Nicola Branchini

Lena Zellinger, Nicola Branchini, Lennert De Smet et al.

Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive mixture models (SMMs), have been proposed as a potentially more expressive alternative. However, how to effectively use SMMs for VI and IS is still an open question as they do not provide latent variable semantics and therefore cannot use sampling schemes for classical MMs. In this work, we study how to circumvent this issue by designing several expectation estimators for IS and learning schemes for VI with SMMs, and we empirically evaluate them for distribution approximation. Finally, we discuss the additional challenges in estimation stability and learning efficiency that they carry and propose ways to overcome them. Code is available at: https://github.com/april-tools/delta-vi.

Nicola Branchini, Virginia Aglietti, Neil Dhir et al.

We study the problem of globally optimizing the causal effect on a target variable of an unknown causal graph in which interventions can be performed. This problem arises in many areas of science including biology, operations research and healthcare. We propose Causal Entropy Optimization (CEO), a framework that generalizes Causal Bayesian Optimization (CBO) to account for all sources of uncertainty, including the one arising from the causal graph structure. CEO incorporates the causal structure uncertainty both in the surrogate models for the causal effects and in the mechanism used to select interventions via an information-theoretic acquisition function. The resulting algorithm automatically trades-off structure learning and causal effect optimization, while naturally accounting for observation noise. For various synthetic and real-world structural causal models, CEO achieves faster convergence to the global optimum compared with CBO while also learning the graph. Furthermore, our joint approach to structure learning and causal optimization improves upon sequential, structure-learning-first approaches.

Oskar Kviman, Kirill Tamogashev, Nicola Branchini et al.

Learning the dynamics of a process given sampled observations at several time points is an important but difficult task in many scientific applications. When no ground-truth trajectories are available, but one has only snapshots of data taken at discrete time steps, the problem of modelling the dynamics, and thus inferring the underlying trajectories, can be solved by multi-marginal generalisations of flow matching algorithms. This paper proposes a novel flow matching method that overcomes the limitations of existing multi-marginal trajectory inference algorithms. Our proposed method, ALI-CFM, uses a GAN-inspired adversarial loss to fit neurally parametrised interpolant curves between source and target points such that the marginal distributions at intermediate time points are close to the observed distributions. The resulting interpolants are smooth trajectories that, as we show, are unique under mild assumptions. These interpolants are subsequently marginalised by a flow matching algorithm, yielding a trained vector field for the underlying dynamics. We showcase the versatility and scalability of our method by outperforming the existing baselines on spatial transcriptomics and cell tracking datasets, while performing on par with them on single-cell trajectory prediction. Code: https://github.com/mmacosha/adversarially-learned-interpolants.

Yorgos Felekis, Fabio Massimo Zennaro, Nicola Branchini et al.

Causal abstraction (CA) theory establishes formal criteria for relating multiple structural causal models (SCMs) at different levels of granularity by defining maps between them. These maps have significant relevance for real-world challenges such as synthesizing causal evidence from multiple experimental environments, learning causally consistent representations at different resolutions, and linking interventions across multiple SCMs. In this work, we propose COTA, the first method to learn abstraction maps from observational and interventional data without assuming complete knowledge of the underlying SCMs. In particular, we introduce a multi-marginal Optimal Transport (OT) formulation that enforces do-calculus causal constraints, together with a cost function that relies on interventional information. We extensively evaluate COTA on synthetic and real world problems, and showcase its advantages over non-causal, independent and aggregated COTA formulations. Finally, we demonstrate the efficiency of our method as a data augmentation tool by comparing it against the state-of-the-art CA learning framework, which assumes fully specified SCMs, on a real-world downstream task.

Lena Zellinger, Nicola Branchini, Víctor Elvira et al.

Many Monte Carlo (MC) and importance sampling (IS) methods use mixture models (MMs) for their simplicity and ability to capture multimodal distributions. Recently, subtractive mixture models (SMMs), i.e. MMs with negative coefficients, have shown greater expressiveness and success in generative modeling. However, their negative parameters complicate sampling, requiring costly auto-regressive techniques or accept-reject algorithms that do not scale in high dimensions. In this work, we use the difference representation of SMMs to construct an unbiased IS estimator ($Δ\text{Ex}$) that removes the need to sample from the SMM, enabling high-dimensional expectation estimation with SMMs. In our experiments, we show that $Δ\text{Ex}$ can achieve comparable estimation quality to auto-regressive sampling while being considerably faster in MC estimation. Moreover, we conduct initial experiments with $Δ\text{Ex}$ using hand-crafted proposals, gaining first insights into how to construct safe proposals for $Δ\text{Ex}$.