Machine learning and data processing techniques relying on covariance information are widespread as they identify meaningful patterns in unsupervised and unlabeled settings. As a prominent example, Principal Component Analysis (PCA) projects data points onto the eigenvectors of their covariance matrix, capturing the directions of maximum variance. This mapping, however, falls short in two directions: it fails to capture information in low-variance directions, relevant when, e.g., the data contains high-variance noise; and it provides unstable results in low-sample regimes, especially when covariance eigenvalues are close. CoVariance Neural Networks (VNNs), i.e., graph neural networks using the covariance matrix as a graph, show improved stability to estimation errors and learn more expressive functions in the covariance spectrum than PCA, but require training and operate in a labeled setup. To get the benefits of both worlds, we propose Covariance Scattering Transforms (CSTs), deep untrained networks that sequentially apply filters localized in the covariance spectrum to the input data and produce expressive hierarchical representations via nonlinearities. We define the filters as covariance wavelets that capture specific and detailed covariance spectral patterns. We improve CSTs' computational and memory efficiency via a pruning mechanism, and we prove that their error due to finite-sample covariance estimations is less sensitive to close covariance eigenvalues compared to PCA, improving their stability. Our experiments on age prediction from cortical thickness measurements on 4 datasets collecting patients with neurodegenerative diseases show that CSTs produce stable representations in low-data settings, as VNNs but without any training, and lead to comparable or better predictions w.r.t. more complex learning models.

Covariance-based data processing is widespread across signal processing and machine learning applications due to its ability to model data interconnectivities and dependencies. However, harmful biases in the data may become encoded in the sample covariance matrix and cause data-driven methods to treat different subpopulations unfairly. Existing works such as fair principal component analysis (PCA) mitigate these effects, but remain unstable in low sample regimes, which in turn may jeopardize the fairness goal. To address both biases and instability, we propose Fair coVariance Neural Networks (FVNNs), which perform graph convolutions on the covariance matrix for both fair and accurate predictions. Our FVNNs provide a flexible model compatible with several existing bias mitigation techniques. In particular, FVNNs allow for mitigating the bias in two ways: first, they operate on fair covariance estimates that remove biases from their principal components; second, they are trained in an end-to-end fashion via a fairness regularizer in the loss function so that the model parameters are tailored to solve the task directly in a fair manner. We prove that FVNNs are intrinsically fairer than analogous PCA approaches thanks to their stability in low sample regimes. We validate the robustness and fairness of our model on synthetic and real-world data, showcasing the flexibility of FVNNs along with the tradeoff between fair and accurate performance.

Topological Deep Learning (TDL) has emerged as a paradigm to process and learn from signals defined on higher-order combinatorial topological spaces, such as simplicial or cell complexes. Although many complex systems have an asymmetric relational structure, most TDL models forcibly symmetrize these relationships. In this paper, we first introduce a novel notion of higher-order directionality and we then design Directed Simplicial Neural Networks (Dir-SNNs) based on it. Dir-SNNs are message-passing networks operating on directed simplicial complexes able to leverage directed and possibly asymmetric interactions among the simplices. To our knowledge, this is the first TDL model using a notion of higher-order directionality. We theoretically and empirically prove that Dir-SNNs are more expressive than their directed graph counterpart in distinguishing non-isomorphic directed graphs. Experiments on a synthetic source localization task demonstrate that Dir-SNNs outperform undirected SNNs when the underlying complex is directed, and perform comparably when the underlying complex is undirected.

BACKGROUND AND OBJECTIVE: In everyday clinical practice, medical decision is currently based on clinical guidelines which are often static and rigid, and do not account for population variability, while individualized, patient-oriented decision and/or treatment are the paradigm change necessary to enter into the era of precision medicine. Most of the limitations of a guideline-based system could be overcome through the adoption of Clinical Decision Support Systems (CDSSs) based on Artificial Intelligence (AI) algorithms. However, the black-box nature of AI algorithms has hampered a large adoption of AI-based CDSSs in clinical practice. In this study, an innovative AI-based method to compress AI-based prediction models into explainable, model-agnostic, and reduced decision support systems (NEAR) with application to healthcare is presented and validated. METHODS: NEAR is based on the Shapley Additive Explanations framework and can be applied to complex input models to obtain the contributions of each input feature to the output. Technically, the simplified NEAR models approximate contributions from input features using a custom library and merge them to determine the final output. Finally, NEAR estimates the confidence error associated with the single input feature contributing to the final score, making the result more interpretable. Here, NEAR is evaluated on a clinical real-world use case, the mortality prediction in patients who experienced Acute Coronary Syndrome (ACS), applying three different Machine Learning/Deep Learning models as implementation examples. RESULTS: NEAR, when applied to the ACS use case, exhibits performances like the ones of the AI-based model from which it is derived, as in the case of the Adaptive Boosting classifier, whose Area Under the Curve is not statistically different from the NEAR one, even the model's simplification. Moreover, NEAR comes with intrinsic explainability and modularity, as it can be tested on the developed web application platform (https://neardashboard.pythonanywhere.com/). CONCLUSIONS: An explainable and reliable CDSS tailored to single-patient analysis has been developed. The proposed AI-based system has the potential to be used alongside the clinical guidelines currently employed in the medical setting making them more personalized and dynamic and assisting doctors in taking their everyday clinical decisions.

Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open research problem. Recent works have proposed extensions to standard GNN architectures to improve performance on heterophilous graphs, trading off model simplicity for prediction accuracy. However, these models fail to capture basic graph properties, such as neighborhood label distribution, which are fundamental for learning. In this work, we propose GCN for Heterophily (GCNH), a simple yet effective GNN architecture applicable to both heterophilous and homophilous scenarios. GCNH learns and combines separate representations for a node and its neighbors, using one learned importance coefficient per layer to balance the contributions of center nodes and neighborhoods. We conduct extensive experiments on eight real-world graphs and a set of synthetic graphs with varying degrees of heterophily to demonstrate how the design choices for GCNH lead to a sizable improvement over a vanilla GCN. Moreover, GCNH outperforms state-of-the-art models of much higher complexity on four out of eight benchmarks, while producing comparable results on the remaining datasets. Finally, we discuss and analyze the lower complexity of GCNH, which results in fewer trainable parameters and faster training times than other methods, and show how GCNH mitigates the oversmoothing problem.

The problem of continuous emotion recognition has been the subject of several studies. The proposed affective computing approaches employ sequential machine learning algorithms for improving the classification stage, accounting for the time ambiguity of emotional responses. Modeling and predicting the affective state over time is not a trivial problem because continuous data labeling is costly and not always feasible. This is a crucial issue in real-life applications, where data labeling is sparse and possibly captures only the most important events rather than the typical continuous subtle affective changes that occur. In this work, we introduce a framework from the machine learning literature called Multiple Instance Learning, which is able to model time intervals by capturing the presence or absence of relevant states, without the need to label the affective responses continuously (as required by standard sequential learning approaches). This choice offers a viable and natural solution for learning in a weakly supervised setting, taking into account the ambiguity of affective responses. We demonstrate the reliability of the proposed approach in a gold-standard scenario and towards real-world usage by employing an existing dataset (DEAP) and a purposely built one (Consumer). We also outline the advantages of this method with respect to standard supervised machine learning algorithms.

Abstract This paper aims at investigating the action prediction problem from a pure kinematic perspective. Specifically, we address the problem of recognizing future actions, indeed human intentions, underlying a same initial (and apparently unrelated) motor act. This study is inspired by neuroscientific findings asserting that motor acts at the very onset are embedding information about the intention with which are performed, even when different intentions originate from a same class of movements. To demonstrate this claim in computational and empirical terms, we designed an ad hoc experiment and built a new 3D and 2D dataset where, in both training and testing, we analyze a same class of grasping movements underlying different intentions. We investigate how much the intention discriminants generalize across subjects, discovering that each subject tends to affect the prediction by his/her own bias. Inspired by the domain adaptation problem, we propose to interpret each subject as a domain, leading to a novel subject adversarial paradigm. The proposed approach favorably copes with our new problem, boosting the considered baseline features encoding 2D and 3D information and which do not exploit the subject information.

Autism is a behavioral neurological disorder affecting a significant percentage of worldwide population. It especially starts manifesting at very low ages, but it is difficult to early diagnose it since there is not a specific exam or trial that is able to spot it safely. Its detection is in fact mainly dependent from the medical expertise used to assess the patient behavior during direct interviews. This work aims at providing an automatic objective support to the doctor for the assessment of (early) diagnosis of possible autistic subjects by only using video sequences. The underlying idea and rationale come from the psychological and neuroscience studies claiming that the executions of simple motor acts are different between pathological and healthy subjects, and this can be sufficient to discriminate between them. To this end, we devised an experiment in which we recorded, using a standard video camera, patient and healthy children performing the same simple gesture of grasping a bottle. By only processing the video clips depicting the grasping action using a recurrent deep neural network, we are able to discriminate with a good accuracy between the 2 classes of subjects. The designed deep model is also able to provide a sort of attention map in which the zones in the video of major interest are identified in space and time: this “explains” in a certain way which areas the model deems more relevant to the classification purpose, which could also be used by the doctor to make the diagnosis. In the end, this work constitutes a first step towards the development of an automatic computational system devoted to the early diagnosis of autistic subjects, providing the medical expert of a supportive objective method, potentially simple to use in clinical and also more open settings.

In this paper, we address the new problem of the prediction of human intentions. There is neuro-psychological evidence that actions performed by humans are anticipated by peculiar motor acts which are discriminant of the type of action going to be performed afterwards. In other words, an actual intention can be forecast by looking at the kinematics of the immediately preceding movement. To prove it in a computational and quantitative manner, we devise a new experimental setup where, without using contextual information, we predict human intentions all originating from the same motor act. We posit the problem as a classification task and we introduce a new multi-modal dataset consisting of a set of motion capture marker 3D data and 2D video sequences, where, by only analysing very similar movements in both training and test phases, we are able to predict the underlying intention, i.e., the future, never observed action. We also present an extensive experimental evaluation as a baseline, customizing state-of-the-art techniques for either 3D and 2D data analysis. Realizing that video processing methods lead to inferior performance but show complementary information with respect to 3D data sequences, we developed a 2D+3D fusion analysis where we achieve better classification accuracies, attesting the superiority of the multimodal approach for the context-free prediction of human intentions.