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State-space models constitute an effective modeling tool to describe multivariate time series and operate by maintaining an updated representation of the system state from which predictions are made. Within this framework, relational inductive biases, e.g., associated with functional dependencies existing among signals, are not explicitly exploited leaving unattended great opportunities for effective modeling approaches. The manuscript aims, for the first time, at filling this gap by matching state-space modeling and spatio-temporal data where the relational information, say the functional graph capturing latent dependencies, is learned directly from data and is allowed to change over time. Within a probabilistic formulation that accounts for the uncertainty in the data-generating process, an encoder-decoder architecture is proposed to learn the state-space model end-to-end on a downstream task. The proposed methodological framework generalizes several state-of-the-art methods and demonstrates to be effective in extracting meaningful relational information while achieving optimal forecasting performance in controlled environments.

This paper introduces a novel residual correlation analysis, called AZ-analysis, to assess the optimality of spatio-temporal predictive models. The proposed AZ-analysis constitutes a valuable asset for discovering and highlighting those space-time regions where the model can be improved with respect to performance. The AZ-analysis operates under very mild assumptions and is based on a spatio-temporal graph that encodes serial and functional dependencies in the data; asymptotically distribution-free summary statistics identify existing residual correlation in space and time regions, hence localizing time frames and/or communities of sensors, where the predictor can be improved.

The well-known Kalman filters model dynamical systems by relying on state-space representations with the next state updated, and its uncertainty controlled, by fresh information associated with newly observed system outputs. This paper generalizes, for the first time in the literature, Kalman and extended Kalman filters to discrete-time settings where inputs, states, and outputs are represented as attributed graphs whose topology and attributes can change with time. The setup allows us to adapt the framework to cases where the output is a vector or a scalar too (node/graph level tasks). Within the proposed theoretical framework, the unknown state-transition and the readout functions are learned end-to-end along with the downstream prediction task., Comment: Added empirical validation

We focus on learning composable policies to control a variety of physical agents with possibly different structures. Among state-of-the-art methods, prominent approaches exploit graph-based representations and weight-sharing modular policies based on the message-passing framework. However, as shown by recent literature, message passing can create bottlenecks in information propagation and hinder global coordination. This drawback can become even more problematic in tasks where high-level planning is crucial. In fact, in similar scenarios, each modular policy - e.g., controlling a joint of a robot - would request to coordinate not only for basic locomotion but also achieve high-level goals, such as navigating a maze. A classical solution to avoid similar pitfalls is to resort to hierarchical decision-making. In this work, we adopt the Feudal Reinforcement Learning paradigm to develop agents where control actions are the outcome of a hierarchical (pyramidal) message-passing process. In the proposed Feudal Graph Reinforcement Learning (FGRL) framework, high-level decisions at the top level of the hierarchy are propagated through a layered graph representing a hierarchy of policies. Lower layers mimic the morphology of the physical system and upper layers can capture more abstract sub-modules. The purpose of this preliminary work is to formalize the framework and provide proof-of-concept experiments on benchmark environments (MuJoCo locomotion tasks). Empirical evaluation shows promising results on both standard benchmarks and zero-shot transfer learning settings.

Spatiotemporal graph neural networks have shown to be effective in time series forecasting applications, achieving better performance than standard univariate predictors in several settings. These architectures take advantage of a graph structure and relational inductive biases to learn a single (global) inductive model to predict any number of the input time series, each associated with a graph node. Despite the gain achieved in computational and data efficiency w.r.t. fitting a set of local models, relying on a single global model can be a limitation whenever some of the time series are generated by a different spatiotemporal stochastic process. The main objective of this paper is to understand the interplay between globality and locality in graph-based spatiotemporal forecasting, while contextually proposing a methodological framework to rationalize the practice of including trainable node embeddings in such architectures. We ascribe to trainable node embeddings the role of amortizing the learning of specialized components. Moreover, embeddings allow for 1) effectively combining the advantages of shared message-passing layers with node-specific parameters and 2) efficiently transferring the learned model to new node sets. Supported by strong empirical evidence, we provide insights and guidelines for specializing graph-based models to the dynamics of each time series and show how this aspect plays a crucial role in obtaining accurate predictions.

Conditioning image generation on specific features of the desired output is a key ingredient of modern generative models. Most existing approaches focus on conditioning the generation based on free-form text, while some niche studies use scene graphs to describe the content of the image to be generated. This paper explores novel methods to condition image generation that are based on object-centric relational representations. In particular, we propose a methodology to condition the generation of a particular object in an image on the attributed graph representing its structure and associated style. We show that such architectural biases entail properties that facilitate the manipulation and conditioning of the generative process and allow for regularizing the training procedure. The proposed framework is implemented by means of a neural network architecture combining convolutional operators that operate on both the underlying graph and the 2D grid that becomes the output image. The resulting model learns to generate multi-channel masks of the object that can be used as a soft inductive bias in the downstream generative task. Empirical results show that the proposed approach compares favorably against relevant baselines on image generation conditioned on human poses.

We present the first whiteness test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph. The statistical test aims at finding serial dependencies among close-in-time observations, as well as spatial dependencies among neighboring observations given the underlying graph. The proposed test is a spatio-temporal extension of traditional tests from the system identification literature and finds applications in similar, yet more general, application scenarios involving graph signals. The AZ-test is versatile, allowing the underlying graph to be dynamic, changing in topology and set of nodes, and weighted, thus accounting for connections of different strength, as is the case in many application scenarios like transportation networks and sensor grids. The asymptotic distribution -- as the number of graph edges or temporal observations increases -- is known, and does not assume identically distributed data. We validate the practical value of the test on both synthetic and real-world problems, and show how the test can be employed to assess the quality of spatio-temporal forecasting models by analyzing the prediction residuals appended to the graphs stream.

Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in most spatiotemporal GNNs, the computational complexity scales up to a quadratic factor with the length of the sequence times the number of links in the graph, hence hindering the application of these models to large graphs and long temporal sequences. While methods to improve scalability have been proposed in the context of static graphs, few research efforts have been devoted to the spatiotemporal case. To fill this gap, we propose a scalable architecture that exploits an efficient encoding of both temporal and spatial dynamics. In particular, we use a randomized recurrent neural network to embed the history of the input time series into high-dimensional state representations encompassing multi-scale temporal dynamics. Such representations are then propagated along the spatial dimension using different powers of the graph adjacency matrix to generate node embeddings characterized by a rich pool of spatiotemporal features. The resulting node embeddings can be efficiently pre-computed in an unsupervised manner, before being fed to a feed-forward decoder that learns to map the multi-scale spatiotemporal representations to predictions. The training procedure can then be parallelized node-wise by sampling the node embeddings without breaking any dependency, thus enabling scalability to large networks. Empirical results on relevant datasets show that our approach achieves results competitive with the state of the art, while dramatically reducing the computational burden., Comment: Published as conference paper at AAAI 23

Graph neural network (GNN)-based fault diagnosis (FD) has received increasing attention in recent years, due to the fact that data coming from several application domains can be advantageously represented as graphs. Indeed, this particular representation form has led to superior performance compared to traditional FD approaches. In this review, an easy introduction to GNN, potential applications to the field of fault diagnosis, and future perspectives are given. First, the paper reviews neural network-based FD methods by focusing on their data representations, namely, time-series, images, and graphs. Second, basic principles and principal architectures of GNN are introduced, with attention to graph convolutional networks, graph attention networks, graph sample and aggregate, graph auto-encoder, and spatial-temporal graph convolutional networks. Third, the most relevant fault diagnosis methods based on GNN are validated through the detailed experiments, and conclusions are made that the GNN-based methods can achieve good fault diagnosis performance. Finally, discussions and future challenges are provided., Comment: 17 pages, 18 figures, 10 tables

Dealing with missing values and incomplete time series is a labor-intensive, tedious, inevitable task when handling data coming from real-world applications. Effective spatio-temporal representations would allow imputation methods to reconstruct missing temporal data by exploiting information coming from sensors at different locations. However, standard methods fall short in capturing the nonlinear time and space dependencies existing within networks of interconnected sensors and do not take full advantage of the available - and often strong - relational information. Notably, most state-of-the-art imputation methods based on deep learning do not explicitly model relational aspects and, in any case, do not exploit processing frameworks able to adequately represent structured spatio-temporal data. Conversely, graph neural networks have recently surged in popularity as both expressive and scalable tools for processing sequential data with relational inductive biases. In this work, we present the first assessment of graph neural networks in the context of multivariate time series imputation. In particular, we introduce a novel graph neural network architecture, named GRIN, which aims at reconstructing missing data in the different channels of a multivariate time series by learning spatio-temporal representations through message passing. Empirical results show that our model outperforms state-of-the-art methods in the imputation task on relevant real-world benchmarks with mean absolute error improvements often higher than 20%., Comment: Accepted at ICLR 2022

The design of efficient hardware accelerators for high-throughput data-processing applications, e.g., deep neural networks, is a challenging task in computer architecture design. In this regard, High-Level Synthesis (HLS) emerges as a solution for fast prototyping application-specific hardware starting from a behavioural description of the application computational flow. This Design-Space Exploration (DSE) aims at identifying Pareto optimal synthesis configurations whose exhaustive search is often unfeasible due to the design-space dimensionality and the prohibitive computational cost of the synthesis process. Within this framework, we effectively and efficiently address the design problem by proposing, for the first time in the literature, graph neural networks that jointly predict acceleration performance and hardware costs of a synthesized behavioral specification given optimization directives. The learned model can be used to rapidly approach the Pareto curve by guiding the DSE, taking into account performance and cost estimates. The proposed method outperforms traditional HLS-driven DSE approaches, by accounting for arbitrary length of computer programs and the invariant properties of the input. We propose a novel hybrid control and data flow graph representation that enables training the graph neural network on specifications of different hardware accelerators; the methodology naturally transfers to unseen data-processing applications too. Moreover, we show that our approach achieves prediction accuracy comparable with that of commonly used simulators without having access to analytical models of the HLS compiler and the target FPGA, while being orders of magnitude faster. Finally, the learned representation can be exploited for DSE in unexplored configuration spaces by fine-tuning on a small number of samples from the new target domain.

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph cellular automata (GCA), in which the lattice structure is replaced by an arbitrary graph. In particular, we extend previous work that used convolutional neural networks to learn the transition rule of conventional CA and we use graph neural networks to learn a variety of transition rules for GCA. First, we present a general-purpose architecture for learning GCA, and we show that it can represent any arbitrary GCA with finite and discrete state space. Then, we test our approach on three different tasks: 1) learning the transition rule of a GCA on a Voronoi tessellation; 2) imitating the behaviour of a group of flocking agents; 3) learning a rule that converges to a desired target state., Comment: 35th Conference on Neural Information Processing Systems (NeurIPS 2021)

Reinforcement learning algorithms based on Q-learning are driving Deep Reinforcement Learning (DRL) research towards solving complex problems and achieving super-human performance on many of them. Nevertheless, Q-Learning is known to be positively biased since it learns by using the maximum over noisy estimates of expected values. Systematic overestimation of the action values coupled with the inherently high variance of DRL methods can lead to incrementally accumulate errors, causing learning algorithms to diverge. Ideally, we would like DRL agents to take into account their own uncertainty about the optimality of each action, and be able to exploit it to make more informed estimations of the expected return. In this regard, Weighted Q-Learning (WQL) effectively reduces bias and shows remarkable results in stochastic environments. WQL uses a weighted sum of the estimated action values, where the weights correspond to the probability of each action value being the maximum; however, the computation of these probabilities is only practical in the tabular setting. In this work, we provide methodological advances to benefit from the WQL properties in DRL, by using neural networks trained with Dropout as an effective approximation of deep Gaussian processes. In particular, we adopt the Concrete Dropout variant to obtain calibrated estimates of epistemic uncertainty in DRL. The estimator, then, is obtained by taking several stochastic forward passes through the action-value network and computing the weights in a Monte Carlo fashion. Such weights are Bayesian estimates of the probability of each action value corresponding to the maximum w.r.t. a posterior probability distribution estimated by Dropout. We show how our novel Deep Weighted Q-Learning algorithm reduces the bias w.r.t. relevant baselines and provides empirical evidence of its advantages on representative benchmarks., Comment: RLDM 2022. For a complete discussion and additional results, check our JMLR paper at https://www.jmlr.org/papers/v22/20-633.html

The extremely rapid spread of the SARS-CoV-2 has already resulted in more than 1 million reported deaths of coronavirus disease 2019 (COVID-19). The ability of infectious particles to persist on environmental surfaces is potentially considered a factor for viral spreading. Therefore, limiting viral diffusion in public environments should be achieved with correct disinfection of objects, tissues, and clothes. This study proves how two widespread disinfection systems, short-wavelength ultraviolet light (UV-C) and ozone (O3), are active in vitro on different commonly used materials. The development of devices equipped with UV-C, or ozone generators, may prevent the virus from spreading in public places.