We study the problem of causal structure learning from a combination of observational and interventional data generated by a linear non-Gaussian structural equation model that might contain cycles. Recent results show that using mere observational data identifies the causal graph only up to a permutation-equivalence class. We obtain a combinatorial characterization of this class by showing that each graph in an equivalence class corresponds to a perfect matching in a bipartite graph. This bipartite representation allows us to analyze how interventions modify or constrain the matchings. Specifically, we show that each atomic intervention reveals one edge of the true matching and eliminates all incompatible causal graphs. Consequently, we formalize the optimal experiment design task as an adaptive stochastic optimization problem over the set of equivalence classes with a natural reward function that quantifies how many graphs are eliminated from the equivalence class by an intervention.

Causal effect estimation is critical to a range of scientific disciplines. Existing methods for this task either require interventional data, knowledge about the ground-truth causal graph, or rely on assumptions such as unconfoundedness, restricting their applicability in real-world settings. In the domain of tabular machine learning, Prior-data fitted networks (PFNs) have achieved state-of-theart predictive performance, having been pre-trained on synthetic causal data to solve tabular prediction problems via in-context learning. To assess whether this can be transferred to the problem of causal effect estimation, we pre-train PFNs on synthetic data drawn from a wide variety of causal structures, including interventions, to predict interventional outcomes given observational data. Through extensive experiments in synthetic and semi-synthetic settings, we show that our approach allows for the accurate estimation of causal effects without knowledge of the underlying causal graph.

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions - hypothetical "what if?" scenarios that go beyond the observed data and provide insight into a model reasoning. In this work, we introduce the notion of causal interpretability, which formalizes when counterfactual queries can be evaluated from a specific class of models and observational data. We analyze two common model classes - blackbox and concept-based predictors - and show that neither is causally interpretable in general. To address this gap, we develop a framework for building models that are causally interpretable by design. Specifically, we derive a complete graphical criterion that determines whether a given model architecture supports a given counterfactual query. This leads to a fundamental tradeoff between causal interpretability and predictive accuracy, which we characterize by identifying the unique maximal set of features that yields an interpretable model with maximal predictive expressiveness. Experiments corroborate the theoretical findings.

Data fusion techniques integrate information from heterogeneous data sources to improve learning, generalization, and decision-making across data sciences. In causal inference, these methods leverage rich observational data to improve causal effect estimation, while maintaining the trustworthiness of randomized controlled trials. Existing approaches often relax the strong "no unobserved confounding" assumption by instead assuming exchangeability of counterfactual outcomes across data sources. However, when both assumptions simultaneously fail--a common scenario in practice--current methods cannot identify or estimate causal effects. We address this limitation by proposing a novel partial identification framework that enables researchers to answer key questions such as: Is the causal effect positive/negative? and How severe must assumption violations be to overturn this conclusion?

We address the open question of counterfactual identification for high-dimensional multivariate outcomes from observational data. Pearl (2000) argues that counterfactuals must be identifiable (i.e., recoverable from the observed data distribution) to justify causal claims. A recent line of work on counterfactual inference shows promising results but lacks identification, undermining the causal validity of its estimates. To address this, we establish a foundation for multivariate counterfactual identification using continuous-time flows, including non-Markovian settings under standard criteria. We characterise the conditions under which flow matching yields a unique, monotone, and rank-preserving counterfactual transport map with tools from dynamic optimal transport, ensuring consistent inference. Building on this, we validate the theory in controlled scenarios with counterfactual ground-truth and demonstrate improvements in axiomatic counterfactual soundness on real images.

LLM routing aims to select the most appropriate model for each query, balancing competing performance metrics such as accuracy and cost across a pool of language models. Prior approaches typically adopt a decoupled strategy, where metrics are first predicted and the model is then selected based on these estimates. This setup is prone to compounding errors and often relies on full-feedback data, where each query is evaluated by all candidate models, which is costly to obtain and maintain in practice. In contrast, we learn from observational data, which records only the outcome of the model actually deployed. We propose a causal end-to-end framework that learns routing policies by minimizing decision-making regret from observational data. To enable efficient optimization, we introduce two theoretically grounded surrogate objectives: a classification-based upper bound, and a softmaxweighted regret approximation shown to recover the optimal policy at convergence. We further extend our framework to handle heterogeneous cost preferences via an interval-conditioned architecture. Experiments on public benchmarks show that our method outperforms existing baselines, achieving state-of-the-art performance across different embedding models.

A central challenge in organ transplantation is the extremely low acceptance rate of donor organ offers--typically in the single digits--leading to high discard rates and suboptimal use of available grafts. Current acceptance models embedded in allocation systems are non-causal, trained on observational data, and fail to generalize to policy-relevant counterfactuals. This limits their reliability for both policy evaluation and simulator-based optimization. In this work, we reframe organ offer acceptance as a counterfactual prediction problem and propose a method to learn from routinely recorded--but often overlooked--refusal explanations. These refusal reasons act as direction-only counterfactual signals: for example, a refusal reason such as old donor age implies acceptance might have occurred had the donor been younger. We formalize this setting and introduce ClexNet, a novel causal model that learns policy-invariant representations via balanced training and an explanation-guided augmentation loss. On both synthetic and semi-synthetic data, ClexNet outperforms existing acceptance models in predictive performance, generalization, and calibration, offering a robust drop-in improvement for simulators and allocation policy evaluation. Beyond transplantation, our approach provides a general method for incorporating human direction-only explanations as a form of model supervision, improving performance in settings where only observational data is available.

In scientific domains---from biology to the social sciences---many questions boil down to \textit{What effect will we observe if we intervene on a particular variable?} If the causal relationships (e.g.~a causal graph) are known, its possible to estimate the intervention distributions. In the absence of this domain knowledge, the causal structure must be discovered from the available observational data. However, observational data are often compatible with multiple causal graphs, making methods that commit to a single structure prone to overconfidence. A principled way to manage this structural uncertainty is via Bayesian inference, which averages over a posterior distribution on possible causal structures and functional mechanisms.

Data-driven approaches, particularly those based on deep learning, are rapidly advancing Earth system modeling. However, their application to ocean forecasting remains limited despite the ocean's pivotal role in climate regulation and marine ecosystems. To address this gap, we present OceanBench, a benchmark designed to evaluate and accelerate global short-range (1-10 days) data-driven ocean forecasting.OceanBench is constructed from a curated dataset comprising first-guess trajectories, nowcasts, and atmospheric forcings from operational physical ocean models, typically unavailable in public datasets due to assimilation cycles. Matched observational data are also included, enabling realistic evaluation in an operational-like forecasting framework.The benchmark defines three complementary evaluation tracks: (i) Model-to-Reanalysis, where models are compared against the reanalysis dataset commonly used for training; (ii) Model-to-Analysis, assessing generalization to a higher-resolution physical analysis; and (iii) Model-to-Observations, Intercomparison and Validation (IV-TT) CLASS-4 evaluation against independent observational data. The first two tracks are further supported by process-oriented diagnostics to assess the dynamical consistency and physical plausibility of forecasts.OceanBench includes key ocean variables: sea surface height, temperature, salinity, and currents, along with standardized metrics grounded in physical oceanography. Baseline comparisons with operational systems and state-of-the-art deep learning models are provided.

Directed acyclic graphs (DAGs) constitute a central modeling tool to enable principled reasoning about cause-effect interactions in complex systems. However, since the causal structure underlying a group of variables is often unknown and interventions may be infeasible or ethically challenging to implement, there is a need to address the task of inferring DAGs from observational data. However, most classical structure identification approaches face two key obstacles: the combinatorial challenge of enforcing acyclicity, which severely limits scalability, and identifiability challenges arising from latent confounding or heterogeneous noise. This tutorial offers an overview of recent signal processing and optimization advances that address these issues by recasting DAG structure learning as a continuous, score-based estimation problem over adjacency matrices. We begin with a didactic introduction to structural equation models and the formulation of causal graph recovery, followed by a historical survey of score-based methods ranging from early combinatorial search schemes and greedy heuristics to modern continuous frameworks that leverage smooth characterizations of acyclicity. Building on this foundation, we describe concomitant DAG estimation methods that jointly infer sparse causal structure and exogenous noise levels, improving robustness under heteroscedasticity and distribution shifts by rendering the estimator noise adaptive. All in all, the tutorial introduces readers to challenges and opportunities for signal processing research at the crossroads of causal inference, high-dimensional statistics, and scalable graph learning, while outlining emerging directions including online, nonlinear, and neural causal discovery.