We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

Closed-loop verification of cyber-physical systems with neural network controllers offers strong safety guarantees under certain assumptions. It is, however, difficult to determine whether these guarantees apply at run time because verification assumptions may be violated. To predict safety violations in a verified system, we propose a three-step framework for monitoring the confidence in verification assumptions. First, we represent the sufficient condition for verified safety with a propositional logical formula over assumptions. Second, we build calibrated confidence monitors that evaluate the probability that each assumption holds. Third, we obtain the confidence in the verification guarantees by composing the assumption monitors using a composition function suitable for the logical formula. Our framework provides theoretical bounds on the calibration and conservatism of compositional monitors. In two case studies, we demonstrate that the composed monitors improve over their constituents and successfully predict safety violations.

Energy-efficient navigation constitutes an important challenge in electric vehicles, due to their limited battery capacity. We employ a Bayesian approach to model the energy consumption at road segments for efficient navigation. In order to learn the model parameters, we develop an online learning framework and investigate several exploration strategies such as Thompson Sampling and Upper Confidence Bound. We then extend our online learning framework to multi-agent setting, where multiple vehicles adaptively navigate and learn the parameters of the energy model. We analyze Thompson Sampling and establish rigorous regret bounds on its performance in the single-agent and multi-agent settings, through an analysis of the algorithm under batched feedback. Finally, we demonstrate the performance of our methods via experiments on several real-world city road networks.

We formulate natural gradient variational inference (VI), expectation propagation (EP), and posterior linearisation (PL) as extensions of Newton's method for optimising the parameters of a Bayesian posterior distribution. This viewpoint explicitly casts inference algorithms under the framework of numerical optimisation. We show that common approximations to Newton's method from the optimisation literature, namely Gauss-Newton and quasi-Newton methods (e.g., the BFGS algorithm), are still valid under this'Bayes-Newton' framework. This leads to a suite of novel algorithms which are guaranteed to result in positive semi-definite covariance matrices, unlike standard VI and EP. Our unifying viewpoint provides new insights into the connections between various inference schemes. All the presented methods apply to any model with a Gaussian prior and non-conjugate likelihood, which we demonstrate with (sparse) Gaussian processes and state space models. Keywords: Approximate Bayesian inference, optimisation, variational inference, expectation propagation, Gaussian processes.

The Internet of Vehicles (IoV), whereby interconnected vehicles communicate with each other and with road infrastructure on a common network, has promising socio-economic benefits but also poses new cyber-physical threats. Data on vehicular attackers can be realistically gathered through cyber threat intelligence using systems like honeypots. Admittedly, configuring honeypots introduces a trade-off between the level of honeypot-attacker interactions and any incurred overheads and costs for implementing and monitoring these honeypots. We argue that effective deception can be achieved through strategically configuring the honeypots to represent components of the IoV and engage attackers to collect cyber threat intelligence. In this paper, we present HoneyCar, a novel decision support framework for honeypot deception in IoV. HoneyCar builds upon a repository of known vulnerabilities of the autonomous and connected vehicles found in the Common Vulnerabilities and Exposure (CVE) data within the National Vulnerability Database (NVD) to compute optimal honeypot configuration strategies. By taking a game-theoretic approach, we model the adversarial interaction as a repeated imperfect-information zero-sum game in which the IoV network administrator chooses a set of vulnerabilities to offer in a honeypot and a strategic attacker chooses a vulnerability of the IoV to exploit under uncertainty. Our investigation is substantiated by examining two different versions of the game, with and without the re-configuration cost to empower the network administrator to determine optimal honeypot configurations. We evaluate HoneyCar in a realistic use case to support decision makers with determining optimal honeypot configuration strategies for strategic deployment in IoV.

We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy network upfront, which can then be deployed quickly at the time of the experiment. The iDAD network can be trained on any model which simulates differentiable samples, unlike previous design policy work that requires a closed form likelihood and conditionally independent experiments. At deployment, iDAD allows design decisions to be made in milliseconds, in contrast to traditional BOED approaches that require heavy computation during the experiment itself. We illustrate the applicability of iDAD on a number of experiments, and show that it provides a fast and effective mechanism for performing adaptive design with implicit models.

We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total resource cost of experiments. For example, in hardware design optimization, we need to find the designs that trade-off performance, energy, and area overhead using expensive computational simulations. The key challenge is to select the sequence of experiments to uncover high-quality solutions using minimal resources. In this paper, we propose a general framework for solving MOO problems based on the principle of output space entropy (OSE) search: select the experiment that maximizes the information gained per unit resource cost about the true Pareto front. We appropriately instantiate the principle of OSE search to derive efficient algorithms for the following four MOO problem settings: 1) The most basic single-fidelity setting, where experiments are expensive and accurate; 2) Handling black-box constraints which cannot be evaluated without performing experiments; 3) The discrete multi-fidelity setting, where experiments can vary in the amount of resources consumed and their evaluation accuracy; and 4) The continuous-fidelity setting, where continuous function approximations result in a huge space of experiments. Experiments on diverse synthetic and real-world benchmarks show that our OSE search based algorithms improve over state-of-the-art methods in terms of both computational-efficiency and accuracy of MOO solutions.

In contrast to conventional (single-label) classification, the setting of multilabel classification (MLC) allows an instance to belong to several classes simultaneously. Thus, instead of selecting a single class label, predictions take the form of a subset of all labels. In this paper, we study an extension of the setting of MLC, in which the learner is allowed to partially abstain from a prediction, that is, to deliver predictions on some but not necessarily all class labels. This option is useful in cases of uncertainty, where the learner does not feel confident enough on the entire label set. Adopting a decision-theoretic perspective, we propose a formal framework of MLC with partial abstention, which builds on two main building blocks: First, the extension of underlying MLC loss functions so as to accommodate abstention in a proper way, and second the problem of optimal prediction, that is, finding the Bayes-optimal prediction minimizing this generalized loss in expectation. It is well known that different (generalized) loss functions may have different risk-minimizing predictions, and finding the Bayes predictor typically comes down to solving a computationally complexity optimization problem. In the most general case, given a prediction of the (conditional) joint distribution of possible labelings, the minimizer of the expected loss needs to be found over a number of candidates which is exponential in the number of class labels. We elaborate on properties of risk minimizers for several commonly used (generalized) MLC loss functions, show them to have a specific structure, and leverage this structure to devise efficient methods for computing Bayes predictors. Experimentally, we show MLC with partial abstention to be effective in the sense of reducing loss when being allowed to abstain.

Energy-based models (EBMs) provide an elegant framework for density estimation, but they are notoriously difficult to train. Recent work has established links to generative adversarial networks, where the EBM is trained through a minimax game with a variational value function. We propose a bidirectional bound on the EBM log-likelihood, such that we maximize a lower bound and minimize an upper bound when solving the minimax game. We link one bound to a gradient penalty that stabilizes training, thereby providing grounding for best engineering practice. To evaluate the bounds we develop a new and efficient estimator of the Jacobi-determinant of the EBM generator. We demonstrate that these developments significantly stabilize training and yield high-quality density estimation and sample generation.

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with respect to time. Our natural gradient approach enables application of parallel filtering and smoothing, further reducing the temporal span complexity to be logarithmic in the number of time steps. We derive a sparse approximation that constructs a state-space model over a reduced set of spatial inducing points, and show that for separable Markov kernels the full and sparse cases exactly recover the standard variational GP, whilst exhibiting favourable computational properties. To further improve the spatial scaling we propose a mean-field assumption of independence between spatial locations which, when coupled with sparsity and parallelisation, leads to an efficient and accurate method for large spatio-temporal problems.