arXiv subjects

Marta Sales-Pardo

Publications and source records attributed to Marta Sales-Pardo.

At least 19 recordsLinked to original sources

arXiv2026

Limits of spectral learning under noise

Learning functional relationships from noisy data is a central problem in scientific inference. Spectral methods approximate unknown functions by expanding them in a basis and estimating the corresponding coefficients from data, but the stability of these coefficients under noise remains poorly understood. Here we study supervised regression with additive label noise using sparse spectral representations across multiple bases and dimensions. We show that noise induces a predictable drift in the learned coefficient vector whose magnitude depends on the effective number of active spectral modes. After whitening the empirical feature geometry, we derive a closed-form expression for the overlap between noisy and noiseless coefficient vectors, revealing a universal degradation curve governed by a single intrinsic noise scale. Numerical experiments across Fourier, Legendre, Bessel, and Haar bases confirm the theoretical prediction. The results demonstrate that spectral learning exhibits a fundamental noise threshold beyond which coefficient estimates become unstable, placing intrinsic limits on recovering functional structure from noisy data.

cs.LG↗

arXiv2025

Integral Bayesian symbolic regression for optimal discovery of governing equations from scarce and noisy data

Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited, and existing approaches struggle, in particular, with the estimation of unobserved derivatives. Here, we introduce an integral Bayesian symbolic regression method that learns governing equations directly from raw time-series data, without requiring manual assumptions or error-prone derivative estimation. By sampling the space of symbolic differential equations and evaluating them via numerical integration, our method robustly identifies governing equations even from noisy or scarce data. We show that this approach accurately recovers ground-truth models in synthetic benchmarks, and that it makes quasi-optimal predictions of system dynamics for all noise regimes. Applying this method to bacterial growth experiments across multiple species and substrates, we discover novel growth equations that outperform classical models in accurately capturing all phases of microbial proliferation, including lag, exponential, and saturation. Unlike standard approaches, our method reveals subtle shifts in growth dynamics, such as double ramp-ups or non-canonical transitions, offering a deeper, data-driven understanding of microbial physiology.

physics.data-an↗

arXiv2025

Bayesian symbolic regression: Automated equation discovery from a physicists' perspective

Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic regularization, and heuristic exploration of model space. Here, we discuss the probabilistic approach to symbolic regression, an alternative to such heuristic approaches with direct connections to information theory and statistical physics. We show how the probabilistic approach establishes model plausibility from basic considerations and explicit approximations, and how it provides guarantees of performance that heuristic approaches lack. We also discuss how the probabilistic approach compels us to consider model ensembles, as opposed to single models.

stat.ML↗

arXiv2025

A collaborative constrained graph diffusion model for the generation of realistic synthetic molecules

Developing new molecular compounds is crucial to address pressing challenges, from health to environmental sustainability. However, exploring the molecular space to discover new molecules is difficult due to the vastness of the space. Here we introduce CoCoGraph, a collaborative and constrained graph diffusion model capable of generating molecules that are guaranteed to be chemically valid. Thanks to the constraints built into the model and to the collaborative mechanism, CoCoGraph outperforms state-of-the-art approaches on standard benchmarks while requiring up to an order of magnitude fewer parameters. Analysis of 36 chemical properties also demonstrates that CoCoGraph generates molecules with distributions more closely matching real molecules than current models. Leveraging the model's efficiency, we created a database of 8.2M million synthetically generated molecules and conducted a Turing-like test with organic chemistry experts to further assess the plausibility of the generated molecules, and potential biases and limitations of CoCoGraph.

cs.LG↗

arXiv2024

Gender and the influence of research environment in topic selection of early-career faculty in STEM

We study the influence that research environments have in shaping careers of early-career faculty in terms of their research portfolio. We find that departments exert an attractive force over early-career newcomer faculty, who after their incorporation increase their within-department collaborations, and work on topics closer to those of incumbent faculty. However, these collaborations are not gender blind: Newcomers collaborate less than expected with female senior incumbents. The analysis of departments grouped by fraction of female incumbents reveals that female newcomers in departments with above the median fractions of female incumbents tend to select research topics farther from their department than female newcomers in the remaining departments -- a difference we do not observe for male newcomers. Our results suggest a relationship between the collaboration deficit with female incumbents and the selection of research topics of female early-faculty, thus highlighting the importance of studying research environments to fully understand gender differences in academia.

physics.soc-ph↗

arXiv2023

Human mobility is well described by closed-form gravity-like models learned automatically from data

Modeling of human mobility is critical to address questions in urban planning and transportation, as well as global challenges in sustainability, public health, and economic development. However, our understanding and ability to model mobility flows within and between urban areas are still incomplete. At one end of the modeling spectrum we have simple so-called gravity models, which are easy to interpret and provide modestly accurate predictions of mobility flows. At the other end, we have complex machine learning and deep learning models, with tens of features and thousands of parameters, which predict mobility more accurately than gravity models at the cost of not being interpretable and not providing insight on human behavior. Here, we show that simple machine-learned, closed-form models of mobility are able to predict mobility flows more accurately, overall, than either gravity or complex machine and deep learning models. At the same time, these models are simple and gravity-like, and can be interpreted in terms similar to standard gravity models. Furthermore, these models work for different datasets and at different scales, suggesting that they may capture the fundamental universal features of human mobility.

physics.soc-ph↗

arXiv2023

Bayesian estimation of information-theoretic metrics for sparsely sampled distributions

Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled discrete distributions, is even harder. Existing approaches to address these problems have shortcomings: they are biased, heuristic, work only for some distributions, and/or cannot be applied to all information-theoretic metrics. Here, we propose a fast, semi-analytical estimator for sparsely sampled distributions that is efficient, precise, and general. Its derivation is grounded in probabilistic considerations and uses a hierarchical Bayesian approach to extract as much information as possible from the few observations available. Our approach provides estimates of the Shannon entropy with precision at least comparable to the state of the art, and most often better. It can also be used to obtain accurate estimates of any other information-theoretic metric, including the notoriously challenging Kullback-Leibler divergence. Here, again, our approach performs consistently better than existing estimators.

physics.data-an↗

arXiv2022

Fundamental limits to learning closed-form mathematical models from data

Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem displays a transition from a low-noise phase in which the true model can be learned, to a phase in which the observation noise is too high for the true model to be learned by any method. Both in the low-noise phase and in the high-noise phase, probabilistic model selection leads to optimal generalization to unseen data. This is in contrast to standard machine learning approaches, including artificial neural networks, which in this particular problem are limited, in the low-noise phase, by their ability to interpolate. In the transition region between the learnable and unlearnable phases, generalization is hard for all approaches including probabilistic model selection.

cs.LG↗

arXiv2022

Differences in collaboration structures and impact among prominent researchers in Europe and North America

Scientists collaborate through intricate networks, which impact the quality and scope of their research. At the same time, funding and institutional arrangements, as well as scientific and political cultures, affect the structure of collaboration networks. Since such arrangements and cultures differ across regions in the world in systematic ways, we surmise that collaboration networks and impact should also differ systematically across regions. To test this, we compare the structure of collaboration networks among prominent researchers in North America and Europe. We find that prominent researchers in Europe establish denser collaboration networks, whereas those in North-America establish more decentralized networks. We also find that the impact of the publications of prominent researchers in North America is significantly higher than for those in Europe, both when they collaborate with other prominent researchers and when they do not. Although Europeans collaborate with other prominent researchers more often, which increases their impact, we also find that repeated collaboration among prominent researchers decreases the synergistic effect of collaborating.

physics.soc-ph↗

arXiv2021

Node metadata can produce predictability transitions in network inference problems

Network inference is the process of learning the properties of complex networks from data. Besides using information about known links in the network, node attributes and other forms of network metadata can help to solve network inference problems. Indeed, several approaches have been proposed to introduce metadata into probabilistic network models and to use them to make better inferences. However, we know little about the effect of such metadata in the inference process. Here, we investigate this issue. We find that, rather than affecting inference gradually, adding metadata causes abrupt transitions in the inference process and in our ability to make accurate predictions, from a situation in which metadata does not play any role to a situation in which metadata completely dominates the inference process. When network data and metadata are partly correlated, metadata optimally contributes to the inference process at the transition between data-dominated and metadata-dominated regimes.

physics.data-an↗

arXiv2021

Complex decision-making strategies in a stock market experiment explained as the combination of few simple strategies

Many studies have shown that there are regularities in the way human beings make decisions. However, our ability to obtain models that capture such regularities and can accurately predict unobserved decisions is still limited. We tackle this problem in the context of individuals who are given information relative to the evolution of market prices and asked to guess the direction of the market. We use a networks inference approach with stochastic block models (SBM) to find the model and network representation that is most predictive of unobserved decisions. Our results suggest that users mostly use recent information (about the market and about their previous decisions) to guess. Furthermore, the analysis of SBM groups reveals a set of strategies used by players to process information and make decisions that is analogous to behaviors observed in other contexts. Our study provides and example on how to quantitatively explore human behavior strategies by representing decisions as networks and using rigorous inference and model-selection approaches.

q-fin.GN↗

arXiv2020

A Bayesian machine scientist to aid in the solution of challenging scientific problems

Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social sciences. However, to deal with increasing amounts of data, we need "machine scientists" that are able to extract these models automatically from data. Here, we introduce a Bayesian machine scientist, which establishes the plausibility of models using explicit approximations to the exact marginal posterior over models and establishes its prior expectations about models by learning from a large empirical corpus of mathematical expressions. It explores the space of models using Markov chain Monte Carlo. We show that this approach uncovers accurate models for synthetic and real data and provides out-of-sample predictions that are more accurate than those of existing approaches and of other nonparametric methods.

cs.LG↗

arXiv2020

Optimal prediction of decisions and model selection in social dilemmas using block models

Advancing our understanding of human behavior hinges on the ability of theories to unveil the mechanisms underlying such behaviors. Measuring the ability of theories and models to predict unobserved behaviors provides a principled method to evaluate their merit and, thus, to help establish which mechanisms are most plausible. Here, we propose models and develop rigorous inference approaches to predict strategic decisions in dyadic social dilemmas. In particular, we use bipartite stochastic block models that incorporate information about the dilemmas faced by individuals. We show, combining these models with empirical data on strategic decisions in dyadic social dilemmas, that individual strategic decisions are to a large extent predictable, despite not being "rational." The analysis of these models also allows us to conclude that: (i) individuals do not perceive games according their game-theoretical structure; (ii) individuals make decisions using combinations of multiple simple strategies, which our approach reveals naturally.

physics.soc-ph↗

arXiv2020

Network-based models for social recommender systems

With the overwhelming online products available in recent years, there is an increasing need to filter and deliver relevant personalized advice for users. Recommender systems solve this problem by modeling and predicting individual preferences for a great variety of items such as movies, books or research articles. In this chapter, we explore rigorous network-based models that outperform leading approaches for recommendation. The network models we consider are based on the explicit assumption that there are groups of individuals and of items, and that the preferences of an individual for an item are determined only by their group memberships. The accurate prediction of individual user preferences over items can be accomplished by different methodologies, such as Monte Carlo sampling or Expectation-Maximization methods, the latter resulting in a scalable algorithm which is suitable for large datasets.

stat.ML↗

arXiv2018

Consistencies and inconsistencies between model selection and link prediction in networks

A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most of cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible, than when we consider only the single most plausible model.

stat.ML↗

arXiv2018

Tensorial and bipartite block models for link prediction in layered networks and temporal networks

Many real-world complex systems are well represented as multilayer networks; predicting interactions in those systems is one of the most pressing problems in predictive network science. To address this challenge, we introduce two stochastic block models for multilayer and temporal networks; one of them uses nodes as its fundamental unit, whereas the other focuses on links. We also develop scalable algorithms for inferring the parameters of these models. Because our models describe all layers simultaneously, our approach takes full advantage of the information contained in the whole network when making predictions about any particular layer. We illustrate the potential of our approach by analyzing two empirical datasets---a temporal network of email communications, and a network of drug interactions for treating different cancer types. We find that modeling all layers simultaneously does result, in general, in more accurate link prediction. However, the most predictive model depends on the dataset under consideration; whereas the node-based model is more appropriate for predicting drug interactions, the link-based model is more appropriate for predicting email communication.

physics.soc-ph↗

arXiv2017

Inferring propagation paths for sparsely observed perturbations on complex networks

In a complex system, perturbations propagate by following paths on the network of interactions among the system's units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very sparse in time (there is a single observation of the perturbed system) and in "space" (only a few perturbed and unperturbed units are observed). A major challenge in many areas, from biology to the social sciences, is to infer the propagation paths from observations of the effects of perturbation under these sparsity conditions. We address this problem and show that it is possible to go beyond the usual approach of using the shortest paths connecting the known perturbed nodes. Specifically, we show that a simple and general probabilistic model, which we solved using belief propagation, provides fast and accurate estimates of the probabilities of nodes being perturbed.

cs.SI↗

arXiv2016

Bone fusion in normal and pathological development is constrained by the network architecture of the human skull

The premature fusion of cranial bones, craniosynostosis, affects the correct development of the skull producing morphological malformations in newborns. To assess the susceptibility of each craniofacial articulation to close prematurely, we used a network model of the skull to quantify the link reliability (an index based on stochastic block modeling and Bayesian inference) of each articulation. We show that, of the 93 human skull articulations at birth, the few articulations that are associated with nonsyndromic craniosynostosis conditions have statistically significant lower reliability scores than the others. In a similar way, articulations that close during the normal postnatal development of the skull have also lower reliability scores than those articulations that persist through adult live. These results indicate a relationship between the architecture of the skull network and the specific articulations that close during normal development and in pathological conditions. Our findings suggest that the topological arrangement of skull bones might act as an epigenetic factor, predisposing some articulations to closure, both in normal and pathological development, and also affecting the long-term evolution of the skull.

q-bio.TO↗