Federico Baldo

Mattia Silvestri, Federico Baldo, Eleonora Misino et al.

In the last decade, the scientific community has devolved its attention to the deployment of data-driven approaches in scientific research to provide accurate and reliable analysis of a plethora of phenomena. Most notably, Physics-informed Neural Networks and, more recently, Universal Differential Equations (UDEs) proved to be effective both in system integration and identification. However, there is a lack of an in-depth analysis of the proposed techniques. In this work, we make a contribution by testing the UDE framework in the context of Ordinary Differential Equations (ODEs) discovery. In our analysis, performed on two case studies, we highlight some of the issues arising when combining data-driven approaches and numerical solvers, and we investigate the importance of the data collection process. We believe that our analysis represents a significant contribution in investigating the capabilities and limitations of Physics-informed Machine Learning frameworks.

Federico Baldo, Charles K. Assaad

Most causal discovery methods recover a completed partially directed acyclic graph representing a Markov equivalence class from observational data. Recent work has extended these methods to federated settings to address data decentralization and privacy constraints, but often under idealized assumptions that all clients share the same causal model. Such assumptions are unrealistic in practice, as client-specific policies or protocols, for example, across hospitals, naturally induce heterogeneous and unknown interventions. In this work, we address federated causal discovery under unknown client-level interventions. We propose I-PERI, a novel federated algorithm that first recovers the CPDAG of the union of client graphs and then orients additional edges by exploiting structural differences induced by interventions across clients. This yields a tighter equivalence class, which we call the $\mathbfΦ$-Markov Equivalence Class, represented by the $\mathbfΦ$-CPDAG. We provide theoretical guarantees on the convergence of I-PERI, as well as on its privacy-preserving properties, and present empirical evaluations on synthetic data demonstrating the effectiveness of the proposed algorithm.

Matteo Testi, Luca Clissa, Matteo Ballabio et al.

Machine Learning (ML) models offer significant potential for advancing cell counting applications in neuroscience, medical research, pharmaceutical development, and environmental monitoring. However, implementing these models effectively requires robust operational frameworks. This paper introduces Cell Counting Machine Learning Operations (CC-MLOps), a comprehensive framework that streamlines the integration of ML in cell counting workflows. CC-MLOps encompasses data access and preprocessing, model training, monitoring, explainability features, and sustainability considerations. Through a practical use case, we demonstrate how MLOps principles can enhance model reliability, reduce human error, and enable scalable Cell Counting solutions. This work provides actionable guidance for researchers and laboratory professionals seeking to implement machine learning (ML)- powered cell counting systems.

Federico Baldo, Simon Ferreira, Charles K. Assaad

Traditional causal discovery methods often rely on strong, untestable assumptions, which makes them unreliable in real applications. In this context, Large Language Models (LLMs) have emerged as a promising alternative for extracting causal knowledge from text-based metadata, which consolidates domain expertise. However, LLMs tend to be unreliable and prone to hallucinations, necessitating strategies that account for their limitations. One effective strategy is to use a consistency measure to assess reliability. Additionally, most text metadata does not clearly distinguish direct causal relationships from indirect ones, further complicating the discovery of a causal DAG. As a result, focusing on causal orders, rather than causal DAGs, emerges as a more practical and robust approach. We present a new method to derive a class of acyclic tournaments, which represent plausible causal orders, maximizing a consistency score derived from an LLM. Our approach starts by calculating pairwise consistency scores between variables, resulting in a semi-complete partially directed graph that consolidates these scores into an abstraction of the maximally consistent causal orders. Using this structure, we identify optimal acyclic tournaments, focusing on those that maximize consistency across all configurations. We subsequently show how both the abstraction and the class of causal orders can be used to estimate causal effects. We tested our method on both well-established benchmarks, as well as, real-world datasets from epidemiology and public health. Our results demonstrate the effectiveness of our approach in recovering the correct causal order.

Federico Baldo, Lorenzo Dall'Olio, Mattia Ceccarelli et al.

The advent of the coronavirus pandemic has sparked the interest in predictive models capable of forecasting virus-spreading, especially for boosting and supporting decision-making processes. In this paper, we will outline the main Deep Learning approaches aimed at predicting the spreading of a disease in space and time. The aim is to show the emerging trends in this area of research and provide a general perspective on the possible strategies to approach this problem. In doing so, we will mainly focus on two macro-categories: classical Deep Learning approaches and Hybrid models. Finally, we will discuss the main advantages and disadvantages of different models, and underline the most promising development directions to improve these approaches.

Michele Lombardi, Federico Baldo, Andrea Borghesi et al.

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the learner) and the regularization term (the degree of constraint satisfaction). The key results of this paper is the formal demonstration that this type of approach cannot guarantee to find all optimal solutions. In particular, in the non-convex case there might be optima for the constrained problem that do not correspond to any multiplier value.

Andrea Borghesi, Federico Baldo, Michela Milano

Deep Learning (DL) models proved themselves to perform extremely well on a wide variety of learning tasks, as they can learn useful patterns from large data sets. However, purely data-driven models might struggle when very difficult functions need to be learned or when there is not enough available training data. Fortunately, in many domains prior information can be retrieved and used to boost the performance of DL models. This paper presents a first survey of the approaches devised to integrate domain knowledge, expressed in the form of constraints, in DL learning models to improve their performance, in particular targeting deep neural networks. We identify five (non-mutually exclusive) categories that encompass the main approaches to inject domain knowledge: 1) acting on the features space, 2) modifications to the hypothesis space, 3) data augmentation, 4) regularization schemes, 5) constrained learning.

Andrea Borghesi, Federico Baldo, Michele Lombardi et al.

Machine Learning (ML) models are very effective in many learning tasks, due to the capability to extract meaningful information from large data sets. Nevertheless, there are learning problems that cannot be easily solved relying on pure data, e.g. scarce data or very complex functions to be approximated. Fortunately, in many contexts domain knowledge is explicitly available and can be used to train better ML models. This paper studies the improvements that can be obtained by integrating prior knowledge when dealing with a non-trivial learning task, namely precision tuning of transprecision computing applications. The domain information is injected in the ML models in different ways: I) additional features, II) ad-hoc graph-based network topology, III) regularization schemes. The results clearly show that ML models exploiting problem-specific information outperform the purely data-driven ones, with an average accuracy improvement around 38%.

Ferdinando Fioretto, Pascal Van Hentenryck, Terrence WK Mak et al.

This paper explores the potential of Lagrangian duality for learning applications that feature complex constraints. Such constraints arise in many science and engineering domains, where the task amounts to learning optimization problems which must be solved repeatedly and include hard physical and operational constraints. The paper also considers applications where the learning task must enforce constraints on the predictor itself, either because they are natural properties of the function to learn or because it is desirable from a societal standpoint to impose them. This paper demonstrates experimentally that Lagrangian duality brings significant benefits for these applications. In energy domains, the combination of Lagrangian duality and deep learning can be used to obtain state-of-the-art results to predict optimal power flows, in energy systems, and optimal compressor settings, in gas networks. In transprecision computing, Lagrangian duality can complement deep learning to impose monotonicity constraints on the predictor without sacrificing accuracy. Finally, Lagrangian duality can be used to enforce fairness constraints on a predictor and obtain state-of-the-art results when minimizing disparate treatments.