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To mitigate the high energy demand of Neural Network (NN) based Autonomous Driving Systems (ADSs), we consider the problem of offloading NN controllers from the ADS to nearby edge-computing infrastructure, but in such a way that formal vehicle safety properties are guaranteed. In particular, we propose the EnergyShield framework, which repurposes a controller ''shield'' as a low-power runtime safety monitor for the ADS vehicle. Specifically, the shield in EnergyShield provides not only safety interventions but also a formal, state-based quantification of the tolerable edge response time before vehicle safety is compromised. Using EnergyShield, an ADS can then save energy by wirelessly offloading NN computations to edge computers, while still maintaining a formal guarantee of safety until it receives a response (on-vehicle hardware provides a just-in-time fail safe). To validate the benefits of EnergyShield, we implemented and tested it in the Carla simulation environment. Our results show that EnergyShield maintains safe vehicle operation while providing significant energy savings compared to on-vehicle NN evaluation: from 24% to 54% less energy across a range of wireless conditions and edge delays.

Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth function: a displacement and a damage field. Their numerical implementation is typically based on the discretization of both fields by nodal $\mathbb{P}^1$ Lagrange finite elements. In this article, we propose a nonconforming approximation by discontinuous elements for the displacement and nonconforming elements, whose gradient is more isotropic, for the damage. The handling of the nonconformity is derived from that of heterogeneous diffusion problems. We illustrate the robustness and versatility of the proposed method through series of examples.

We develop a novel full-Bayesian approach for multiple correlated precision matrices, called multiple Graphical Horseshoe (mGHS). The proposed approach relies on a novel multivariate shrinkage prior based on the Horseshoe prior that borrows strength and shares sparsity patterns across groups, improving posterior edge selection when the precision matrices are similar. On the other hand, there is no loss of performance when the groups are independent. Moreover, mGHS provides a similarity matrix estimate, useful for understanding network similarities across groups. We implement an efficient Metropolis-within-Gibbs for posterior inference; specifically, local variance parameters are updated via a novel and efficient modified rejection sampling algorithm that samples from a three-parameter Gamma distribution. The method scales well with respect to the number of variables and provides one of the fastest full-Bayesian approaches for the estimation of multiple precision matrices. Finally, edge selection is performed with a novel approach based on model cuts. We empirically demonstrate that mGHS outperforms competing approaches through both simulation studies and an application to a bike-sharing dataset.

This paper explores reward mechanisms for a query incentive network in which agents seek information from social networks. In a query tree issued by the task owner, each agent is rewarded by the owner for contributing to the solution, for instance, solving the task or inviting others to solve it. The reward mechanism determines the reward for each agent and motivates all agents to propagate and report their information truthfully. In particular, the reward cannot exceed the budget set by the task owner. However, our impossibility results demonstrate that a reward mechanism cannot simultaneously achieve Sybil-proof (agents benefit from manipulating multiple fake identities), collusion-proof (multiple agents pretend as a single agent to improve the reward), and other essential properties. In order to address these issues, we propose two novel reward mechanisms. The first mechanism achieves Sybil-proof and collusion-proof, respectively; the second mechanism sacrifices Sybil-proof to achieve the approximate versions of Sybil-proof and collusion-proof. Additionally, we show experimentally that our second reward mechanism outperforms the existing ones.

In this work, we advocate for the importance of singular learning theory (SLT) as it pertains to the theory and practice of variational inference in Bayesian neural networks (BNNs). To begin, using SLT, we lay to rest some of the confusion surrounding discrepancies between downstream predictive performance measured via e.g., the test log predictive density, and the variational objective. Next, we use the SLT-corrected asymptotic form for singular posterior distributions to inform the design of the variational family itself. Specifically, we build upon the idealized variational family introduced in \citet{bhattacharya_evidence_2020} which is theoretically appealing but practically intractable. Our proposal takes shape as a normalizing flow where the base distribution is a carefully-initialized generalized gamma. We conduct experiments comparing this to the canonical Gaussian base distribution and show improvements in terms of variational free energy and variational generalization error.

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^\alpha$ is positive definite in the limit when $\alpha=1$, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically normal when $\alpha\in(0,1]$ albeit at slower rates and under additional assumptions on the sample size. The results hold whether $\alpha$ is constant or varies across factor loadings. The framework developed for heterogeneous loadings and the simplified proofs that can be also used in strong factor analysis are of independent interest.

We propose and analyze a first-order finite difference scheme for the functionalized Cahn-Hilliard (FCH) equation with a logarithmic Flory-Huggins potential. The semi-implicit numerical scheme is designed based on a suitable convex-concave decomposition of the FCH free energy. We prove unique solvability of the numerical algorithm and verify its unconditional energy stability without any restriction on the time step size. Thanks to the singular nature of the logarithmic part in the Flory-Huggins potential near the pure states $\pm 1$, we establish the so-called positivity-preserving property for the phase function at a theoretic level. As a consequence, the numerical solutions will never reach the singular values $\pm 1$ in the point-wise sense and the fully discrete scheme is well defined at each time step. Next, we present a detailed optimal rate convergence analysis and derive error estimates in $l^{\infty}(0,T;L_h^2)\cap l^2(0,T;H^3_h)$ under a linear refinement requirement $\Delta t\leq C_1 h$. To achieve the goal, a higher order asymptotic expansion (up to the second order temporal and spatial accuracy) based on the Fourier projection is utilized to control the discrete maximum norm of solutions to the numerical scheme. We show that if the exact solution to the continuous problem is strictly separated from the pure states $\pm 1$, then the numerical solutions can be kept away from $\pm 1$ by a positive distance that is uniform with respect to the size of the time step and the grid. Finally, a few numerical experiments are presented. Convergence test is performed to demonstrate the accuracy and robustness of the proposed numerical scheme. Pearling bifurcation, meandering instability and spinodal decomposition are observed in the numerical simulations.

Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo derivatives have been proposed. We numerically study ten algorithms based on slice sampling, hit-and-run and differential evolution algorithms in ellipsoidal, non-ellipsoidal and non-convex problems from 2 to 100 dimensions. Mixing capabilities are evaluated with the nested sampling shrinkage test. This makes our results valid independent of how heavy-tailed the posteriors are. Given the same number of steps, slice sampling is outperformed by hit-and-run and whitened slice sampling, while whitened hit-and-run does not provide as good results. Proposing along differential vectors of live point pairs also leads to the highest efficiencies, and appears promising for multi-modal problems. The tested proposals are implemented in the UltraNest nested sampling package, enabling efficient low and high-dimensional inference of a large class of practical inference problems relevant to astronomy, cosmology, particle physics and astronomy.

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified multiple-testing procedure of time-lagged cross-correlation functions with a fixed or diverging number of lags, our method can accurately disclose flexible time-varying network structures associated with complex functional structures at all time points. We broaden the applicability of our method to the structure breaks by developing difference-based nonparametric estimators of cross-correlations, achieve accurate family-wise error control via a bootstrap-assisted procedure adaptive to the complex temporal dynamics, and enhance the probability of recovering the time-varying network structures using a new uniform variance reduction technique. We prove the asymptotic validity of the proposed method and demonstrate its effectiveness in finite samples through simulation studies and empirical applications.

In this paper, we propose novel Gaussian process-gated hierarchical mixtures of experts (GPHMEs) that are used for building gates and experts. Unlike in other mixtures of experts where the gating models are linear to the input, the gating functions of our model are inner nodes built with Gaussian processes based on random features that are non-linear and non-parametric. Further, the experts are also built with Gaussian processes and provide predictions that depend on test data. The optimization of the GPHMEs is carried out by variational inference. There are several advantages of the proposed GPHMEs. One is that they outperform tree-based HME benchmarks that partition the data in the input space. Another advantage is that they achieve good performance with reduced complexity. A third advantage of the GPHMEs is that they provide interpretability of deep Gaussian processes and more generally of deep Bayesian neural networks. Our GPHMEs demonstrate excellent performance for large-scale data sets even with quite modest sizes.