A confidence sequence (CS) is a sequence of confidence intervals that is valid at arbitrary data-dependent stopping times. These are useful in applications like A/B testing, multi-armed bandits, off-policy evaluation, election auditing, etc. We present three approaches to constructing a confidence sequence for the population mean, under the minimal assumption that only an upper bound $\sigma^2$ on the variance is known. While previous works rely on light-tail assumptions like boundedness or subGaussianity (under which all moments of a distribution exist), the confidence sequences in our work are able to handle data from a wide range of heavy-tailed distributions. The best among our three methods -- the Catoni-style confidence sequence -- performs remarkably well in practice, essentially matching the state-of-the-art methods for $\sigma^2$-subGaussian data, and provably attains the $\sqrt{\log \log t/t}$ lower bound due to the law of the iterated logarithm. Our findings have important implications for sequential experimentation with unbounded observations, since the $\sigma^2$-bounded-variance assumption is more realistic and easier to verify than $\sigma^2$-subGaussianity (which implies the former). We also extend our methods to data with infinite variance, but having $p$-th central moment ($1<p<2$).
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Cooperative Intelligent Transport Systems (C-ITS) create, share and process massive amounts of data which needs to be real-time managed to enable new cooperative and autonomous driving applications. Vehicle-to-Everything (V2X) communications facilitate information exchange among vehicles and infrastructures using various protocols. By providing computer power, data storage, and low latency capabilities, Multi-access Edge Computing (MEC) has become a key enabling technology in the transport industry. The Local Dynamic Map (LDM) concept has consequently been extended to its utilisation in MECs, into an efficient, collaborative, and centralised Edge Dynamic Map (EDM) for C-ITS applications. This research presents an EDM architecture for V2X communications and implements a real-time proof-of-concept using a Time-Series Database (TSDB) engine to store vehicular message information. The performance evaluation includes data insertion and querying, assessing the system's capacity and scale for low-latency Cooperative Awareness Message (CAM) applications. Traffic simulations using SUMO have been employed to generate virtual routes for thousands of vehicles, demonstrating the transmission of virtual CAM messages to the EDM.
In recent years, the concept of introducing physics to machine learning has become widely popular. Most physics-inclusive ML-techniques however are still limited to a single geometry or a set of parametrizable geometries. Thus, there remains the need to train a new model for a new geometry, even if it is only slightly modified. With this work we introduce a technique with which it is possible to learn approximate solutions to the steady-state Navier--Stokes equations in varying geometries without the need of parametrization. This technique is based on a combination of a U-Net-like CNN and well established discretization methods from the field of the finite difference method.The results of our physics-aware CNN are compared to a state-of-the-art data-based approach. Additionally, it is also shown how our approach performs when combined with the data-based approach.
We investigate error of the Euler scheme in the case when the right-hand side function of the underlying ODE satisfies nonstandard assumptions such as local one-sided Lipschitz condition and local H\"older continuity. Moreover, we assume two cases in regards to information availability: exact and noisy with respect to the right-hand side function. Optimality analysis of the Euler scheme is also provided. Finally, we present the results of some numerical experiments.
We consider the problem of identifying the acoustic impedance of a wall surface from noisy pressure measurements in a closed room using a Bayesian approach. The room acoustics is modeled by the interior Helmholtz equation with impedance boundary conditions. The aim is to compute moments of the acoustic impedance to estimate a suitable density function of the impedance coefficient. For the computation of moments we use ratio estimators and Monte-Carlo sampling. We consider two different experimental scenarios. In the first scenario, the noisy measurements correspond to a wall modeled by impedance boundary conditions. In this case, the Bayesian algorithm uses a model that is (up to the noise) consistent with the measurements and our algorithm is able to identify acoustic impedance with high accuracy. In the second scenario, the noisy measurements come from a coupled acoustic-structural problem, modeling a wall made of glass, whereas the Bayesian algorithm still uses a model with impedance boundary conditions. In this case, the parameter identification model is inconsistent with the measurements and therefore is not capable to represent them well. Nonetheless, for particular frequency bands the Bayesian algorithm identifies estimates with high likelihood. Outside these frequency bands the algorithm fails. We discuss the results of both examples and possible reasons for the failure of the latter case for particular frequency values.
Sequential algorithms such as sequential importance sampling (SIS) and sequential Monte Carlo (SMC) have proven fundamental in Bayesian inference for models not admitting a readily available likelihood function. For approximate Bayesian computation (ABC), SMC-ABC is the state-of-art sampler. However, since the ABC paradigm is intrinsically wasteful, sequential ABC schemes can benefit from well-targeted proposal samplers that efficiently avoid improbable parameter regions. We contribute to the ABC modeller's toolbox with novel proposal samplers that are conditional to summary statistics of the data. In a sense, the proposed parameters are "guided" to rapidly reach regions of the posterior surface that are compatible with the observed data. This speeds up the convergence of these sequential samplers, thus reducing the computational effort, while preserving the accuracy in the inference. We provide a variety of guided Gaussian and copula-based samplers for both SIS-ABC and SMC-ABC easing inference for challenging case-studies, including multimodal posteriors, highly correlated posteriors, hierarchical models with high-dimensional summary statistics (180 summaries used to infer 21 parameters) and a simulation study of cell movements (using more than 400 summaries).
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the correspondence-interleaving distance, a metric for hierarchical clusterings that we introduce. Taking certain one-parameter slices of degree-Rips recovers well-known methods for density-based clustering, but we show that these methods are unstable. However, we prove that degree-Rips, as a multiparameter object, is stable, and we propose an alternative approach for taking slices of degree-Rips, which yields a one-parameter hierarchical clustering algorithm with better stability properties. We prove that this algorithm is consistent, using the correspondence-interleaving distance. We provide an algorithm for extracting a single clustering from one-parameter hierarchical clusterings, which is stable with respect to the correspondence-interleaving distance. And, we integrate these methods into a pipeline for density-based clustering, which we call Persistable. Adapting tools from multiparameter persistent homology, we propose visualization tools that guide the selection of all parameters of the pipeline. We demonstrate Persistable on benchmark datasets, showing that it identifies multi-scale cluster structure in data.
Navigating automated driving systems (ADSs) through complex driving environments is difficult. Predicting the driving behavior of surrounding human-driven vehicles (HDVs) is a critical component of an ADS. This paper proposes an enhanced motion-planning approach for an ADS in a highway-merging scenario. The proposed enhanced approach utilizes the results of two aspects: the driving behavior and long-term trajectory of surrounding HDVs, which are coupled using a hierarchical model that is used for the motion planning of an ADS to improve driving safety.
Modulating the stiffness of soft actuators is crucial for improving the efficiency of interaction with the environment. However, current stiffness modulation mechanisms are hard to achieve high lateral stiffness and a wide range of bending stiffness simultaneously. Here, we draw inspiration from the anatomical structure of the finger and propose a bi-directional tunable stiffness actuator (BTSA). BTSA is a soft-rigid hybrid structure that combines air-tendon hybrid actuation (ATA) and bone-like structures (BLS). We develop a corresponding fabrication method and a stiffness analysis model to support the design of BLS. The results show that the influence of the BLS on bending deformation is negligible, with a distal point distance error of less than 1.5 mm. Moreover, the bi-directional tunable stiffness is proved to be functional. The bending stiffness can be tuned by ATA from 0.23 N/mm to 0.70 N/mm, with a magnification of 3 times. The addition of BLS improves lateral stiffness up to 4.2 times compared with the one without BLS, and the lateral stiffness can be tuned decoupling within 1.2 to 2.1 times (e.g. from 0.35 N/mm to 0.46 N/mm when the bending angle is 45 deg). Finally, a four-BTSA gripper is developed to conduct horizontal lifting and grasping tasks to demonstrate the advantages of BTSA.
We consider the information fiber optical channel modeled by the nonlinear Schrodinger equation with additive Gaussian noise. Using path-integral approach and perturbation theory for the small dimensionless parameter of the second dispersion, we calculate the conditional probability density functional in the leading and next-to-leading order in the dimensionless second dispersion parameter associated with the input signal bandwidth. Taking into account specific filtering of the output signal by the output signal receiver, we calculate the mutual information in the leading and next-to-leading order in the dispersion parameter and in the leading order in the parameter signal-to-noise ratio (SNR). Further, we find the explicit expression for the mutual information in case of the modified Gaussian input signal distribution taking into account the limited frequency bandwidth of the input signal.
The goal of this short note is to discuss the relation between Kullback--Leibler divergence and total variation distance, starting with the celebrated Pinsker's inequality relating the two, before switching to a simple, yet (arguably) more useful inequality, apparently not as well known, due to Bretagnolle and Huber. We also discuss applications of this bound for minimax testing lower bounds.
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