed reasonable predictive accuracy (e.g., mean heart rate MAE 4.71 bpm) and high counterfactual plausibility (median 0.9643). Crucially, these interventions highlighted significant inter-individual variability in response to hypothetical lifestyle changes, showing the framework's potential for personalized insights. This work provides a tool to explore personalized health dynamics and generate hypotheses on individual responses to lifestyle changes.

As machine learning models are increasingly used in educational settings, from detecting at-risk students to predicting student performance, algorithmic bias and its potential impacts on students raise critical concerns about algorithmic fairness. Although group fairness is widely explored in education, works on individual fairness in a causal context are understudied, especially on counterfactual fairness. This paper explores the notion of counterfactual fairness for educational data by conducting counterfactual fairness analysis of machine learning models on benchmark educational datasets. We demonstrate that counterfactual fairness provides meaningful insight into the causality of sensitive attributes and causal-based individual fairness in education.

Knowledge editing aims to efficiently and cost-effectively correct inaccuracies and update outdated information. Recently, there has been growing interest in extending knowledge editing from Large Language Models (LLMs) to Multimodal Large Language Models (MLLMs), which integrate both textual and visual information, introducing additional editing complexities. Existing multimodal knowledge editing works primarily focus on text-oriented, coarse-grained scenarios, failing to address the unique challenges posed by multimodal contexts. In this paper, we propose a visual-oriented, fine-grained multimodal knowledge editing task that targets precise editing in images with multiple interacting entities. We introduce the Fine-Grained Visual Knowledge Editing (FGVEdit) benchmark to evaluate this task. Moreover, we propose a Multimodal Scope Classifier-based Knowledge Editor (MSCKE) framework. MSCKE leverages a multimodal scope classifier that integrates both visual and textual information to accurately identify and update knowledge related to specific entities within images. This approach ensures precise editing while preserving irrelevant information, overcoming the limitations of traditional text-only editing methods. Extensive experiments on the FGVEdit benchmark demonstrate that MSCKE outperforms existing methods, showcasing its effectiveness in solving the complex challenges of multimodal knowledge editing.

Decision-makers are faced with the challenge of estimating what is likely to happen when they take an action. For instance, if I choose not to treat this patient, are they likely to die? Practitioners commonly use supervised learning algorithms to fit predictive models that help decision-makers reason about likely future outcomes, but we show that this approach is unreliable, and sometimes even dangerous. The key issue is that supervised learning algorithms are highly sensitive to the policy used to choose actions in the training data, which causes the model to capture relationships that do not generalize. We propose using a different learning objective that predicts counterfactuals instead of predicting outcomes under an existing action policy as in supervised learning. To support decision-making in temporal settings, we introduce the Counterfactual Gaussian Process (CGP) to predict the counterfactual future progression of continuous-time trajectories under sequences of future actions. We demonstrate the benefits of the CGP on two important decision-support tasks: risk prediction and "what if?" reasoning for individualized treatment planning.

Causal reasoning, in particular, counterfactual reasoning plays a central role in testing for discrimination. Counterfactual reasoning materializes when testing for discrimination, what is known as the counterfactual model of discrimination, when we compare the discrimination comparator with the discrimination complainant, where the comparator is a similar (or similarly situated) profile to that of the complainant used for testing the discrimination claim of the complainant. In this paper, we revisit the comparator by presenting two kinds of comparators based on the sort of causal intervention we want to represent. We present the ceteris paribus and the mutatis mutandis comparator, where the former is the standard and the latter is a new kind of comparator. We argue for the use of the mutatis mutandis comparator, which is built on the fairness given the difference notion, for testing future algorithmic discrimination cases.