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Most real-world systems exhibit a multiscale behaviour that needs to be taken into consideration when fitting the effective dynamics to data sampled at a given scale. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the Maximum Likelihood Estimators of the parameters of the limiting dynamics to be consistent, data needs to be subsampled at an appropriate rate. Recent advances in extracting effective dynamics for fractional multiscale systems make the same question relevant in the fractional diffusion setting. We study the problem of parameter estimation of the diffusion coefficient in this context. In particular, we consider the multiscale fractional Ornstein-Uhlenbeck system (fractional kinetic Brownian motion) and we provide convergence results for the Maximum Likelihood Estimator of the diffusion coefficient of the limiting dynamics, using multiscale data. To do so, we derive asymptotic bounds for the spectral norm of the inverse covariance matrix of fractional Gaussian noise., Comment: 34 pages, 5 figures

Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the task at hand, thus hindering the interpretability of their predictions. In contrast to prior work, in this paper we propose a GNN \emph{training} approach that jointly i) finds the most predictive subgraph by removing edges and/or nodes -- -\emph{without making assumptions about the subgraph structure} -- while ii) optimizing the performance of the graph classification task. To that end, we rely on reinforcement learning to solve the resulting bi-level optimization with a reward function based on conformal predictions to account for the current in-training uncertainty of the classifier. Our empirical results on nine different graph classification datasets show that our method competes in performance with baselines while relying on significantly sparser subgraphs, leading to more interpretable GNN-based predictions.

Ambient awareness refers to the ability of social media users to obtain knowledge about who knows what (i.e., users' expertise) in their network, by simply being exposed to other users' content (e.g, tweets on Twitter). Previous work, based on user surveys, reveals that individuals self-report ambient awareness only for parts of their networks. However, it is unclear whether it is their limited cognitive capacity or the limited exposure to diagnostic tweets (i.e., online content) that prevents people from developing ambient awareness for their complete network. In this work, we focus on in-wall ambient awareness (IWAA) in Twitter and conduct a two-step data-driven analysis, that allows us to explore to which extent IWAA is likely, or even possible. First, we rely on reactions (e.g., likes), as strong evidence of users being aware of experts in Twitter. Unfortunately, such strong evidence can be only measured for active users, which represent the minority in the network. Thus to study the boundaries of IWAA to a larger extent, in the second part of our analysis, we instead focus on the passive exposure to content generated by other users -- which we refer to as in-wall visibility. This analysis shows that (in line with \citet{levordashka2016ambient}) only for a subset of users IWAA is plausible, while for the majority it is unlikely, if even possible, to develop IWAA. We hope that our methodology paves the way for the emergence of data-driven approaches for the study of ambient awareness.

Determining the size distribution of asteroids is key for understanding the collisional history and evolution of the inner Solar System. We aim at improving our knowledge on the size distribution of small asteroids in the Main Belt by determining the parallaxes of newly detected asteroids in the Hubble Space Telescope (HST) Archive and hence their absolute magnitudes and sizes. Asteroids appear as curved trails in HST images due to the parallax induced by the fast orbital motion of the spacecraft. The parallax effect can be computed to obtain the distance to the asteroids by fitting simulated trajectories to the observed trails. Using distance, we can obtain the object's absolute magnitude and size estimation assuming an albedo value, along with some boundaries for its orbital parameters. In this work we analyse a set of 632 serendipitously imaged asteroids found in the ESA HST Archive. An object-detection machine learning algorithm was used to perform this task during previous work. Our raw data consists of 1,031 asteroids trails from unknown objects (not matching any entries in the MPC database). We also found 670 trails from known objects (objects featuring matching entries in the MPC). After an accuracy assessment and filtering process, our analysed HST set consists of 454 unknown objects and 178 known objects. We obtain a sample dominated by potential Main Belt objects featuring absolute magnitudes (H) mostly between 15 and 22 mag. The absolute magnitude cumulative distribution confirms the previously reported slope change for 15 < H < 18, from 0.56 to 0.26, maintained in our case down to absolute magnitudes around H = 20, hence expanding the previous results by approximately two magnitudes. HST archival observations can be used as an asteroid survey since the telescope pointings are statistically randomly oriented in the sky and they cover long periods of time., Comment: Accepted for publication in A&A. 10 pages, 2 tables, 17 figures

In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and thus can be recovered using autoregressive normalizing flows (NFs). Second, we analyze different design and learning choices for causal normalizing flows to capture the underlying causal data-generating process. Third, we describe how to implement the do-operator in causal NFs, and thus, how to answer interventional and counterfactual questions. Finally, in our experiments, we validate our design and training choices through a comprehensive ablation study; compare causal NFs to other approaches for approximating causal models; and empirically demonstrate that causal NFs can be used to address real-world problems, where the presence of mixed discrete-continuous data and partial knowledge on the causal graph is the norm. The code for this work can be found at https://github.com/psanch21/causal-flows., Comment: 32 pages, 15 figures. Accepted as an Oral presentation at NeurIPS 2023

Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VAMoH. VAMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VAMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VAMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VAMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding., Comment: Accepted at ICML 2023. Camera ready version

Existing Graph Neural Networks (GNNs) compute the message exchange between nodes by either aggregating uniformly (convolving) the features of all the neighboring nodes, or by applying a non-uniform score (attending) to the features. Recent works have shown the strengths and weaknesses of the resulting GNN architectures, respectively, GCNs and GATs. In this work, we aim at exploiting the strengths of both approaches to their full extent. To this end, we first introduce the graph convolutional attention layer (CAT), which relies on convolutions to compute the attention scores. Unfortunately, as in the case of GCNs and GATs, we show that there exists no clear winner between the three (neither theoretically nor in practice) as their performance directly depends on the nature of the data (i.e., of the graph and features). This result brings us to the main contribution of our work, the learnable graph convolutional attention network (L-CAT): a GNN architecture that automatically interpolates between GCN, GAT and CAT in each layer, by adding only two scalar parameters. Our results demonstrate that L-CAT is able to efficiently combine different GNN layers along the network, outperforming competing methods in a wide range of datasets, and resulting in a more robust model that reduces the need of cross-validating., Comment: Published as a conference paper at ICLR 2023. 35 pages, 5 figures

Large and publicly available astronomical archives open up new possibilities to search and study Solar System objects. However, advanced techniques are required to deal with the large amounts of data. These unbiased surveys can be used to constrain the size distribution of minor bodies, which represents a piece of the puzzle for the formation models of the Solar System. We aim to identify asteroids in archival images from the ESA Hubble Space Telescope (HST) Science data archive using data mining. We developed a citizen science project on the Zooniverse platform, Hubble Asteroid Hunter (www.asteroidhunter.org) asking members of the public to identify asteroid trails in archival HST images. We used the labels provided by the volunteers to train an automated deep learning model built with Google Cloud AutoML Vision to explore the entire HST archive to detect asteroids crossing the field-of-view. We report the detection of 1701 new asteroid trails identified in archival HST data via our citizen science project and the subsequent machine learning exploration of the ESA HST science data archive. We detect asteroids to a magnitude of 24.5, which are statistically fainter than the populations of asteroids identified from ground-based surveys. The majority of asteroids are distributed near the ecliptic plane, as expected, where we find an approximate density of 80 asteroids per square degree. We match 670 trails (39% of the trails found) with 454 known Solar System objects in the Minor Planet Center database, however, no matches are found for 1031 (61%) trails. The unidentified asteroids are faint, being on average 1.6 magnitudes fainter than the asteroids we succeeded to identify. They probably correspond to previously unknown objects. This work demonstrates that citizen science and machine learning are useful techniques for the systematic search of SSOs in existing astronomy science archives., Comment: 15 pages, 16 figures, 2 tables. Replaced to match the A&A journal version, https://www.aanda.org/10.1051/0004-6361/202142998

In this paper, we introduce VACA, a novel class of variational graph autoencoders for causal inference in the absence of hidden confounders, when only observational data and the causal graph are available. Without making any parametric assumptions, VACA mimics the necessary properties of a Structural Causal Model (SCM) to provide a flexible and practical framework for approximating interventions (do-operator) and abduction-action-prediction steps. As a result, and as shown by our empirical results, VACA accurately approximates the interventional and counterfactual distributions on diverse SCMs. Finally, we apply VACA to evaluate counterfactual fairness in fair classification problems, as well as to learn fair classifiers without compromising performance.

We propose a novel training procedure for improving the performance of generative adversarial networks (GANs), especially to bidirectional GANs. First, we enforce that the empirical distribution of the inverse inference network matches the prior distribution, which favors the generator network reproducibility on the seen samples. Second, we have found that the marginal log-likelihood of the samples shows a severe overrepresentation of a certain type of samples. To address this issue, we propose to train the bidirectional GAN using a non-uniform sampling for the mini-batch selection, resulting in improved quality and variety in generated samples measured quantitatively and by visual inspection. We illustrate our new procedure with the well-known CIFAR10, Fashion MNIST and CelebA datasets.

We propose a new method to evaluate GANs, namely EvalGAN. EvalGAN relies on a test set to directly measure the reconstruction quality in the original sample space (no auxiliary networks are necessary), and it also computes the (log)likelihood for the reconstructed samples in the test set. Further, EvalGAN is agnostic to the GAN algorithm and the dataset. We decided to test it on three state-of-the-art GANs over the well-known CIFAR-10 and CelebA datasets.