We propose a computationally and statistically efficient procedure for segmenting univariate data under piecewise linearity. The proposed moving sum (MOSUM) methodology detects multiple change points where the underlying signal undergoes discontinuous jumps and/or slope changes. Theoretically, it controls the family-wise error rate at a given significance level asymptotically and achieves consistency in multiple change point detection, as well as matching the minimax optimal rate of estimation when the signal is piecewise linear and continuous, all under weak assumptions permitting serial dependence and heavy-tailedness. Computationally, the complexity of the MOSUM procedure is $O(n)$ which, combined with its good performance on simulated datasets, making it highly attractive in comparison with the existing methods. We further demonstrate its good performance on a real data example on rolling element-bearing prognostics.
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In this paper, we compare three different model-based risk measures by evaluating their stengths and weaknesses qualitatively and testing them quantitatively on a set of real longitudinal and intersection scenarios. We start with the traditional heuristic Time-To-Collision (TTC), which we extend towards 2D operation and non-crash cases to retrieve the Time-To-Closest-Encounter (TTCE). The second risk measure models position uncertainty with a Gaussian distribution and uses spatial occupancy probabilities for collision risks. We then derive a novel risk measure based on the statistics of sparse critical events and so-called survival conditions. The resulting survival analysis shows to have an earlier detection time of crashes and less false positive detections in near-crash and non-crash cases supported by its solid theoretical grounding. It can be seen as a generalization of TTCE and the Gaussian method which is suitable for the validation of ADAS and AD.
As the Internet of Things (IoT) continues to expand, data security has become increasingly important for ensuring privacy and safety, especially given the sensitive and, sometimes, critical nature of the data handled by IoT devices. There exist hardware-based trusted execution environments used to protect data, but they are not compatible with low-cost devices that lack hardware-assisted security features. The research in this paper presents software-based protection and encryption mechanisms explicitly designed for embedded devices. The proposed architecture is designed to work with low-cost, low-end devices without requiring the usual changes on the underlying hardware. It protects against hardware attacks and supports runtime updates, enabling devices to write data in protected memory. The proposed solution is an alternative data security approach for low-cost IoT devices without compromising performance or functionality. Our work underscores the importance of developing secure and cost-effective solutions for protecting data in the context of IoT.
We consider a high-dimensional dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model with potential changes at unknown times. The demand model is assumed to be a high-dimensional generalized linear model (GLM), allowing for a feature vector in $\mathbb R^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential change-points. To tackle such a problem, we first design a novel penalized likelihood-based online change-point detection algorithm for high-dimensional GLMs, which is the first algorithm in the change-point literature that achieves optimal minimax localization error rate for high-dimensional GLMs. A change-point detection assisted dynamic pricing (CPDP) policy is further proposed and achieves a near-optimal regret of order $O(s\sqrt{\Upsilon_T T}\log(Td))$, where $s$ is the sparsity level and $\Upsilon_T$ is the number of change-points. This regret is accompanied with a minimax lower bound, demonstrating the optimality of CPDP (up to logarithmic factors). In particular, the optimality with respect to $\Upsilon_T$ is seen for the first time in the dynamic pricing literature, and is achieved via a novel accelerated exploration mechanism. Extensive simulation experiments and a real data application on online lending illustrate the efficiency of the proposed policy and the importance and practical value of handling non-stationarity in dynamic pricing.
Mobile mapping, in particular, Mobile Lidar Scanning (MLS) is increasingly widespread to monitor and map urban scenes at city scale with unprecedented resolution and accuracy. The resulting point cloud sampling of the scene geometry can be meshed in order to create a continuous representation for different applications: visualization, simulation, navigation, etc. Because of the highly dynamic nature of these urban scenes, long term mapping should rely on frequent map updates. A trivial solution is to simply replace old data with newer data each time a new acquisition is made. However it has two drawbacks: 1) the old data may be of higher quality (resolution, precision) than the new and 2) the coverage of the scene might be different in various acquisitions, including varying occlusions. In this paper, we propose a fully automatic pipeline to address these two issues by formulating the problem of merging meshes with different quality, coverage and acquisition time. Our method is based on a combined distance and visibility based change detection, a time series analysis to assess the sustainability of changes, a mesh mosaicking based on a global boolean optimization and finally a stitching of the resulting mesh pieces boundaries with triangle strips. Finally, our method is demonstrated on Robotcar and Stereopolis datasets.
We consider the problem of correct motion planning for T-intersection merge-ins of arbitrary geometry and vehicle density. A merge-in support system has to estimate the chances that a gap between two consecutive vehicles can be taken successfully. In contrast to previous models based on heuristic gap size rules, we present an approach which optimizes the integral risk of the situation using parametrized velocity ramps. It accounts for the risks from curves and all involved vehicles (front and rear on all paths) with a so-called survival analysis. For comparison, we also introduce a specially designed extension of the Intelligent Driver Model (IDM) for entering intersections. We show in a quantitative statistical evaluation that the survival method provides advantages in terms of lower absolute risk (i.e., no crash happens) and better risk-utility tradeoff (i.e., making better use of appearing gaps). Furthermore, our approach generalizes to more complex situations with additional risk sources.
End-to-end deep neural networks (DNNs) have become the state-of-the-art (SOTA) for solving inverse problems. Despite their outstanding performance, during deployment, such networks are sensitive to minor variations in the testing pipeline and often fail to reconstruct small but important details, a feature critical in medical imaging, astronomy, or defence. Such instabilities in DNNs can be explained by the fact that they ignore the forward measurement model during deployment, and thus fail to enforce consistency between their output and the input measurements. To overcome this, we propose a framework that transforms any DNN for inverse problems into a measurement-consistent one. This is done by appending to it an implicit layer (or deep equilibrium network) designed to solve a model-based optimization problem. The implicit layer consists of a shallow learnable network that can be integrated into the end-to-end training while keeping the SOTA DNN fixed. Experiments on single-image super-resolution show that the proposed framework leads to significant improvements in reconstruction quality and robustness over the SOTA DNNs.
Forward simulation-based uncertainty quantification that studies the output distribution of quantities of interest (QoI) is a crucial component for computationally robust statistics and engineering. There is a large body of literature devoted to accurately assessing statistics of QoI, and in particular, multilevel or multifidelity approaches are known to be effective, leveraging cost-accuracy tradeoffs between a given ensemble of models. However, effective algorithms that can estimate the full distribution of outputs are still under active development. In this paper, we introduce a general multifidelity framework for estimating the cumulative distribution functions (CDFs) of vector-valued QoI associated with a high-fidelity model under a budget constraint. Given a family of appropriate control variates obtained from lower fidelity surrogates, our framework involves identifying the most cost-effective model subset and then using it to build an approximate control variates estimator for the target CDF. We instantiate the framework by constructing a family of control variates using intermediate linear approximators and rigorously analyze the corresponding algorithm. Our analysis reveals that the resulting CDF estimator is uniformly consistent and budget-asymptotically optimal, with only mild moment and regularity assumptions. The approach provides a robust multifidelity CDF estimator that is adaptive to the available budget, does not require \textit{a priori} knowledge of cross-model statistics or model hierarchy, and is applicable to general output dimensions. We demonstrate the efficiency and robustness of the approach using several test examples.
We suggest a novel procedure for online change point detection. Our approach expands an idea of maximizing a discrepancy measure between points from pre-change and post-change distributions. This leads to a flexible procedure suitable for both parametric and nonparametric scenarios. We prove non-asymptotic bounds on the average running length of the procedure and its expected detection delay. The efficiency of the algorithm is illustrated with numerical experiments on synthetic and real-world data sets.
The acquisition of the channel covariance matrix is of paramount importance to many strategies in multiple-input-multiple-output (MIMO) communications, such as the minimum mean-square error (MMSE) channel estimation. Therefore, plenty of efficient channel covariance matrix estimation schemes have been proposed in the literature. However, an abrupt change in the channel covariance matrix may happen occasionally in practice due to the change in the scattering environment and the user location. Our paper aims to adopt the classic change detection theory to detect the change in the channel covariance matrix as accurately and quickly as possible such that the new covariance matrix can be re-estimated in time. Specifically, this paper first considers the technique of on-line change detection (also known as quickest/sequential change detection), where we need to detect whether a change in the channel covariance matrix occurs at each channel coherence time interval. Next, because the complexity of detecting the change in a high-dimension covariance matrix at each coherence time interval is too high, we devise a low-complexity off-line strategy in massive MIMO systems, where change detection is merely performed at the last channel coherence time interval of a given time period. Numerical results show that our proposed on-line and off-line schemes can detect the channel covariance change with a small delay and a low false alarm rate. Therefore, our paper theoretically and numerically verifies the feasibility of detecting the channel covariance change accurately and quickly in practice.
We present a parallelized optimization method based on fast Neural Radiance Fields (NeRF) for estimating 6-DoF pose of a camera with respect to an object or scene. Given a single observed RGB image of the target, we can predict the translation and rotation of the camera by minimizing the residual between pixels rendered from a fast NeRF model and pixels in the observed image. We integrate a momentum-based camera extrinsic optimization procedure into Instant Neural Graphics Primitives, a recent exceptionally fast NeRF implementation. By introducing parallel Monte Carlo sampling into the pose estimation task, our method overcomes local minima and improves efficiency in a more extensive search space. We also show the importance of adopting a more robust pixel-based loss function to reduce error. Experiments demonstrate that our method can achieve improved generalization and robustness on both synthetic and real-world benchmarks.
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