Francesco Marchetti

Francesco Marchetti, Federico Becattini, Lorenzo Seidenari et al.

Effective modeling of human interactions is of utmost importance when forecasting behaviors such as future trajectories. Each individual, with its motion, influences surrounding agents since everyone obeys to social non-written rules such as collision avoidance or group following. In this paper we model such interactions, which constantly evolve through time, by looking at the problem from an algorithmic point of view, i.e. as a data manipulation task. We present a neural network based on an end-to-end trainable working memory, which acts as an external storage where information about each agent can be continuously written, updated and recalled. We show that our method is capable of learning explainable cause-effect relationships between motions of different agents, obtaining state-of-the-art results on multiple trajectory forecasting datasets.

Sabrina Guastavino, Francesco Marchetti, Federico Benvenuto et al.

Operational flare forecasting aims at providing predictions that can be used to make decisions, typically at a daily scale, about the space weather impacts of flare occurrence. This study shows that video-based deep learning can be used for operational purposes when the training and validation sets used for the network optimization are generated while accounting for the periodicity of the solar cycle. Specifically, the paper describes an algorithm that can be applied to build up sets of active regions that are balanced according to the flare class rates associated to a specific cycle phase. These sets are used to train and validate a Long-term Recurrent Convolutional Network made of a combination of a convolutional neural network and a Long-Short Memory network. The reliability of this approach is assessed in the case of two prediction windows containing the solar storm of March 2015 and September 2017, respectively.

Alessandro Simoni, Francesco Marchetti, Guido Borghi et al.

Technologies to enable safe and effective collaboration and coexistence between humans and robots have gained significant importance in the last few years. A critical component useful for realizing this collaborative paradigm is the understanding of human and robot 3D poses using non-invasive systems. Therefore, in this paper, we propose a novel vision-based system leveraging depth data to accurately establish the 3D locations of skeleton joints. Specifically, we introduce the concept of Pose Nowcasting, denoting the capability of the proposed system to enhance its current pose estimation accuracy by jointly learning to forecast future poses. The experimental evaluation is conducted on two different datasets, providing accurate and real-time performance and confirming the validity of the proposed method on both the robotic and human scenarios.

Stefano De Marchi, Wolfgang Erb, Francesco Marchetti et al.

Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study an RBF type method for scattered data interpolation that incorporates discontinuities via a variable scaling function. For the construction of the discontinuous basis of kernel functions, information on the edges of the interpolated function is necessary. We characterize the native space spanned by these kernel functions and study error bounds in terms of the fill distance of the node set. To extract the location of the discontinuities, we use a segmentation method based on a classification algorithm from machine learning. The conducted numerical experiments confirm the theoretically derived convergence rates in case that the discontinuities are a priori known. Further, an application to interpolation in magnetic particle imaging shows that the presented method is very promising.

Alessandro Simoni, Francesco Marchetti, Guido Borghi et al.

Despite the recent advances in computer vision research, estimating the 3D human pose from single RGB images remains a challenging task, as multiple 3D poses can correspond to the same 2D projection on the image. In this context, depth data could help to disambiguate the 2D information by providing additional constraints about the distance between objects in the scene and the camera. Unfortunately, the acquisition of accurate depth data is limited to indoor spaces and usually is tied to specific depth technologies and devices, thus limiting generalization capabilities. In this paper, we propose a method able to leverage the benefits of depth information without compromising its broader applicability and adaptability in a predominantly RGB-camera-centric landscape. Our approach consists of a heatmap-based 3D pose estimator that, leveraging the paradigm of Privileged Information, is able to hallucinate depth information from the RGB frames given at inference time. More precisely, depth information is used exclusively during training by enforcing our RGB-based hallucination network to learn similar features to a backbone pre-trained only on depth data. This approach proves to be effective even when dealing with limited and small datasets. Experimental results reveal that the paradigm of Privileged Information significantly enhances the model's performance, enabling efficient extraction of depth information by using only RGB images.

Giacomo Elefante, Wolfgang Erb, Francesco Marchetti et al.

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their lack of strict positive definiteness. In particular they do not enjoy the usual property of unisolvency for arbitrary point sets, which is one of the key properties used to build kernel-based interpolation methods. This paper is devoted to establish some initial results for the study of these kernels, and their related interpolation algorithms, in the context of approximation theory. We will first prove necessary and sufficient conditions on point sets which guarantee the existence and uniqueness of an interpolant. We will then study the Reproducing Kernel Hilbert Spaces (or native spaces) of these kernels and their norms, and provide inclusion relations between spaces corresponding to different kernel parameters. With these spaces at hand, it will be further possible to derive generic error estimates which apply to sufficiently smooth functions, thus escaping the native space. Finally, we will show how to employ an efficient stable algorithm to these kernels to obtain accurate interpolants, and we will test them in some numerical experiment. After this analysis several computational and theoretical aspects remain open, and we will outline possible further research directions in a concluding section. This work builds some bridges between kernel and polynomial interpolation, two topics to which the authors, to different extents, have been introduced under the supervision or through the work of Stefano De Marchi. For this reason, they wish to dedicate this work to him in the occasion of his 60th birthday.

Gianluca Audone, Francesco Marchetti, Emma Perracchione et al.

Classical Gaussian processes and Kriging models are commonly based on stationary kernels, whereby correlations between observations depend exclusively on the relative distance between scattered data. While this assumption ensures analytical tractability, it limits the ability of Gaussian processes to represent heterogeneous correlation structures. In this work, we investigate variably scaled kernels as an effective tool for constructing non-stationary Gaussian processes by explicitly modifying the correlation structure of the data. Through a scaling function, variably scaled kernels alter the correlations between data and enable the modeling of targets exhibiting abrupt changes or discontinuities. We analyse the resulting predictive uncertainty via the variably scaled kernel power function and clarify the relationship between variably scaled kernels-based constructions and classical non-stationary kernels. Numerical experiments demonstrate that variably scaled kernels-based Gaussian processes yield improved reconstruction accuracy and provide uncertainty estimates that reflect the underlying structure of the data

Fabiana Camattari, Sabrina Guastavino, Francesco Marchetti et al.

The purpose of this study is to introduce a new approach to feature ranking for classification tasks, called in what follows greedy feature selection. In statistical learning, feature selection is usually realized by means of methods that are independent of the classifier applied to perform the prediction using that reduced number of features. Instead, greedy feature selection identifies the most important feature at each step and according to the selected classifier. In the paper, the benefits of such scheme are investigated theoretically in terms of model capacity indicators, such as the Vapnik-Chervonenkis (VC) dimension or the kernel alignment, and tested numerically by considering its application to the problem of predicting geo-effective manifestations of the active Sun.

Francesco Marchetti, Edoardo Legnaro, Sabrina Guastavino

In the supervised binary classification setting, score-oriented losses have been introduced with the aim of optimizing a chosen performance metric directly during the training phase, thus avoiding \textit{a posteriori} threshold tuning. To do this, in their construction, the decision threshold is treated as a random variable provided with a certain \textit{a priori} distribution. In this paper, we use a recently introduced multidimensional threshold-based classification framework to extend such score-oriented losses to multiclass classification, defining the Multiclass Score-Oriented Loss (MultiSOL) functions. As also demonstrated by several classification experiments, this proposed family of losses is designed to preserve the main advantages observed in the binary setting, such as the direct optimization of the target metric and the robustness to class imbalance, achieving performance comparable to other state-of-the-art loss functions and providing new insights into the interaction between simplex geometry and score-oriented learning.

Edoardo Legnaro, Sabrina Guastavino, Francesco Marchetti

In this paper, we introduce a threshold-based framework for multiclass classification that generalizes the standard argmax rule. This is done by replacing the probabilistic interpretation of softmax outputs with a geometric one on the multidimensional simplex, where the classification depends on a multidimensional threshold. This change of perspective enables for any trained classification network an \textit{a posteriori} optimization of the classification score by means of threshold tuning, as usually carried out in the binary setting, thus allowing for a further refinement of the prediction capability of any network. Our experiments show indeed that multidimensional threshold tuning yields performance improvements across various networks and datasets. Moreover, we derive a multiclass ROC analysis based on \emph{ROC clouds} -- the attainable (FPR,TPR) operating points induced by a single multiclass threshold -- and summarize them via a \emph{Distance From Point} (DFP) score to $(0,1)$. This yields a coherent alternative to standard One-vs-Rest (OvR) curves and aligns with the observed tuning gains.

Michele Piana, Federico Benvenuto, Anna Maria Massone et al.

AI-FLARES (Artificial Intelligence for the Analysis of Solar Flares Data) is a research project funded by the Agenzia Spaziale Italiana and by the Istituto Nazionale di Astrofisica within the framework of the ``Attività di Studio per la Comunità Scientifica Nazionale Sole, Sistema Solare ed Esopianeti'' program. The topic addressed by this project was the development and use of computational methods for the analysis of remote sensing space data associated to solar flare emission. This paper overviews the main results obtained by the project, with specific focus on solar flare forecasting, reconstruction of morphologies of the flaring sources, and interpretation of acceleration mechanisms triggered by solar flares.

Francesco Marchetti, Sabrina Guastavino, Cristina Campi et al.

In many contexts, customized and weighted classification scores are designed in order to evaluate the goodness of the predictions carried out by neural networks. However, there exists a discrepancy between the maximization of such scores and the minimization of the loss function in the training phase. In this paper, we provide a complete theoretical setting that formalizes weighted classification metrics and then allows the construction of losses that drive the model to optimize these metrics of interest. After a detailed theoretical analysis, we show that our framework includes as particular instances well-established approaches such as classical cost-sensitive learning, weighted cross entropy loss functions and value-weighted skill scores.

Sabrina Guastavino, Valentina Candiani, Alessandro Bemporad et al.

Coronal Mass Ejections (CMEs) correspond to dramatic expulsions of plasma and magnetic field from the solar corona into the heliosphere. CMEs are scientifically relevant because they are involved in the physical mechanisms characterizing the active Sun. However, more recently CMEs have attracted attention for their impact on space weather, as they are correlated to geomagnetic storms and may induce the generation of Solar Energetic Particles streams. In this space weather framework, the present paper introduces a physics-driven artificial intelligence (AI) approach to the prediction of CMEs travel time, in which the deterministic drag-based model is exploited to improve the training phase of a cascade of two neural networks fed with both remote sensing and in-situ data. This study shows that the use of physical information in the AI architecture significantly improves both the accuracy and the robustness of the travel time prediction.

Francesco Marchetti, Sabrina Guastavino, Michele Piana et al.

Loss functions engineering and the assessment of forecasting performances are two crucial and intertwined aspects of supervised machine learning. This paper focuses on binary classification to introduce a class of loss functions that are defined on probabilistic confusion matrices and that allow an automatic and a priori maximization of the skill scores. The performances of these loss functions are validated during the training phase of two experimental forecasting problems, thus showing that the probability distribution function associated with the confusion matrices significantly impacts the outcome of the score maximization process.

Francesco Marchetti, Federico Becattini, Lorenzo Seidenari et al.

Autonomous vehicles are expected to drive in complex scenarios with several independent non cooperating agents. Path planning for safely navigating in such environments can not just rely on perceiving present location and motion of other agents. It requires instead to predict such variables in a far enough future. In this paper we address the problem of multimodal trajectory prediction exploiting a Memory Augmented Neural Network. Our method learns past and future trajectory embeddings using recurrent neural networks and exploits an associative external memory to store and retrieve such embeddings. Trajectory prediction is then performed by decoding in-memory future encodings conditioned with the observed past. We incorporate scene knowledge in the decoding state by learning a CNN on top of semantic scene maps. Memory growth is limited by learning a writing controller based on the predictive capability of existing embeddings. We show that our method is able to natively perform multi-modal trajectory prediction obtaining state-of-the art results on three datasets. Moreover, thanks to the non-parametric nature of the memory module, we show how once trained our system can continuously improve by ingesting novel patterns.