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Testing possible variations in fundamental constants of nature is a crucial endeavor in observational cosmology. This paper investigates potential cosmological variations in the fine structure constant ($\alpha$) through a non-parametric approach, using galaxy cluster observations as the primary cosmological probe. We employ two methodologies based on galaxy cluster gas mass fraction measurements derived from X-ray and Sunyaev-Zeldovich observations, along with luminosity distances from type Ia supernovae. We also explore how different values of the Hubble constant ($H_0$) impact the variation of $\alpha$ across cosmic history. When using the Planck satellite's $H_0$ observations, a constant $\alpha$ is ruled out at approximately the 3$\sigma$ confidence level for $z \lesssim 0.5$. Conversely, employing local estimates of $H_0$ restores agreement with a constant $\alpha$., Comment: 10 pages, 3 figures, I table. Accepted by the The European Physical Journal C

Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first derive novel metrics that balance accuracy in factual and counterfactual questions, capturing a more complete view of the reasoning abilities of language models than traditional factual-only based metrics. Second, we propose several fine-tuning approaches that aim to elicit better reasoning mechanisms, in the sense of the proposed metrics. Finally, we evaluate the performance of the fine-tuned language models in a variety of realistic scenarios. In particular, we investigate to what extent our fine-tuning approaches systemically achieve better generalization with respect to the base models in several problems that require, among others, inductive and deductive reasoning capabilities.

Matching is a popular approach in causal inference to estimate treatment effects by pairing treated and control units that are most similar in terms of their covariate information. However, classic matching methods completely ignore the geometry of the data manifold, which is crucial to define a meaningful distance for matching, and struggle when covariates are noisy and high-dimensional. In this work, we propose GeoMatching, a matching method to estimate treatment effects that takes into account the intrinsic data geometry induced by existing causal mechanisms among the confounding variables. First, we learn a low-dimensional, latent Riemannian manifold that accounts for uncertainty and geometry of the original input data. Second, we estimate treatment effects via matching in the latent space based on the learned latent Riemannian metric. We provide theoretical insights and empirical results in synthetic and real-world scenarios, demonstrating that GeoMatching yields more effective treatment effect estimators, even as we increase input dimensionality, in the presence of outliers, or in semi-supervised scenarios.

Recent advances in AI have been significantly driven by the capabilities of large language models (LLMs) to solve complex problems in ways that resemble human thinking. However, there is an ongoing debate about the extent to which LLMs are capable of actual reasoning. Central to this debate are two key probabilistic concepts that are essential for connecting causes to their effects: the probability of necessity (PN) and the probability of sufficiency (PS). This paper introduces a framework that is both theoretical and practical, aimed at assessing how effectively LLMs are able to replicate real-world reasoning mechanisms using these probabilistic measures. By viewing LLMs as abstract machines that process information through a natural language interface, we examine the conditions under which it is possible to compute suitable approximations of PN and PS. Our research marks an important step towards gaining a deeper understanding of when LLMs are capable of reasoning, as illustrated by a series of math examples.

In this work, we obtain Hubble constant ($H_0$) estimates by using two galaxy cluster gas mass fraction measurement samples, Type Ia supernovae luminosity distances, and the validity of the cosmic distance duality relation. Notably, the angular diameter distance (ADD) to each galaxy cluster in the samples is determined by combining its gas mass fraction measurement with galaxy clustering observations, more precisely, the $\Omega_b/\Omega_m$ ratio. Such a combination results in a $H_0$ estimate that is independent of a specific cosmological framework. In one of the samples, the gas fraction measurements were calculated in spherical shells at radii near $r_{\rm 2500}$ (44 data points), while in the other (103 data points) the measurements were calculated within $ r_{\rm 500}$. We find $H_0=72.7^{+6.3}_{-5.6}$ km/s/Mpc at 68\% CL for the joint analysis of these data sets. We also investigate the impact on the $H_0$ determination by exploring the precision and number of gas mass fraction data by performing a data Monte Carlo simulation. Our simulations show that future measurements could achieve a precision of up to 5\% for $H_0$., Comment: 9 pages, 5 figures. H0 estimate updated with joint analysis of the two gas mass fraction samples

It is well-known that Einstein's equations constrain only the total energy-momentum tensor of the cosmic substratum, without specifying the characteristics of its individual constituents. Consequently, cosmological models featuring distinct decompositions within the dark sector, while sharing identical values for the sum of dark components' energy-momentum tensor, remain indistinguishable when assessed through observables based on distance measurements. Notably, it has been already demonstrated that cosmological models with dynamical descriptions of dark energy, characterized by a time-dependent equation of state (EoS), can always be mapped into a model featuring a decaying vacuum ($w=-1$) coupled with dark matter. We explore the possibility of breaking this degeneracy by using measurements of the gas mass fraction observed in massive and relaxed galaxy clusters. This data is particularly interesting for this purpose because it isolates the matter contribution, possibly allowing the degeneracy breaking. We study the particular case of the $w$CDM model with its interactive counterpart. We compare the results obtained from both descriptions with a non-parametric analysis obtained through Gaussian Process. Even though the degeneracy may be broken from the theoretical point of view, we find that current gas mass fraction data seems to be insufficient for a final conclusion about which approach is favored, even when combined with SNIa, BAO and CMB., Comment: 14+2 pages, 4+4 figures, 3+1 tables. Comments are welcome

Synthetic control (SC) methods have gained rapid popularity in economics recently, where they have been applied in the context of inferring the effects of treatments on standard continuous outcomes assuming linear input-output relations. In medical applications, conversely, survival outcomes are often of primary interest, a setup in which both commonly assumed data-generating processes (DGPs) and target parameters are different. In this paper, we therefore investigate whether and when SCs could serve as an alternative to matching methods in survival analyses. We find that, because SCs rely on a linearity assumption, they will generally be biased for the true expected survival time in commonly assumed survival DGPs -- even when taking into account the possibility of linearity on another scale as in accelerated failure time models. Additionally, we find that, because SC units follow distributions with lower variance than real control units, summaries of their distributions, such as survival curves, will be biased for the parameters of interest in many survival analyses. Nonetheless, we also highlight that using SCs can still improve upon matching whenever the biases described above are outweighed by extrapolation biases exhibited by imperfect matches, and investigate the use of regularization to trade off the shortcomings of both approaches., Comment: To appear in the 3rd Conference on Causal Learning and Reasoning (CLeaR 2024)

Large language models (LLMs) are powerful AI tools that can generate and comprehend natural language text and other complex information. However, the field lacks a mathematical framework to systematically describe, compare and improve LLMs. We propose Hex a framework that clarifies key terms and concepts in LLM research, such as hallucinations, alignment, self-verification and chain-of-thought reasoning. The Hex framework offers a precise and consistent way to characterize LLMs, identify their strengths and weaknesses, and integrate new findings. Using Hex, we differentiate chain-of-thought reasoning from chain-of-thought prompting and establish the conditions under which they are equivalent. This distinction clarifies the basic assumptions behind chain-of-thought prompting and its implications for methods that use it, such as self-verification and prompt programming. Our goal is to provide a formal framework for LLMs that can help both researchers and practitioners explore new possibilities for generative AI. We do not claim to have a definitive solution, but rather a tool for opening up new research avenues. We argue that our formal definitions and results are crucial for advancing the discussion on how to build generative AI systems that are safe, reliable, fair and robust, especially in domains like healthcare and software engineering., Comment: 4 figures, 18 pages

The rapid digitization of real-world data offers an unprecedented opportunity for optimizing healthcare delivery and accelerating biomedical discovery. In practice, however, such data is most abundantly available in unstructured forms, such as clinical notes in electronic medical records (EMRs), and it is generally plagued by confounders. In this paper, we present TRIALSCOPE, a unifying framework for distilling real-world evidence from population-level observational data. TRIALSCOPE leverages biomedical language models to structure clinical text at scale, employs advanced probabilistic modeling for denoising and imputation, and incorporates state-of-the-art causal inference techniques to combat common confounders. Using clinical trial specification as generic representation, TRIALSCOPE provides a turn-key solution to generate and reason with clinical hypotheses using observational data. In extensive experiments and analyses on a large-scale real-world dataset with over one million cancer patients from a large US healthcare network, we show that TRIALSCOPE can produce high-quality structuring of real-world data and generates comparable results to marquee cancer trials. In addition to facilitating in-silicon clinical trial design and optimization, TRIALSCOPE may be used to empower synthetic controls, pragmatic trials, post-market surveillance, as well as support fine-grained patient-like-me reasoning in precision diagnosis and treatment., Comment: 6 Figures, 22 Pages, 3 Tables

We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes the class of morphisms of schemes for which the conclusion of the aforementioned Theorem holds. The key is giving a weaker definition of locally finitely presented morphisms.

Recent advances in immunomics have shown that T-cell receptor (TCR) signatures can accurately predict active or recent infection by leveraging the high specificity of TCR binding to disease antigens. However, the extreme diversity of the adaptive immune repertoire presents challenges in reliably identifying disease-specific TCRs. Population genetics and sequencing depth can also have strong systematic effects on repertoires, which requires careful consideration when developing diagnostic models. We present an Adaptive Immune Repertoire-Invariant Variational Autoencoder (AIRIVA), a generative model that learns a low-dimensional, interpretable, and compositional representation of TCR repertoires to disentangle such systematic effects in repertoires. We apply AIRIVA to two infectious disease case-studies: COVID-19 (natural infection and vaccination) and the Herpes Simplex Virus (HSV-1 and HSV-2), and empirically show that we can disentangle the individual disease signals. We further demonstrate AIRIVA's capability to: learn from unlabelled samples; generate in-silico TCR repertoires by intervening on the latent factors; and identify disease-associated TCRs validated using TCR annotations from external assay data.

Radio-loud quasars at high redshift (z > 4) are rare objects in the Universe and rarely observed with Very Long Baseline Interferometry (VLBI). But some of them have flux density sufficiently high for monitoring of their apparent position. The instability of the astrometric positions could be linked to the astrophysical process in the jetted active galactic nuclei in the early Universe. Regular observations of the high-redshift quasars are used for estimating their apparent proper motion over several years. We have undertaken regular VLBI observations of several high-redshift quasars at 2.3 GHz (S band) and 8.4 GHz (X band) with a network of five radio telescopes: 40-m Yebes (Spain), 25-m Sheshan (China), and three 32-m telescopes of the Quasar VLBI Network (Russia) -- Svetloe, Zelenchukskaya, and Badary. Additional facilities joined this network occasionally. The sources have also been observed in three sessions with the European VLBI Network (EVN) in 2018--2019 and one Long Baseline Array (LBA) experiment in 2018. In addition, several experiments conducted with the Very Long Baseline Array (VLBA) in 2017--2018were used to improve the time sampling and the statistics. Based on these 37 astrometric VLBI experiments between 2017 and 2021, we estimated the apparent proper motions of four quasars: 0901+697, 1428+422, 1508+572, and 2101+600.

Probing the solar corona is crucial to study the coronal heating and solar wind acceleration. However, the transient and inhomogeneous solar wind flows carry large-amplitude inherent Alfven waves and turbulence, which make detection more difficult. We report the oscillation and propagation of the solar wind at 2.6 solar radii (Rs) by observation of China Tianwen and ESA Mars Express with radio telescopes. The observations were carried out on Oct.9 2021, when one coronal mass ejection (CME) passed across the ray paths of the telescope beams. We obtain the frequency fluctuations (FF) of the spacecraft signals from each individual telescope. Firstly, we visually identify the drift of the frequency spikes at a high spatial resolution of thousands of kilometers along the projected baselines. They are used as traces to estimate the solar wind velocity. Then we perform the cross-correlation analysis on the time series of FF from different telescopes. The velocity variations of solar wind structure along radial and tangential directions during the CME passage are obtained. The oscillation of tangential velocity confirms the detection of streamer wave. Moreover, at the tail of the CME, we detect the propagation of an accelerating fast field-aligned density structure indicating the presence of magnetohydrodynamic waves. This study confirm that the ground station-pairs are able to form particular spatial projection baselines with high resolution and sensitivity to study the detailed propagation of the nascent dynamic solar wind structure., Comment: 13 pages, 9 figures

We prove that given a planar embedding of a graph in the sphere the expansion of the graph structure by predicates encoding separation of vertices by simple cycles of the graph is dp-minimal.

Astrometric positions of radio-emitting active galactic nuclei (AGNs) can be determined with sub-milliarcsec accuracy using very long baseline interferometry (VLBI). The usually small apparent proper motion of distant extragalactic targets allow us to realize the fundamental celestial reference frame with VLBI observations. However, long-term astrometric monitoring may reveal extreme changes in some AGN positions. Using new VLBI observations in 2018-2021, we show here that four extragalactic radio sources (3C48, CTA21, 1144+352, 1328+254) have a dramatic shift in their positions by 20-130 milliarcsec over two decades. For all four sources, the apparent positional shift is caused by their radio structure change., Comment: Accepted for publication in MNRAS

We prove that no subgroup of the group of boundary-fixing homeomorphisms of a compact surface whose action on the interior of the surface is sufficiently transitive can be Roelcke precompact with the topology inherited from the compact-open topology.

Bayesian quadrature (BQ) is a model-based numerical integration method that is able to increase sample efficiency by encoding and leveraging known structure of the integration task at hand. In this paper, we explore priors that encode invariance of the integrand under a set of bijective transformations in the input domain, in particular some unitary transformations, such as rotations, axis-flips, or point symmetries. We show initial results on superior performance in comparison to standard Bayesian quadrature on several synthetic and one real world application.

This paper studies the problem of performing a sequence of optimal interventions in a causal dynamical system where both the target variable of interest and the inputs evolve over time. This problem arises in a variety of domains e.g. system biology and operational research. Dynamic Causal Bayesian Optimization (DCBO) brings together ideas from sequential decision making, causal inference and Gaussian process (GP) emulation. DCBO is useful in scenarios where all causal effects in a graph are changing over time. At every time step DCBO identifies a local optimal intervention by integrating both observational and past interventional data collected from the system. We give theoretical results detailing how one can transfer interventional information across time steps and define a dynamic causal GP model which can be used to quantify uncertainty and find optimal interventions in practice. We demonstrate how DCBO identifies optimal interventions faster than competing approaches in multiple settings and applications.

Decision making in uncertain scenarios is an ubiquitous challenge in real world systems. Tools to deal with this challenge include simulations to gather information and statistical emulation to quantify uncertainty. The machine learning community has developed a number of methods to facilitate decision making, but so far they are scattered in multiple different toolkits, and generally rely on a fixed backend. In this paper, we present Emukit, a highly adaptable Python toolkit for enriching decision making under uncertainty. Emukit allows users to: (i) use state of the art methods including Bayesian optimization, multi-fidelity emulation, experimental design, Bayesian quadrature and sensitivity analysis; (ii) easily prototype new decision making methods for new problems. Emukit is agnostic to the underlying modeling framework and enables users to use their own custom models. We show how Emukit can be used on three exemplary case studies., Comment: Second Workshop on Machine Learning and the Physical Sciences, NeurIPS 2019

Feature attribution for kernel methods is often heuristic and not individualised for each prediction. To address this, we turn to the concept of Shapley values~(SV), a coalition game theoretical framework that has previously been applied to different machine learning model interpretation tasks, such as linear models, tree ensembles and deep networks. By analysing SVs from a functional perspective, we propose \textsc{RKHS-SHAP}, an attribution method for kernel machines that can efficiently compute both \emph{Interventional} and \emph{Observational Shapley values} using kernel mean embeddings of distributions. We show theoretically that our method is robust with respect to local perturbations - a key yet often overlooked desideratum for consistent model interpretation. Further, we propose \emph{Shapley regulariser}, applicable to a general empirical risk minimisation framework, allowing learning while controlling the level of specific feature's contributions to the model. We demonstrate that the Shapley regulariser enables learning which is robust to covariate shift of a given feature and fair learning which controls the SVs of sensitive features.

In this paper we study the elementary theory of graph products of groups and show that under natural conditions on the vertex groups we can recover (the core of) the underlying graph and the associated vertex groups. More precisely, we require the vertex groups to satisfy a non-generic almost positive sentence, a condition which generalizes a range of natural ``non-freeness conditions" such as the satisfaction of a group law, having nontrivial center or being boundedly simple. As a corollary, we determine an invariant of the elementary theory of a right-angled Artin group, the core of the defining graph, which we conjecture to determine the elementary class of the RAAG. We further combine our results with the results of Sela on free products of groups to describe all finitely generated groups elementarily equivalent to certain RAAGs. We also deduce rigidity results on the elementary classification of graph products of groups for specific types of vertex groups, such as finite, nilpotent or classical linear groups., Comment: 80 pages, 5 figures

While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where datasets pertaining to multiple causal graphs are combined to estimate the average treatment effect of a target variable. As data arises from multiple sources and can vary in quality and quantity, principled uncertainty quantification becomes essential. To that end, we introduce Bayesian Interventional Mean Processes, a framework which combines ideas from probabilistic integration and kernel mean embeddings to represent interventional distributions in the reproducing kernel Hilbert space, while taking into account the uncertainty within each causal graph. To demonstrate the utility of our uncertainty estimation, we apply our method to the Causal Bayesian Optimisation task and show improvements over state-of-the-art methods., Comment: 10 pages main text, 10 pages supplementary materials

The results of joint analyses of available cosmological data have motivated an important debate about a possible detection of a non-zero spatial curvature. If confirmed, such a result would imply a change in our present understanding of cosmic evolution with important theoretical and observational consequences. In this paper we discuss the legitimacy of carrying out joint analyses with the currently available data sets and explore their implications for a non-flat universe and extensions of the standard cosmological model. We use a robust tension estimator to perform a quantitative analysis of the physical consistency between the latest data of Cosmic Microwave Background, type Ia supernovae, Baryonic Acoustic Oscillations and Cosmic Chronometers. We consider the flat and non-flat cases of the $\Lambda$CDM cosmology and of two dark energy models with a constant and varying dark energy EoS parameter. The present study allows us to better understand if possible inconsistencies between these data sets are significant enough to make the results of their joint analyses misleading, as well as the actual dependence of such results with the spatial curvature and dark energy parameterizations., Comment: 11 pages, 6 figures, 1 table

Within the scientific goals of the THESEUS ESA/M5 candidate mission, a critical item is a fast (within a few s) and accurate (<15 arcmin) Gamma-Ray Burst and high-energy transient location from a few keV up to hard X-ray energy band. For that purpose, the signal multiplexing based on coded masks is the selected option to achieve this goal. This contribution is implemented by the XGIS Imaging System, based on that technique. The XGIS Imaging System has the heritage of previous payload developments: LEGRI/Minisat-01, INTEGRAL, UFFO/Lomonosov and ASIM/ISS. In particular the XGIS Imaging System is an upgrade of the ASIM system in operation since 2018 on the International Space Station. The scientific goal is similar: to detect a gamma-ray transient. But while ASIM focuses on Terrestrial Gamma-ray Flashes, THESEUS aims for the GRBs. For each of the two XGIS Cameras, the coded mask is located at 630 mm from the detector layer. The coding pattern is implemented in a Tungsten plate (1 mm thickness) providing a good multiplexing capability up to 150 keV. In that way both XGIS detector layers (based on Si and CsI detectors) have imaging capabilities at the medium - hard X-ray domain. This is an improvement achieved during the current THESEUS Phase-A. The mask is mounted on top of a collimator that provides the mechanical assembly support, as well as good cosmic X-ray background shielding. The XGIS Imaging System preliminary structural and thermal design, and the corresponding analyses, are included in this contribution, as it is a preliminary performance evaluation., Comment: Proceedings of the SPIE 2020, paper 11444-278

THESEUS is one of the three missions selected by ESA as fifth medium class mission (M5) candidates in its Cosmic Vision science program, currently under assessment in a phase A study with a planned launch date in 2032. THESEUS is designed to carry on-board two wide and deep sky monitoring instruments for X/gamma-ray transients detection: a wide-field soft X-ray monitor with imaging capability (Soft X-ray Imager, SXI, 0.3 - 5 keV), a hard X-ray, partially-imaging spectroscopic instrument (X and Gamma Imaging Spectrometer, XGIS, 2 keV - 10 MeV), and an optical/near-IR telescope with both imaging and spectroscopic capability (InfraRed Telescope, IRT, 0.7 - 1.8 $\mu$m). The spacecraft will be capable of performing fast repointing of the IRT to the error region provided by the monitors, thus allowing it to detect and localize the transient sources down to a few arcsec accuracy, for immediate identification and redshift determination. The prime goal of the XGIS will be to detect transient sources, with monitoring timescales down to milliseconds, both independently of, or following, up SXI detections, and identify the sources performing localisation at < 15 arcmin and characterize them over a broad energy band, thus providing also unique clues to their emission physics. The XGIS system consists of two independent but identical coded mask cameras, arranged to cover 2 steradians . The XGIS will exploit an innovative technology coupling Silicon Drift Detectors (SDD) with crystal scintillator bars and a very low-noise distributed front-end electronics (ORION ASICs), which will produce a position sensitive detection plane, with a large effective area over a huge energy band (from soft X-rays to soft gamma-rays) with timing resolution down to a few $\mu$s.Here is presented an overview of the XGIS instrument design, its configuration, and capabilities., Comment: Proceedings of the SPIE 2020, paper 11444-303

This paper describes a general-purpose extension of max-value entropy search, a popular approach for Bayesian Optimisation (BO). A novel approximation is proposed for the information gain -- an information-theoretic quantity central to solving a range of BO problems, including noisy, multi-fidelity and batch optimisations across both continuous and highly-structured discrete spaces. Previously, these problems have been tackled separately within information-theoretic BO, each requiring a different sophisticated approximation scheme, except for batch BO, for which no computationally-lightweight information-theoretic approach has previously been proposed. GIBBON (General-purpose Information-Based Bayesian OptimisatioN) provides a single principled framework suitable for all the above, out-performing existing approaches whilst incurring substantially lower computational overheads. In addition, GIBBON does not require the problem's search space to be Euclidean and so is the first high-performance yet computationally light-weight acquisition function that supports batch BO over general highly structured input spaces like molecular search and gene design. Moreover, our principled derivation of GIBBON yields a natural interpretation of a popular batch BO heuristic based on determinantal point processes. Finally, we analyse GIBBON across a suite of synthetic benchmark tasks, a molecular search loop, and as part of a challenging batch multi-fidelity framework for problems with controllable experimental noise.

The increasing availability of structured but high dimensional data has opened new opportunities for optimization. One emerging and promising avenue is the exploration of unsupervised methods for projecting structured high dimensional data into low dimensional continuous representations, simplifying the optimization problem and enabling the application of traditional optimization methods. However, this line of research has been purely methodological with little connection to the needs of practitioners so far. In this paper, we study the effect of different search space design choices for performing Bayesian Optimization in high dimensional structured datasets. In particular, we analyse the influence of the dimensionality of the latent space, the role of the acquisition function and evaluate new methods to automatically define the optimization bounds in the latent space. Finally, based on experimental results using synthetic and real datasets, we provide recommendations for the practitioners.

The calibration and analysis of polarization observations in Very Long Baseline Interferometry (VLBI) requires the use of specific algorithms that suffer from several limitations, closely related to assumptions in the data properties that may not hold in observations taken with new-generation VLBI equipment. Nowadays, the instantaneous bandwidth achievable with VLBI backends can be as high as several GHz, covering several radio bands simultaneously. In addition, the sensitivity of VLBI observations with state-of-the-art equipment may reach dynamic ranges of tens of thousands, both in total intensity and in polarization. In this paper, we discuss the impact of the limitations of common VLBI polarimetry algorithms on narrow-field observations taken with modern VLBI arrays (from the VLBI Global Observing System, VGOS, to the Event Horizon Telescope, EHT) and present new software that overcomes these limitations. In particular, our software is able to perform a simultaneous fit of multiple calibrator sources, include non-linear terms in the model of the instrumental polarization and use a self-calibration approach for the estimate of the polarization leakage in the antenna receivers., Comment: Accepted for publications in Astronomy and Astrophysics

Relaxing the conventional assumption of a minimal coupling between the dark matter (DM) and dark energy (DE) fields introduces significant changes in the predicted evolution of the Universe. Therefore, testing such a possibility constitutes an essential task not only for cosmology but also for fundamental physics. In a previous communication [Phys. Rev. D99, 043521, 2019], we proposed a new null test for the $\Lambda$CDM model based on the time dependence of the ratio between the DM and DE energy densities which is also able to detect potential signatures of interaction between the dark components. In this work, we extend that analysis avoiding the $ \Lambda$CDM assumption and reconstruct the interaction in the dark sector in a fully model-independent way using data from type Ia supernovae, cosmic chronometers and baryonic acoustic oscillations. According to our analysis, the $\Lambda$CDM model is consistent with our model-independent approach at least at $3\sigma$ CL over the entire range of redshift studied. On the other hand, our analysis shows that the current background data do not allow us to rule out the existence of an interaction in the dark sector. Finally, we present a forecast for next-generation LSS surveys. In particular, we show that Euclid and SKA will be able to distinguish interacting models with about 4\% of precision at $z\approx 1$., Comment: 12 pages, 7 figures. Accepted for publication in Physical Review D