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The amount of debris in orbit has increased significantly over the years. With the recent growth of interest in space exploration, conjunction assessment has become a central issue. One important metric to evaluate conjunction risk is the miss distance. However, this metric does not intrinsically take into account uncertainty distributions. Some work has been developed to consider the uncertainty associated with the position of the orbiting objects, in particular, to know if these uncertainty distributions overlap (e.g., ellipsoids when considering Gaussian distributions). With this work, we present fast solutions to not only check if the ellipsoids overlap but to compute the distance between them, which we call margin. We present two fast solution methods for two different paradigms: when the best-known data from both objects can be centralized (e.g., debris-satellite conjunctions) and when the most precise covariances cannot be shared (conjunctions of satellites owned by different operators). Our methods are both accurate and fast, being able to process 15,000 conjunctions per minute with the centralized solution and approximately 490 conjunctions per minute with the distributed solution.

With the increase in the number of active satellites and space debris in orbit, the problem of initial orbit determination (IOD) becomes increasingly important, demanding a high accuracy. Over the years, different approaches have been presented such as filtering methods (for example, Extended Kalman Filter), differential algebra or solving Lambert's problem. In this work, we consider a setting of three monostatic radars, where all available measurements are taken approximately at the same instant. This follows a similar setting as trilateration, a state-of-the-art approach, where each radar is able to obtain a single measurement of range and range-rate. Differently, and due to advances in Multiple-Input Multiple-Output (MIMO) radars, we assume that each location is able to obtain a larger set of range, angle and Doppler shift measurements. Thus, our method can be understood as an extension of trilateration leveraging more recent technology and incorporating additional data. We formulate the problem as a Maximum Likelihood Estimator (MLE), which for some number of observations is asymptotically unbiased and asymptotically efficient. Through numerical experiments, we demonstrate that our method attains the same accuracy as the trilateration method for the same number of measurements and offers an alternative and generalization, returning a more accurate estimation of the satellite's state vector, as the number of available measurements increases.

The increasing volume of space objects in Earth's orbit presents a significant challenge for Space Situational Awareness (SSA). And in particular, accurate orbit prediction is crucial to anticipate the position and velocity of space objects, for collision avoidance and space debris mitigation. When performing Orbit Prediction (OP), it is necessary to consider the impact of non-conservative forces, such as atmospheric drag and gravitational perturbations, that contribute to uncertainty around the future position of spacecraft and space debris alike. Conventional propagator methods like the SGP4 inadequately account for these forces, while numerical propagators are able to model the forces at a high computational cost. To address these limitations, we propose an orbit prediction algorithm utilizing machine learning. This algorithm forecasts state vectors on a spacecraft using past positions and environmental variables like atmospheric density from external sources. The orbital data used in the paper is gathered from precision ephemeris data from the International Laser Ranging Service (ILRS), for the period of almost a year. We show how the use of machine learning and time-series techniques can produce low positioning errors at a very low computational cost, thus significantly improving SSA capabilities by providing faster and reliable orbit determination for an ever increasing number of space objects., Comment: presented at IEEE WCCI CEC Congress 2024

Communication overhead is a known bottleneck in federated learning (FL). To address this, lossy compression is commonly used on the information communicated between the server and clients during training. In horizontal FL, where each client holds a subset of the samples, such communication-compressed training methods have recently seen significant progress. However, in their vertical FL counterparts, where each client holds a subset of the features, our understanding remains limited. To address this, we propose an error feedback compressed vertical federated learning (EFVFL) method to train split neural networks. In contrast with previous communication-compressed methods for vertical FL, EFVFL does not require a vanishing compression error for the gradient norm to converge to zero for smooth nonconvex problems. By leveraging error feedback, our method can achieve a $\mathcal{O}(1/T)$ convergence rate in the full-batch case, improving over the state-of-the-art $\mathcal{O}(1/\sqrt{T})$ rate under $\mathcal{O}(1/\sqrt{T})$ compression error, and matching the rate of uncompressed methods. Further, when the objective function satisfies the Polyak-{\L}ojasiewicz inequality, our method converges linearly. In addition to improving convergence rates, our method also supports the use of private labels. Numerical experiments show that EFVFL significantly improves over the prior art, confirming our theoretical results.

Research on supervised learning algorithms in 3D scene understanding has risen in prominence and witness great increases in performance across several datasets. The leading force of this research is the problem of autonomous driving followed by indoor scene segmentation. However, openly available 3D data on these tasks mainly focuses on urban scenarios. In this paper, we propose TS40K, a 3D point cloud dataset that encompasses more than 40,000 Km on electrical transmission systems situated in European rural terrain. This is not only a novel problem for the research community that can aid in the high-risk mission of power-grid inspection, but it also offers 3D point clouds with distinct characteristics from those in self-driving and indoor 3D data, such as high point-density and no occlusion. In our dataset, each 3D point is labeled with 1 out of 22 annotated classes. We evaluate the performance of state-of-the-art methods on our dataset concerning 3D semantic segmentation and 3D object detection. Finally, we provide a comprehensive analysis of the results along with key challenges such as using labels that were not originally intended for learning tasks.

Task offloading, crucial for balancing computational loads across devices in networks such as the Internet of Things, poses significant optimization challenges, including minimizing latency and energy usage under strict communication and storage constraints. While traditional optimization falls short in scalability; and heuristic approaches lack in achieving optimal outcomes, Reinforcement Learning (RL) offers a promising avenue by enabling the learning of optimal offloading strategies through iterative interactions. However, the efficacy of RL hinges on access to rich datasets and custom-tailored, realistic training environments. To address this, we introduce PeersimGym, an open-source, customizable simulation environment tailored for developing and optimizing task offloading strategies within computational networks. PeersimGym supports a wide range of network topologies and computational constraints and integrates a \textit{PettingZoo}-based interface for RL agent deployment in both solo and multi-agent setups. Furthermore, we demonstrate the utility of the environment through experiments with Deep Reinforcement Learning agents, showcasing the potential of RL-based approaches to significantly enhance offloading strategies in distributed computing settings. PeersimGym thus bridges the gap between theoretical RL models and their practical applications, paving the way for advancements in efficient task offloading methodologies., Comment: Published in the proceedings of the conference on Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track. ECML PKDD 2024. Lecture Notes in Computer Science(), vol 14949. Springer, Cham

In this paper, we present an advanced approach to solving the inverse rig problem in blendshape animation, using high-quality corrective blendshapes. Our algorithm introduces novel enhancements in three key areas: ensuring high data fidelity in reconstructed meshes, achieving greater sparsity in weight distributions, and facilitating smoother frame-to-frame transitions. While the incorporation of corrective terms is a known practice, our method differentiates itself by employing a unique combination of $l_1$ norm regularization for sparsity and a temporal smoothness constraint through roughness penalty, focusing on the sum of second differences in consecutive frame weights. A significant innovation in our approach is the temporal decoupling of blendshapes, which permits simultaneous optimization across entire animation sequences. This feature sets our work apart from existing methods and contributes to a more efficient and effective solution. Our algorithm exhibits a marked improvement in maintaining data fidelity and ensuring smooth frame transitions when compared to prior approaches that either lack smoothness regularization or rely solely on linear blendshape models. In addition to superior mesh resemblance and smoothness, our method offers practical benefits, including reduced computational complexity and execution time, achieved through a novel parallelization strategy using clustering methods. Our results not only advance the state of the art in terms of fidelity, sparsity, and smoothness in inverse rigging but also introduce significant efficiency improvements. The source code will be made available upon acceptance of the paper.

Due to the importance of satellites for society and the exponential increase in the number of objects in orbit, it is important to accurately determine the state (e.g., position and velocity) of these Resident Space Objects (RSOs) at any time and in a timely manner. State-of-the-art methodologies for initial orbit determination consist of Kalman-type filters that process sequential data over time and return the state and associated uncertainty of the object, as is the case of the Extended Kalman Filter (EKF). However, these methodologies are dependent on a good initial guess for the state vector and usually simplify the physical dynamical model, due to the difficulty of precisely modeling perturbative forces, such as atmospheric drag and solar radiation pressure. Other approaches do not require assumptions about the dynamical system, such as the trilateration method, and require simultaneous measurements, such as three measurements of range and range-rate for the particular case of trilateration. We consider the same setting of simultaneous measurements (one-shot), resorting to time delay and Doppler shift measurements. Based on recent advancements in the problem of moving target localization for sonar multistatic systems, we are able to formulate the problem of initial orbit determination as a Weighted Least Squares. With this approach, we are able to directly obtain the state of the object (position and velocity) and the associated covariance matrix from the Fisher's Information Matrix (FIM). We demonstrate that, for small noise, our estimator is able to attain the Cram\'er-Rao Lower Bound accuracy, i.e., the accuracy attained by the unbiased estimator with minimum variance. We also numerically demonstrate that our estimator is able to attain better accuracy on the state estimation than the trilateration method and returns a smaller uncertainty associated with the estimation.

Medical referrals between primary care physicians (PC) and specialist care (SC) physicians profoundly impact patient care regarding quality, satisfaction, and cost. This paper investigates the influence of professional networks among medical doctors on referring patients from PC to SC. Using five-year consultation data from a Portuguese private health provider, we conducted exploratory data analysis and constructed both professional and referral networks among physicians. We then apply Graph Neural Network (GNN) models to learn latent representations of the referral network. Our analysis supports the hypothesis that doctors' professional social connections can predict medical referrals, potentially enhancing collaboration within organizations and improving healthcare services. This research contributes to dissecting the underlying mechanisms in primary-specialty referrals, thereby providing valuable insights for enhancing patient care and effective healthcare management., Comment: 27 pages, 9 figures, 2 tables

Space is becoming more crowded in Low Earth Orbit due to increased space activity. Such a dense space environment increases the risk of collisions between space objects endangering the whole space population. Therefore, the need to consider collision avoidance as part of routine operations is evident to satellite operators. Current procedures rely on the analysis of multiple collision warnings by human analysts. However, with the continuous growth of the space population, this manual approach may become unfeasible, highlighting the importance of automation in risk assessment. In 2019, ESA launched a competition to study the feasibility of applying machine learning in collision risk estimation and released a dataset that contained sequences of Conjunction Data Messages (CDMs) in support of real close encounters. The competition results showed that the naive forecast and its variants are strong predictors for this problem, which suggests that the CDMs may follow the Markov property. The proposed work investigates this theory by benchmarking Hidden Markov Models (HMM) in predicting the risk of collision between two resident space objects by using one feature of the entire dataset: the sequence of the probability in the CDMs. In addition, Bayesian statistics are used to infer a joint distribution for the parameters of the models, which allows the development of robust and reliable probabilistic predictive models that can incorporate physical or prior knowledge about the problem within a rigorous theoretical framework and provides prediction uncertainties that nicely reflect the accuracy of the predicted risk. This work shows that the implemented HMM outperforms the naive solution in some metrics, which further adds to the idea that the collision warnings may be Markovian and suggests that this is a powerful method to be further explored.

A novel approach is presented for discovering PDEs that govern the motion of satellites in space. The method is based on SINDy, a data-driven technique capable of identifying the underlying dynamics of complex physical systems from time series data. SINDy is utilized to uncover PDEs that describe the laws of physics in space, which are non-deterministic and influenced by various factors such as drag or the reference area (related to the attitude of the satellite). In contrast to prior works, the physically interpretable coordinate system is maintained, and no dimensionality reduction technique is applied to the data. By training the model with multiple representative trajectories of LEO - encompassing various inclinations, eccentricities, and altitudes - and testing it with unseen orbital motion patterns, a mean error of around 140 km for the positions and 0.12 km/s for the velocities is achieved. The method offers the advantage of delivering interpretable, accurate, and complex models of orbital motion that can be employed for propagation or as inputs to predictive models for other variables of interest, such as atmospheric drag or the probability of collision in an encounter with a spacecraft or space objects. In conclusion, the work demonstrates the promising potential of using SINDy to discover the equations governing the behaviour of satellites in space. The technique has been successfully applied to uncover PDEs describing the motion of satellites in LEO with high accuracy. The method possesses several advantages over traditional models, including the ability to provide physically interpretable, accurate, and complex models of orbital motion derived from high-entropy datasets. These models can be utilised for propagation or as inputs to predictive models for other variables of interest.

The proliferation of space debris in LEO has become a major concern for the space industry. With the growing interest in space exploration, the prediction of potential collisions between objects in orbit has become a crucial issue. It is estimated that, in orbit, there are millions of fragments a few millimeters in size and thousands of inoperative satellites and discarded rocket stages. Given the high speeds that these fragments can reach, even fragments a few millimeters in size can cause fractures in a satellite's hull or put a serious crack in the window of a space shuttle. The conventional method proposed by Akella and Alfriend in 2000 remains widely used to estimate the probability of collision in short-term encounters. Given the small period of time, it is assumed that, during the encounter: (1) trajectories are represented by straight lines with constant velocity; (2) there is no velocity uncertainty and the position exhibits a stationary distribution throughout the encounter; and (3) position uncertainties are independent and represented by Gaussian distributions. This study introduces a novel derivation based on first principles that naturally allows for tight and fast upper and lower bounds for the probability of collision. We tested implementations of both probability and bound computations with the original and our formulation on a real CDM dataset used in ESA's Collision Avoidance Challenge. Our approach reduces the calculation of the probability to two one-dimensional integrals and has the potential to significantly reduce the processing time compared to the traditional method, from 80% to nearly real-time.

The increasing number of RSOs has raised concerns about the risk of collisions and catastrophic incidents for all direct and indirect users of space. To mitigate this issue, it is essential to have a good understanding of the various RSOs in orbit and their behaviour. A well-established taxonomy defining several classes of RSOs is a critical step in achieving this understanding. This taxonomy helps assign objects to specific categories based on their main characteristics, leading to better tracking services. Furthermore, a well-established taxonomy can facilitate research and analysis processes by providing a common language and framework for better understanding the factors that influence RSO behaviour in space. These factors, in turn, help design more efficient and effective strategies for space traffic management. Our work proposes a new taxonomy for RSOs focusing on the low Earth orbit regime to enhance space traffic management. In addition, we present a deep learning-based model that uses an autoencoder architecture to reduce the features representing the characteristics of the RSOs. The autoencoder generates a lower-dimensional space representation that is then explored using techniques such as Uniform Manifold Approximation and Projection to identify fundamental clusters of RSOs based on their unique characteristics. This approach captures the complex and non-linear relationships between the features and the RSOs' classes identified. Our proposed taxonomy and model offer a significant contribution to the ongoing efforts to mitigate the overall risks posed by the increasing number of RSOs in orbit.

Current approaches for collision avoidance and space traffic management face many challenges, mainly due to the continuous increase in the number of objects in orbit and the lack of scalable and automated solutions. To avoid catastrophic incidents, satellite owners/operators must be aware of their assets' collision risk to decide whether a collision avoidance manoeuvre needs to be performed. This process is typically executed through the use of warnings issued in the form of CDMs which contain information about the event, such as the expected TCA and the probability of collision. Our previous work presented a statistical learning model that allowed us to answer two important questions: (1) Will any new conjunctions be issued in the next specified time interval? (2) When and with what uncertainty will the next CDM arrive? However, the model was based on an empirical Bayes homogeneous Poisson process, which assumes that the arrival rates of CDMs are constant over time. In fact, the rate at which the CDMs are issued depends on the behaviour of the objects as well as on the screening process performed by third parties. Thus, in this work, we extend the previous study and propose a Bayesian non-homogeneous Poisson process implemented with high precision using a Probabilistic Programming Language to fully describe the underlying phenomena. We compare the proposed solution with a baseline model to demonstrate the added value of our approach. The results show that this problem can be successfully modelled by our Bayesian non-homogeneous Poisson Process with greater accuracy, contributing to the development of automated collision avoidance systems and helping operators react timely but sparingly with satellite manoeuvres.

The risk of collision between resident space objects has significantly increased in recent years. As a result, spacecraft collision avoidance procedures have become an essential part of satellite operations. To ensure safe and effective space activities, satellite owners and operators rely on constantly updated estimates of encounters. These estimates include the uncertainty associated with the position of each object at the expected TCA. These estimates are crucial in planning risk mitigation measures, such as collision avoidance manoeuvres. As the TCA approaches, the accuracy of these estimates improves, as both objects' orbit determination and propagation procedures are made for increasingly shorter time intervals. However, this improvement comes at the cost of taking place close to the critical decision moment. This means that safe avoidance manoeuvres might not be possible or could incur significant costs. Therefore, knowing the evolution of this variable in advance can be crucial for operators. This work proposes a machine learning model based on diffusion models to forecast the position uncertainty of objects involved in a close encounter, particularly for the secondary object (usually debris), which tends to be more unpredictable. We compare the performance of our model with other state-of-the-art solutions and a na\"ive baseline approach, showing that the proposed solution has the potential to significantly improve the safety and effectiveness of spacecraft operations.

Regularizing Deep Neural Networks (DNNs) is essential for improving generalizability and preventing overfitting. Fixed penalty methods, though common, lack adaptability and suffer from hyperparameter sensitivity. In this paper, we propose a novel approach to DNN regularization by framing the training process as a constrained optimization problem. Where the data fidelity term is the minimization objective and the regularization terms serve as constraints. Then, we employ the Stochastic Augmented Lagrangian (SAL) method to achieve a more flexible and efficient regularization mechanism. Our approach extends beyond black-box regularization, demonstrating significant improvements in white-box models, where weights are often subject to hard constraints to ensure interpretability. Experimental results on image-based classification on MNIST, CIFAR10, and CIFAR100 datasets validate the effectiveness of our approach. SAL consistently achieves higher Accuracy while also achieving better constraint satisfaction, thus showcasing its potential for optimizing DNNs under constrained settings.

Communication efficiency is a major challenge in federated learning (FL). In client-server schemes, the server constitutes a bottleneck, and while decentralized setups spread communications, they do not necessarily reduce them due to slower convergence. We propose Multi-Token Coordinate Descent (MTCD), a communication-efficient algorithm for semi-decentralized vertical federated learning, exploiting both client-server and client-client communications when each client holds a small subset of features. Our multi-token method can be seen as a parallel Markov chain (block) coordinate descent algorithm and it subsumes the client-server and decentralized setups as special cases. We obtain a convergence rate of $\mathcal{O}(1/T)$ for nonconvex objectives when tokens roam over disjoint subsets of clients and for convex objectives when they roam over possibly overlapping subsets. Numerical results show that MTCD improves the state-of-the-art communication efficiency and allows for a tunable amount of parallel communications.

Recommendation Systems (RS) are often used to address the issue of medical doctor referrals. However, these systems require access to patient feedback and medical records, which may not always be available in real-world scenarios. Our research focuses on medical referrals and aims to predict recommendations in different specialties of physicians for both new patients and those with a consultation history. We use Extreme Multilabel Classification (XML), commonly employed in text-based classification tasks, to encode available features and explore different scenarios. While its potential for recommendation tasks has often been suggested, this has not been thoroughly explored in the literature. Motivated by the doctor referral case, we show how to recast a traditional recommender setting into a multilabel classification problem that current XML methods can solve. Further, we propose a unified model leveraging patient history across different specialties. Compared to state-of-the-art RS using the same features, our approach consistently improves standard recommendation metrics up to approximately $10\%$ for patients with a previous consultation history. For new patients, XML proves better at exploiting available features, outperforming the benchmark in favorable scenarios, with particular emphasis on recall metrics. Thus, our approach brings us one step closer to creating more effective and personalized doctor referral systems. Additionally, it highlights XML as a promising alternative to current hybrid or content-based RS, while identifying key aspects to take into account when using XML for recommendation tasks.

Research in 3D semantic segmentation has been increasing performance metrics, like the IoU, by scaling model complexity and computational resources, leaving behind researchers and practitioners that (1) cannot access the necessary resources and (2) do need transparency on the model decision mechanisms. In this paper, we propose SCENE-Net, a low-resource white-box model for 3D point cloud semantic segmentation. SCENE-Net identifies signature shapes on the point cloud via group equivariant non-expansive operators (GENEOs), providing intrinsic geometric interpretability. Our training time on a laptop is 85~min, and our inference time is 20~ms. SCENE-Net has 11 trainable geometrical parameters and requires fewer data than black-box models. SCENE--Net offers robustness to noisy labeling and data imbalance and has comparable IoU to state-of-the-art methods. With this paper, we release a 40~000 Km labeled dataset of rural terrain point clouds and our code implementation.

The use of machine learning for time series prediction has become increasingly popular across various industries thanks to the availability of time series data and advancements in machine learning algorithms. However, traditional methods for time series forecasting rely on pre-optimized models that are ill-equipped to handle unpredictable patterns in data. In this paper, we present EAMDrift, a novel method that combines forecasts from multiple individual predictors by weighting each prediction according to a performance metric. EAMDrift is designed to automatically adapt to out-of-distribution patterns in data and identify the most appropriate models to use at each moment through interpretable mechanisms, which include an automatic retraining process. Specifically, we encode different concepts with different models, each functioning as an observer of specific behaviors. The activation of the overall model then identifies which subset of the concept observers is identifying concepts in the data. This activation is interpretable and based on learned rules, allowing to study of input variables relations. Our study on real-world datasets shows that EAMDrift outperforms individual baseline models by 20% and achieves comparable accuracy results to non-interpretable ensemble models. These findings demonstrate the efficacy of EAMDrift for time-series prediction and highlight the importance of interpretability in machine learning models., Comment: Submitted to ECML PKDD 2023

Localization is a fundamental enabler technology for many applications, like vehicular networks, IoT, and even medicine. While Global Navigation Satellite Systems solutions offer great performance, they are unavailable in scenarios like indoor or underwater environments, and, for large networks, the instrumentation cost is prohibitive. We develop a localization algorithm from ranges and bearings, suitable for generic mobile networks. Our algorithm is built on a tight convex relaxation of the Maximum Likelihood position estimator. To serve positioning to mobile agents, a horizon-based version is developed accounting for velocity measurements at each agent. To solve the convex problem, a distributed gradient-based method is provided. This constitutes an advantage over centralized approaches, which usually exhibit high latency for large networks and present a single point of failure. Additionally, the algorithm estimates all required parameters and effectively becomes parameter-free. Our solution to the dynamic network localization problem is theoretically well-founded and still easy to understand. We obtain a parameter-free, outlier-robust and trajectory-agnostic algorithm, with nearly constant positioning error regardless of the trajectories of agents and anchors, achieving better or comparable performance to state-of-the-art methods, as our simulations show. Furthermore, the method is distributed, convex and does not require any particular anchor configuration., Comment: Accepted for publication in Signal Processing

Space debris is a major problem in space exploration. International bodies continuously monitor a large database of orbiting objects and emit warnings in the form of conjunction data messages. An important question for satellite operators is to estimate when fresh information will arrive so that they can react timely but sparingly with satellite maneuvers. We propose a statistical learning model of the message arrival process, allowing us to answer two important questions: (1) Will there be any new message in the next specified time interval? (2) When exactly and with what uncertainty will the next message arrive? The average prediction error for question (2) of our Bayesian Poisson process model is smaller than the baseline in more than 4 hours in a test set of 50k close encounter events., Comment: Submitted to EUSIPCO '23. arXiv admin note: substantial text overlap with arXiv:2105.08509

The problem of rig inversion is central in facial animation as it allows for a realistic and appealing performance of avatars. With the increasing complexity of modern blendshape models, execution times increase beyond practically feasible solutions. A possible approach towards a faster solution is clustering, which exploits the spacial nature of the face, leading to a distributed method. In this paper, we go a step further, involving cluster coupling to get more confident estimates of the overlapping components. Our algorithm applies the Alternating Direction Method of Multipliers, sharing the overlapping weights between the subproblems. The results obtained with this technique show a clear advantage over the naive clustered approach, as measured in different metrics of success and visual inspection. The method applies to an arbitrary clustering of the face. We also introduce a novel method for choosing the number of clusters in a data-free manner. The method tends to find a clustering such that the resulting clustering graph is sparse but without losing essential information. Finally, we give a new variant of a data-free clustering algorithm that produces good scores with respect to the mentioned strategy for choosing the optimal clustering.

We propose a new model-based algorithm solving the inverse rig problem in facial animation retargeting, exhibiting higher accuracy of the fit and sparser, more interpretable weight vector compared to SOTA. The proposed method targets a specific subdomain of human face animation - highly-realistic blendshape models used in the production of movies and video games. In this paper, we formulate an optimization problem that takes into account all the requirements of targeted models. Our objective goes beyond a linear blendshape model and employs the quadratic corrective terms necessary for correctly fitting fine details of the mesh. We show that the solution to the proposed problem yields highly accurate mesh reconstruction even when general-purpose solvers, like SQP, are used. The results obtained using SQP are highly accurate in the mesh space but do not exhibit favorable qualities in terms of weight sparsity and smoothness, and for this reason, we further propose a novel algorithm relying on a MM technique. The algorithm is specifically suited for solving the proposed objective, yielding a high-accuracy mesh fit while respecting the constraints and producing a sparse and smooth set of weights easy to manipulate and interpret by artists. Our algorithm is benchmarked with SOTA approaches, and shows an overall superiority of the results, yielding a smooth animation reconstruction with a relative improvement up to 45 percent in root mean squared mesh error while keeping the cardinality comparable with benchmark methods. This paper gives a comprehensive set of evaluation metrics that cover different aspects of the solution, including mesh accuracy, sparsity of the weights, and smoothness of the animation curves, as well as the appearance of the produced animation, which human experts evaluated.

We propose a method to fit arbitrarily accurate blendshape rig models by solving the inverse rig problem in realistic human face animation. The method considers blendshape models with different levels of added corrections and solves the regularized least-squares problem using coordinate descent, i.e., iteratively estimating blendshape weights. Besides making the optimization easier to solve, this approach ensures that mutually exclusive controllers will not be activated simultaneously and improves the goodness of fit after each iteration. We show experimentally that the proposed method yields solutions with mesh error comparable to or lower than the state-of-the-art approaches while significantly reducing the cardinality of the weight vector (over 20 percent), hence giving a high-fidelity reconstruction of the reference expression that is easier to manipulate in the post-production manually. Python scripts for the algorithm will be publicly available upon acceptance of the paper.

This paper addresses target localization with an online active learning algorithm defined by distributed, simple and fast computations at each node, with no parameters to tune and where the estimate of the target position at each agent is asymptotically equal in expectation to the centralized maximum-likelihood estimator. ISEE.U takes noisy distances at each agent and finds a control that maximizes localization accuracy. We do not assume specific target dynamics and, thus, our method is robust when facing unpredictable targets. Each agent computes the control that maximizes overall target position accuracy via a local estimate of the Fisher Information Matrix. We compared the proposed method with a state of the art algorithm outperforming it when the target movements do not follow a prescribed trajectory, with x100 less computation time, even when our method is running in one central CPU.

Since the late 1950s, when the first artificial satellite was launched, the number of Resident Space Objects has steadily increased. It is estimated that around one million objects larger than one cm are currently orbiting the Earth, with only thirty thousand larger than ten cm being tracked. To avert a chain reaction of collisions, known as Kessler Syndrome, it is essential to accurately track and predict debris and satellites' orbits. Current approximate physics-based methods have errors in the order of kilometers for seven-day predictions, which is insufficient when considering space debris, typically with less than one meter. This failure is usually due to uncertainty around the state of the space object at the beginning of the trajectory, forecasting errors in environmental conditions such as atmospheric drag, and unknown characteristics such as the mass or geometry of the space object. Operators can enhance Orbit Prediction accuracy by deriving unmeasured objects' characteristics and improving non-conservative forces' effects by leveraging data-driven techniques, such as Machine Learning. In this survey, we provide an overview of the work in applying Machine Learning for Orbit Determination, Orbit Prediction, and atmospheric density modeling., Comment: Accepted for Publication to Acta Astronautica

Emergency Departments (EDs) are a fundamental element of the Portuguese National Health Service, serving as an entry point for users with diverse and very serious medical problems. Due to the inherent characteristics of the ED; forecasting the number of patients using the services is particularly challenging. And a mismatch between the affluence and the number of medical professionals can lead to a decrease in the quality of the services provided and create problems that have repercussions for the entire hospital, with the requisition of health care workers from other departments and the postponement of surgeries. ED overcrowding is driven, in part, by non-urgent patients, that resort to emergency services despite not having a medical emergency and which represent almost half of the total number of daily patients. This paper describes a novel deep learning architecture, the Temporal Fusion Transformer, that uses calendar and time-series covariates to forecast prediction intervals and point predictions for a 4 week period. We have concluded that patient volume can be forecasted with a Mean Absolute Percentage Error (MAPE) of 5.90% for Portugal's Health Regional Areas (HRA) and a Root Mean Squared Error (RMSE) of 84.4102 people/day. The paper shows empirical evidence supporting the use of a multivariate approach with static and time-series covariates while surpassing other models commonly found in the literature., Comment: Extended Abstract presented at Machine Learning for Health (ML4H) symposium 2022, November 28th, 2022, New Orleans, United States & Virtual, http://www.ml4h.cc, 16 pages

Automated methods for facial animation are a necessary tool in the modern industry since the standard blendshape head models consist of hundreds of controllers and a manual approach is painfully slow. Different solutions have been proposed that produce output in real-time or generalize well for different face topologies. However, all these prior works consider a linear approximation of the blendshape function and hence do not provide a high-enough level of details for modern realistic human face reconstruction. We build a method for solving the inverse rig in blendshape animation using quadratic corrective terms, which increase accuracy. At the same time, due to the proposed construction of the objective function, it yields a sparser estimated weight vector compared to the state-of-the-art methods. The former feature means lower demand for subsequent manual corrections of the solution, while the latter indicates that the manual modifications are also easier to include. Our algorithm is iterative and employs a Majorization Minimization paradigm to cope with the increased complexity produced by adding the corrective terms. The surrogate function is easy to solve and allows for further parallelization on the component level within each iteration. This paper is complementary to an accompanying paper, Rackovi\'c et al. (2023), where we provide detailed experimental results and discussion, including highly-realistic animation data, and show a clear superiority of the results compared to the state-of-the-art methods.

We propose a shape fitting/registration method based on a Gaussian Processes formulation, suitable for shapes with extensive regions of missing data. Gaussian Processes are a proven powerful tool, as they provide a unified setting for shape modelling and fitting. While the existing methods in this area prove to work well for the general case of the human head, when looking at more detailed and deformed data, with a high prevalence of missing data, such as the ears, the results are not satisfactory. In order to overcome this, we formulate the shape fitting problem as a multi-annotator Gaussian Process Regression and establish a parallel with the standard probabilistic registration. The achieved method SFGP shows better performance when dealing with extensive areas of missing data when compared to a state-of-the-art registration method and current approaches for registration with pre-existing shape models. Experiments are conducted both for a 2D small dataset with diverse transformations and a 3D dataset of ears., Comment: 18 pages, 6 figures. Accepted for publication in SIAM Journal on Mathematics of Data Science (SIMODS)

In this work, we leverage a generative data model considering comparison noise to develop a fast, precise, and informative ranking algorithm from pairwise comparisons that produces a measure of confidence on each comparison. The problem of ranking a large number of items from noisy and sparse pairwise comparison data arises in diverse applications, like ranking players in online games, document retrieval or ranking human perceptions. Although different algorithms are available, we need fast, large-scale algorithms whose accuracy degrades gracefully when the number of comparisons is too small. Fitting our proposed model entails solving a non-convex optimization problem, which we tightly approximate by a sum of quasi-convex functions and a regularization term. Resorting to an iterative reweighted minimization and the Primal-Dual Hybrid Gradient method, we obtain PD-Rank, achieving a Kendall tau 0.1 higher than all comparing methods, even for 10\% of wrong comparisons in simulated data matching our data model, and leading in accuracy if data is generated according to the Bradley-Terry model, in both cases faster by one order of magnitude, in seconds. In real data, PD-Rank requires less computational time to achieve the same Kendall tau than active learning methods., Comment: 17 pages, 10 figures

Expectation Maximization (EM) is the standard method to learn Gaussian mixtures. Yet its classic, centralized form is often infeasible, due to privacy concerns and computational and communication bottlenecks. Prior work dealt with data distributed by examples, horizontal partitioning, but we lack a counterpart for data scattered by features, an increasingly common scheme (e.g. user profiling with data from multiple entities). To fill this gap, we provide an EM-based algorithm to fit Gaussian mixtures to Vertically Partitioned data (VP-EM). In federated learning setups, our algorithm matches the centralized EM fitting of Gaussian mixtures constrained to a subspace. In arbitrary communication graphs, consensus averaging allows VP-EM to run on large peer-to-peer networks as an EM approximation. This mismatch comes from consensus error only, which vanishes exponentially fast with the number of consensus rounds. We demonstrate VP-EM on various topologies for both synthetic and real data, evaluating its approximation of centralized EM and seeing that it outperforms the available benchmark.

Bike Sharing Systems (BSSs) are emerging as an innovative transportation service. Ensuring the proper functioning of a BSS is crucial given that these systems are committed to eradicating many of the current global concerns, by promoting environmental and economic sustainability and contributing to improving the life quality of the population. Good knowledge of users' transition patterns is a decisive contribution to the quality and operability of the service. The analogous and unbalanced users' transition patterns cause these systems to suffer from bicycle imbalance, leading to a drastic customer loss in the long term. Strategies for bicycle rebalancing become important to tackle this problem and for this, bicycle traffic prediction is essential, as it allows to operate more efficiently and to react in advance. In this work, we propose a bicycle trips predictor based on Graph Neural Network embeddings, taking into consideration station groupings, meteorology conditions, geographical distances, and trip patterns. We evaluated our approach in the New York City BSS (CitiBike) data and compared it with four baselines, including the non-clustered approach. To address our problem's specificities, we developed the Adaptive Transition Constraint Clustering Plus (AdaTC+) algorithm, eliminating shortcomings of previous work. Our experiments evidence the clustering pertinence (88% accuracy compared with 83% without clustering) and which clustering technique best suits this problem. Accuracy on the Link Prediction task is always higher for AdaTC+ than benchmark clustering methods when the stations are the same, while not degrading performance when the network is upgraded, in a mismatch with the trained model., Comment: 12 pages, 15 figures, 4 tables

We introduce a closed-form method for identification of discrete-time linear time-variant systems from data, formulating the learning problem as a regularized least squares problem where the regularizer favors smooth solutions within a trajectory. We develop a closed-form algorithm with guarantees of optimality and with a complexity that increases linearly with the number of instants considered per trajectory. The COSMIC algorithm achieves the desired result even in the presence of large volumes of data. Our method solved the problem using two orders of magnitude less computational power than a general purpose convex solver and was about 3 times faster than a Stochastic Block Coordinate Descent especially designed method. Computational times of our method remained in the order of magnitude of the second even for 10k and 100k time instants, where the general purpose solver crashed. To prove its applicability to real world systems, we test with spring-mass-damper system and use the estimated model to find the optimal control path. Our algorithm was applied to both a Low Fidelity and Functional Engineering Simulators for the Comet Interceptor mission, that requires precise pointing of the on-board cameras in a fast dynamics environment. Thus, this paper provides a fast alternative to classical system identification techniques for linear time-variant systems, while proving to be a solid base for applications in the Space industry and a step forward to the incorporation of algorithms that leverage data in such a safety-critical environment.

Predicting if passengers in a connecting flight will lose their connection is paramount for airline profitability. We present novel machine learning-based decision support models for the different stages of connection flight management, namely for strategic, pre-tactical, tactical and post-operations. We predict missed flight connections in an airline's hub airport using historical data on flights and passengers, and analyse the factors that contribute additively to the predicted outcome for each decision horizon. Our data is high-dimensional, heterogeneous, imbalanced and noisy, and does not inform about passenger arrival/departure transit time. We employ probabilistic encoding of categorical classes, data balancing with Gaussian Mixture Models, and boosting. For all planning horizons, our models attain an AUC of the ROC higher than 0.93. SHAP value explanations of our models indicate that scheduled/perceived connection times contribute the most to the prediction, followed by passenger age and whether border controls are required., Comment: Submitted to IEEE Transactions on Intelligent Transportation Systems

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable, applications require localization methods that assume minimal knowledge on the noise distribution. We present a scalable algorithm delimiting a tight superset of all possible target locations, assuming range measurements to known landmarks, contaminated with bounded noise and unknown distributions. This superset is of primary interest in robust statistics since it is a tight majorizer of the set of Maximum-Likelihood (ML) estimates parametrized by noise densities respecting two main assumptions: (1) the noise distribution is supported on a ellipsoidal uncertainty region and (2) the measurements are non-negative with probability one. We create the superset through convex relaxations that use Linear Fractional Representations (LFRs), a well-known technique in robust control. For low noise regimes the supersets created by our method double the accuracy of a standard semidefinite relaxation. For moderate to high noise regimes our method still improves the benchmark but the benefit tends to be less significant, as both supersets tend to have the same size (area)., Comment: 15 pages, 7 figures. Originally submitted in -IEEE Transactions on Signal Processing- on 01-Oct-2021. Accepted in -IEEE Transactions on Signal Processing- on 06-Jun-2022

Digital human animation relies on high-quality 3D models of the human face -- rigs. A face rig must be accurate and, at the same time, fast to compute. One of the most common rigging models is the blendshape model. We present a novel approach for learning the inverse rig parameters at increased accuracy and decreased computational cost at the same time. It is based on a two-fold clustering of the blendshape face model. Our method focuses exclusively on the underlying space of deformation and produces clusters in both the mesh space and the controller space -- something that was not investigated in previous literature. This segmentation finds intuitive and meaningful connections between groups of vertices on the face and deformation controls, and further these segments can be observed independently. A separate model for solving the inverse rig problem is then learned for each segment. Our method is completely unsupervised and highly parallelizable.

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where, despite the abundance of technical literature, prior research seldom considered outlier data. We propose robust, fast, and distributed network localization algorithms, resilient to high-power noise, but also precise under regular Gaussian noise. We use a Huber M-estimator, thus obtaining a robust (but nonconvex) optimization problem. We convexify and change the problem representation, to allow for distributed robust localization algorithms: a synchronous distributed method that has optimal convergence rate and an asynchronous one with proven convergence guarantees. A major highlight of our contribution lies on the fact that we pay no price for provable distributed computation neither in accuracy, nor in communication cost or convergence speed. Simulations showcase the superior performance of our algorithms, both in the presence of outliers and under regular Gaussian noise: our method exceeds the accuracy of alternative approaches, distributed and centralized, even under heavy additive and multiplicative outlier noise., Comment: arXiv admin note: substantial text overlap with arXiv:1610.09020

Hybrid localization in GNSS-challenged environments using measured ranges and angles is becoming increasingly popular, in particular with the advent of multimodal communication systems. Here, we address the hybrid network localization problem using ranges and bearings to jointly determine the positions of a number of agents through a single maximum-likelihood (ML) optimization problem that seamlessly fuses all the available pairwise range and angle measurements. We propose a tight convex surrogate to the ML estimator, we examine practical measures for the accuracy of the relaxation, and we comprehensively characterize its behavior in simulation. We found that our relaxation outperforms a state of the art SDP relaxation by one order of magnitude in terms of localization error, and is amenable to much more lightweight solution algorithms.

Digital human animation relies on high-quality 3D models of the human face: rigs. A face rig must be accurate and, at the same time, fast to compute. One of the most common rigging models is the blendshape model. We propose a novel algorithm for solving the nonconvex inverse rig problem in facial animation. Our approach is model-based, but in contrast with previous model-based approaches, we use a quadratic instead of the linear approximation to the higher order rig model. This increases the accuracy of the solution by 8 percent on average and, confirmed by the empirical results, increases the sparsity of the resulting parameter vector -- an important feature for interpretability by animation artists. The proposed solution is based on a Levenberg-Marquardt (LM) algorithm, applied to a nonconvex constrained problem with sparsity regularization. In order to reduce the complexity of the iterates, a paradigm of Majorization Minimization (MM) is further invoked, which leads to an easy to solve problem that is separable in the parameters at each algorithm iteration. The algorithm is evaluated on a number of animation datasets, proprietary and open-source, and the results indicate the superiority of our method compared to the standard approach based on the linear rig approximation. Although our algorithm targets the specific problem, it might have additional signal processing applications.

Space debris is a major problem in space exploration. International bodies continuously monitor a large database of orbiting objects and emit warnings in the form of conjunction data messages. An important question for satellite operators is to estimate when fresh information will arrive so that they can react timely but sparingly with satellite maneuvers. We propose a statistical learning model of the message arrival process, allowing us to answer two important questions: (1) Will there be any new message in the next specified time interval? (2) When exactly and with what uncertainty will the next message arrive? The average prediction error for question (2) of our Bayesian Poisson process model is smaller than the baseline in more than 4 hours in a test set of 50k close encounter events., Comment: Presented at AI4Spacecraft (IJCAI 2021 workshop)

Ears are a particularly difficult region of the human face to model, not only due to the non-rigid deformations existing between shapes but also to the challenges in processing the retrieved data. The first step towards obtaining a good model is to have complete scans in correspondence, but these usually present a higher amount of occlusions, noise and outliers when compared to most face regions, thus requiring a specific procedure. Therefore, we propose a complete pipeline taking as input unordered 3D point clouds with the aforementioned problems, and producing as output a dataset in correspondence, with completion of the missing data. We provide a comparison of several state-of-the-art registration methods and propose a new approach for one of the steps of the pipeline, with better performance for our data.