In this paper, we focus on estimating the causal effect of an intervention over time on a dynamical system. To that end, we formally define causal interventions and their effects over time on discrete-time stochastic processes (DSPs). Then, we show under which conditions the equilibrium states of a DSP, both before and after a causal intervention, can be captured by a structural causal model (SCM). With such an equivalence at hand, we provide an explicit mapping from vector autoregressive models (VARs), broadly applied in econometrics, to linear, but potentially cyclic and/or affected by unmeasured confounders, SCMs. The resulting causal VAR framework allows us to perform causal inference over time from observational time series data. Our experiments on synthetic and real-world datasets show that the proposed framework achieves strong performance in terms of observational forecasting while enabling accurate estimation of the causal effect of interventions on dynamical systems. We demonstrate, through a case study, the potential practical questions that can be addressed using the proposed causal VAR framework.

To ensure that Machine Learning systems produce unharmful outcomes, pursuing a joint optimization of performance and ethical profiles such as privacy and fairness is crucial. However, jointly optimizing these two ethical dimensions while maintaining predictive accuracy remains a fundamental challenge. Indeed, privacy-preserving techniques may worsen fairness and restrain the model’s ability to learn accurate statistical patterns, while data mitigation techniques may inadvertently compromise privacy. Aiming to bridge this gap, we propose safeGen, a preprocessing fairness enhancing and privacy-preserving method for tabular data. SafeGen employs synthetic data generation through a genetic algorithm to ensure that sensitive attributes are protected while maintaining the necessary statistical properties. We assess our method across multiple datasets, comparing it against state-of-the-art privacy-preserving and fairness approaches through a threefold evaluation: privacy preservation, fairness enhancement, and generated data plausibility. Through extensive experiments, we demonstrate that SafeGen consistently achieves strong anonymization while preserving or improving dataset fairness across several benchmarks. Additionally, through hybrid privacy-fairness constraints and the use of a genetic synthesizer, SafeGen ensures the plausibility of synthetic records while minimizing discrimination. Our findings demonstrate that modeling fairness and privacy within a unified generative method yields significantly better outcomes than addressing these constraints separately, reinforcing the importance of integrated approaches when multiple ethical objectives must be simultaneously satisfied.

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize an optimization problem with a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper, we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method lies a novel differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous works, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite this absence, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.