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We train a neural network model to predict the full phase space evolution of cosmological N-body simulations. Its success implies that the neural network model is accurately approximating the Green's function expansion that relates the initial conditions of the simulations to its outcome at later times in the deeply nonlinear regime. We test the accuracy of this approximation by assessing its performance on well understood simple cases that have either known exact solutions or well understood expansions. These scenarios include spherical configurations, isolated plane waves, and two interacting plane waves: initial conditions that are very different from the Gaussian random fields used for training. We find our model generalizes well to these well understood scenarios, demonstrating that the networks have inferred general physical principles and learned the nonlinear mode couplings from the complex, random Gaussian training data. These tests also provide a useful diagnostic for finding the model's strengths and weaknesses, and identifying strategies for model improvement. We also test the model on initial conditions that contain only transverse modes, a family of modes that differ not only in their phases but also in their evolution from the longitudinal growing modes used in the training set. When the network encounters these initial conditions that are orthogonal to the training set, the model fails completely. In addition to these simple configurations, we evaluate the model's predictions for the density, displacement, and momentum power spectra with standard initial conditions for N-body simulations. We compare these summary statistics against N-body results and an approximate, fast simulation method called COLA. Our model achieves percent level accuracy at nonlinear scales of $k\sim 1\ \mathrm{Mpc}^{-1}\, h$, representing a significant improvement over COLA.

We commonly assume that data are a homogeneous set of observations when learning the structure of Bayesian networks. However, they often comprise different data sets that are related but not homogeneous because they have been collected in different ways or from different populations. In our previous work (Azzimonti, Corani and Scutari, 2021), we proposed a closed-form Bayesian Hierarchical Dirichlet score for discrete data that pools information across related data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. In this paper, we provide an analogous solution for learning a Bayesian network from continuous data using mixed-effects models to pool information across the related data sets. We study its structural, parametric, predictive and classification accuracy and we show that it outperforms both conditional Gaussian Bayesian networks (that do not perform any pooling) and classical Gaussian Bayesian networks (that disregard the heterogeneous nature of the data). The improvement is marked for low sample sizes and for unbalanced data sets.

Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision rules. In this paper, we consider a submodular optimization based approach for learning rule sets. The learning problem is framed as a subset selection task in which a subset of all possible rules needs to be selected to form an accurate and interpretable rule set. We employ an objective function that exhibits submodularity and thus is amenable to submodular optimization techniques. To overcome the difficulty arose from dealing with the exponential-sized ground set of rules, the subproblem of searching a rule is casted as another subset selection task that asks for a subset of features. We show it is possible to write the induced objective function for the subproblem as a difference of two submodular (DS) functions to make it approximately solvable by DS optimization algorithms. Overall, the proposed approach is simple, scalable, and likely to be benefited from further research on submodular optimization. Experiments on real datasets demonstrate the effectiveness of our method.

We present an historical overview about the connections between the analysis of risk and the control of autonomous systems. We offer two main contributions. Our first contribution is to propose three overlapping paradigms to classify the vast body of literature: the worst-case, risk-neutral, and risk-averse paradigms. We consider an appropriate assessment for the risk of an autonomous system to depend on the application at hand. In contrast, it is typical to assess risk using an expectation, variance, or probability alone. Our second contribution is to unify the concepts of risk and autonomous systems. We achieve this by connecting approaches for quantifying and optimizing the risk that arises from a system's behaviour across academic fields. The survey is highly multidisciplinary. We include research from the communities of reinforcement learning, stochastic and robust control theory, operations research, and formal verification. We describe both model-based and model-free methods, with emphasis on the former. Lastly, we highlight fruitful areas for further research. A key direction is to blend risk-averse model-based and model-free methods to enhance the real-time adaptive capabilities of systems to improve human and environmental welfare.

Estimating worst-case execution times (WCET) is an important activity at early design stages of real-time systems. Based on WCET estimates, engineers make design and implementation decisions to ensure that task executions always complete before their specified deadlines. However, in practice, engineers often cannot provide precise point WCET estimates and prefer to provide plausible WCET ranges. Given a set of real-time tasks with such ranges, we provide an automated technique to determine for what WCET values the system is likely to meet its deadlines, and hence operate safely with a probabilistic guarantee. Our approach combines a search algorithm for generating worst-case scheduling scenarios with polynomial logistic regression for inferring probabilistic safe WCET ranges. We evaluated our approach by applying it to three industrial systems from different domains and several synthetic systems. Our approach efficiently and accurately estimates probabilistic safe WCET ranges within which deadlines are likely to be satisfied with a high degree of confidence.

Our main result shows that when agents' private information about an event are independent conditioning on the event's outcome, then, after an initial announcement, whenever agents have similar beliefs about the outcome, their information is aggregated. That is, there is no false consensus. Our main result has a short proof based on a natural information theoretic framework. A key ingredient of the framework is the equivalence between the sign of the ``interaction information'' and a super/sub-additive property of the value of people's information. This provides an intuitive interpretation and an interesting application of the interaction information, which measures the amount of information shared by three random variables. We illustrate the power of this information theoretic framework by reproving two additional results within it: 1) that agents quickly agree when while announcing beliefs in round robin fashion [Aaronson 2005]; and 2) results from [Chen et al 2010] on when prediction market agents should release information to maximize their payment. We also interpret the information theoretic framework and the above results in prediction markets by proving that the expected reward of revealing information is the conditional mutual information of the information revealed.

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how neural activity relates to perception and behavior. Models of neural dynamics often focus on either low-dimensional projections of neural activity, or on learning dynamical systems that explicitly relate to the neural state over time. We discuss how these two approaches are interrelated by considering dynamical systems as representative of flows on a low-dimensional manifold. Building on this concept, we propose a new decomposed dynamical system model that represents complex non-stationary and nonlinear dynamics of time-series data as a sparse combination of simpler, more interpretable components. The decomposed nature of the dynamics generalizes over previous switched approaches and enables modeling of overlapping and non-stationary drifts in the dynamics. We further present a dictionary learning-driven approach to model fitting, where we leverage recent results in tracking sparse vectors over time. We demonstrate that our model can learn efficient representations and smooth transitions between dynamical modes in both continuous-time and discrete-time examples. We show results on low-dimensional linear and nonlinear attractors to demonstrate that our decomposed dynamical systems model can well approximate nonlinear dynamics. Additionally, we apply our model to C. elegans data, illustrating a diversity of dynamics that is obscured when classified into discrete states.

Machine Learning (ML) systems are a building part of the modern tools which impact our daily life in several application domains. Due to their black-box nature, those systems are hardly adopted in application domains (e.g. health, finance) where understanding the decision process is of paramount importance. Explanation methods were developed to explain how the ML model has taken a specific decision for a given case/instance. Graph Counterfactual Explanations (GCE) is one of the explanation techniques adopted in the Graph Learning domain. The existing works of Graph Counterfactual Explanations diverge mostly in the problem definition, application domain, test data, and evaluation metrics, and most existing works do not compare exhaustively against other counterfactual explanation techniques present in the literature. We present GRETEL, a unified framework to develop and test GCE methods in several settings. GRETEL is a highly extensible evaluation framework which promotes the Open Science and the evaluations reproducibility by providing a set of well-defined mechanisms to integrate and manage easily: both real and synthetic datasets, ML models, state-of-the-art explanation techniques, and evaluation measures. To present GRETEL, we show the experiments conducted to integrate and test several synthetic and real datasets with several existing explanation techniques and base ML models.

Recommender system is one of the most important information services on today's Internet. Recently, graph neural networks have become the new state-of-the-art approach of recommender systems. In this survey, we conduct a comprehensive review of the literature in graph neural network-based recommender systems. We first introduce the background and the history of the development of both recommender systems and graph neural networks. For recommender systems, in general, there are four aspects for categorizing existing works: stage, scenario, objective, and application. For graph neural networks, the existing methods consist of two categories, spectral models and spatial ones. We then discuss the motivation of applying graph neural networks into recommender systems, mainly consisting of the high-order connectivity, the structural property of data, and the enhanced supervision signal. We then systematically analyze the challenges in graph construction, embedding propagation/aggregation, model optimization, and computation efficiency. Afterward and primarily, we provide a comprehensive overview of a multitude of existing works of graph neural network-based recommender systems, following the taxonomy above. Finally, we raise discussions on the open problems and promising future directions of this area. We summarize the representative papers along with their codes repositories in //github.com/tsinghua-fib-lab/GNN-Recommender-Systems.

To address the sparsity and cold start problem of collaborative filtering, researchers usually make use of side information, such as social networks or item attributes, to improve recommendation performance. This paper considers the knowledge graph as the source of side information. To address the limitations of existing embedding-based and path-based methods for knowledge-graph-aware recommendation, we propose Ripple Network, an end-to-end framework that naturally incorporates the knowledge graph into recommender systems. Similar to actual ripples propagating on the surface of water, Ripple Network stimulates the propagation of user preferences over the set of knowledge entities by automatically and iteratively extending a user's potential interests along links in the knowledge graph. The multiple "ripples" activated by a user's historically clicked items are thus superposed to form the preference distribution of the user with respect to a candidate item, which could be used for predicting the final clicking probability. Through extensive experiments on real-world datasets, we demonstrate that Ripple Network achieves substantial gains in a variety of scenarios, including movie, book and news recommendation, over several state-of-the-art baselines.