This paper presents a Bayesian optimization framework for the automatic tuning of shared controllers which are defined as a Model Predictive Control (MPC) problem. The proposed framework includes the design of performance metrics as well as the representation of user inputs for simulation-based optimization. The framework is applied to the optimization of a shared controller for an Image Guided Therapy robot. VR-based user experiments confirm the increase in performance of the automatically tuned MPC shared controller with respect to a hand-tuned baseline version as well as its generalization ability.
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This work studies nonparametric Bayesian estimation of the intensity function of an inhomogeneous Poisson point process in the important case where the intensity depends on covariates, based on the observation of a single realisation of the point pattern over a large area. It is shown how the presence of covariates allows to borrow information from far away locations in the observation window, enabling consistent inference in the growing domain asymptotics. In particular, optimal posterior contraction rates under both global and point-wise loss functions are derived. The rates in global loss are obtained under conditions on the prior distribution resembling those in the well established theory of Bayesian nonparametrics, here combined with concentration inequalities for functionals of stationary processes to control certain random covariate-dependent loss functions appearing in the analysis. The local rates are derived with an ad-hoc study that builds on recent advances in the theory of P\'olya tree priors, extended to the present multivariate setting with a novel construction that makes use of the random geometry induced by the covariates.
Deep generative models require large amounts of training data. This often poses a problem as the collection of datasets can be expensive and difficult, in particular datasets that are representative of the appropriate underlying distribution (e.g. demographic). This introduces biases in datasets which are further propagated in the models. We present an approach to construct an unbiased generative adversarial network (GAN) from an existing biased GAN by rebalancing the model distribution. We do so by generating balanced data from an existing imbalanced deep generative model using an evolutionary algorithm and then using this data to train a balanced generative model. Additionally, we propose a bias mitigation loss function that minimizes the deviation of the learned class distribution from being equiprobable. We show results for the StyleGAN2 models while training on the Flickr Faces High Quality (FFHQ) dataset for racial fairness and see that the proposed approach improves on the fairness metric by almost 5 times, whilst maintaining image quality. We further validate our approach by applying it to an imbalanced CIFAR10 dataset where we show that we can obtain comparable fairness and image quality as when training on a balanced CIFAR10 dataset which is also twice as large. Lastly, we argue that the traditionally used image quality metrics such as Frechet inception distance (FID) are unsuitable for scenarios where the class distributions are imbalanced and a balanced reference set is not available.
Aircraft are composed of many electronic systems: sensors, displays, navigation equipment and communication elements. These elements require a reliable interconnection, which is a major challenge for communication networks as high reliability and predictability requirements must be verified for safe operation. In addition, their verification via hardware deployments is limited because these are costly and make difficult to try different architectures and configurations, thus delaying the design and development in this area. Therefore, verification at early stages in the design process is of great importance and must be supported by simulation. In this context, this work presents an event-driven link level framework and simulator for the validation of avionics networks. The presented tool supports communication protocols such as Avionics Full-Duplex Switched Ethernet (AFDX), which is a common protocol in avionics, as well as Ethernet, used with static routing. Alsa, accurate results are facilitated by the simulator through the utilization of realistic models for the different devices. The proposed platform is evaluated in Clean Sky's Disruptive Cockpit for Large Passenger Aircraft architecture scenario showing capabilities of the simulator. The speed of the verification is a key factor in its application, so the computational cost is analysed, proving that the execution time is linearly dependent on the number of messages sent.
This paper considers the epistemic justification for a simplicity preference in inductive inference that may be obtained from the machine learning framework of statistical learning theory. Uniting elements from both earlier arguments suggesting and rejecting such a justification, the paper spells out a qualified means-ends and model-relative justificatory argument, built on statistical learning theory's central mathematical learning guarantee for the method of empirical risk minimization.
Any experiment with climate models relies on a potentially large set of spatio-temporal boundary conditions. These can represent both the initial state of the system and/or forcings driving the model output throughout the experiment. Whilst these boundary conditions are typically fixed using available reconstructions in climate modelling studies, they are highly uncertain, that uncertainty is unquantified, and the effect on the output of the experiment can be considerable. We develop efficient quantification of these uncertainties that combines relevant data from multiple models and observations. Starting from the coexchangeability model, we develop a coexchangable process model to capture multiple correlated spatio-temporal fields of variables. We demonstrate that further exchangeability judgements over the parameters within this representation lead to a Bayes linear analogy of a hierarchical model. We use the framework to provide a joint reconstruction of sea-surface temperature and sea-ice concentration boundary conditions at the last glacial maximum (19-23 ka) and use it to force an ensemble of ice-sheet simulations using the FAMOUS-Ice coupled atmosphere and ice-sheet model. We demonstrate that existing boundary conditions typically used in these experiments are implausible given our uncertainties and demonstrate the impact of using more plausible boundary conditions on ice-sheet simulation.
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the number of features p are both increasing such that $p/n \to \gamma\in (0,1)$. An estimator of the out-of-sample error of a robust M-estimator is analysed and proved to be consistent for a large family of loss functions that includes the Huber loss. As an application of this result, we propose an adaptive tuning procedure of the scale parameter $\lambda>0$ of a given loss function $\rho$: choosing$\hat \lambda$ in a given interval $I$ that minimizes the out-of-sample error estimate of the M-estimator constructed with loss $\rho_\lambda(\cdot) = \lambda^2 \rho(\cdot/\lambda)$ leads to the optimal out-of-sample error over $I$. The proof relies on a smoothing argument: the unregularized M-estimation objective function is perturbed, or smoothed, with a Ridge penalty that vanishes as $n\to+\infty$, and show that the unregularized M-estimator of interest inherits properties of its smoothed version.
Explicit bases for the subfield subcodes of projective Reed-Muller codes over the projective plane and their duals are obtained. In particular, we provide a formula for the dimension of these codes. For the general case over the projective space, we generalize the necessary tools to deal with this case as well: we obtain a universal Gr\"obner basis for the vanishing ideal of the set of standard representatives of the projective space and we show how to reduce any monomial with respect to this Gr\"obner basis. With respect to the parameters of these codes, by considering subfield subcodes of projective Reed-Muller codes we obtain long linear codes with good parameters over a small finite field.
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell's equations also solves the wave equation which makes calculations very efficient. In this way our problem can be considered as a coupling problem for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.
In this contribution, we derive a consistent variational formulation for computational homogenization methods and show that traditional FE2 and IGA2 approaches are special discretization and solution techniques of this most general framework. This allows us to enhance dramatically the numerical analysis as well as the solution of the arising algebraic system. In particular, we expand the dimension of the continuous system, discretize the higher dimensional problem consistently and apply afterwards a discrete null-space matrix to remove the additional dimensions. A benchmark problem, for which we can obtain an analytical solution, demonstrates the superiority of the chosen approach aiming to reduce the immense computational costs of traditional FE2 and IGA2 formulations to a fraction of the original requirements. Finally, we demonstrate a further reduction of the computational costs for the solution of general non-linear problems.
We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.
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