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Cross-validation is the standard approach for tuning parameter selection in many non-parametric regression problems. However its use is less common in change-point regression, perhaps as its prediction error-based criterion may appear to permit small spurious changes and hence be less well-suited to estimation of the number and location of change-points. We show that in fact the problems of cross-validation with squared error loss are more severe and can lead to systematic under- or over-estimation of the number of change-points, and highly suboptimal estimation of the mean function in simple settings where changes are easily detectable. We propose two simple approaches to remedy these issues, the first involving the use of absolute error rather than squared error loss, and the second involving modifying the holdout sets used. For the latter, we provide conditions that permit consistent estimation of the number of change-points for a general change-point estimation procedure. We show these conditions are satisfied for optimal partitioning using new results on its performance when supplied with the incorrect number of change-points. Numerical experiments show that the absolute error approach in particular is competitive with common change-point methods using classical tuning parameter choices when error distributions are well-specified, but can substantially outperform these in misspecified models. An implementation of our methodology is available in the R package crossvalidationCP on CRAN.

In this work, we propose an efficient two-stage algorithm solving a joint problem of correlation detection and partial alignment recovery between two Gaussian databases. Correlation detection is a hypothesis testing problem; under the null hypothesis, the databases are independent, and under the alternate hypothesis, they are correlated, under an unknown row permutation. We develop bounds on the type-I and type-II error probabilities, and show that the analyzed detector performs better than a recently proposed detector, at least for some specific parameter choices. Since the proposed detector relies on a statistic, which is a sum of dependent indicator random variables, then in order to bound the type-I probability of error, we develop a novel graph-theoretic technique for bounding the $k$-th order moments of such statistics. When the databases are accepted as correlated, the algorithm also recovers some partial alignment between the given databases. We also propose two more algorithms: (i) One more algorithm for partial alignment recovery, whose reliability and computational complexity are both higher than those of the first proposed algorithm. (ii) An algorithm for full alignment recovery, which has a reduced amount of calculations and a not much lower error probability, when compared to the optimal recovery procedure.

Autonomous exploration has many important applications. However, classic information gain-based or frontier-based exploration only relies on the robot current state to determine the immediate exploration goal, which lacks the capability of predicting the value of future states and thus leads to inefficient exploration decisions. This paper presents a method to learn how "good" states are, measured by the state value function, to provide a guidance for robot exploration in real-world challenging environments. We formulate our work as an off-policy evaluation (OPE) problem for robot exploration (OPERE). It consists of offline Monte-Carlo training on real-world data and performs Temporal Difference (TD) online adaptation to optimize the trained value estimator. We also design an intrinsic reward function based on sensor information coverage to enable the robot to gain more information with sparse extrinsic rewards. Results show that our method enables the robot to predict the value of future states so as to better guide robot exploration. The proposed algorithm achieves better prediction and exploration performance compared with the state-of-the-arts. To the best of our knowledge, this work for the first time demonstrates value function prediction on real-world dataset for robot exploration in challenging subterranean and urban environments. More details and demo videos can be found at //jeffreyyh.github.io/opere/.

Augmenting LiDAR input with multiple previous frames provides richer semantic information and thus boosts performance in 3D object detection, However, crowded point clouds in multi-frames can hurt the precise position information due to the motion blur and inaccurate point projection. In this work, we propose a novel feature fusion strategy, DynStaF (Dynamic-Static Fusion), which enhances the rich semantic information provided by the multi-frame (dynamic branch) with the accurate location information from the current single-frame (static branch). To effectively extract and aggregate complimentary features, DynStaF contains two modules, Neighborhood Cross Attention (NCA) and Dynamic-Static Interaction (DSI), operating through a dual pathway architecture. NCA takes the features in the static branch as queries and the features in the dynamic branch as keys (values). When computing the attention, we address the sparsity of point clouds and take only neighborhood positions into consideration. NCA fuses two features at different feature map scales, followed by DSI providing the comprehensive interaction. To analyze our proposed strategy DynStaF, we conduct extensive experiments on the nuScenes dataset. On the test set, DynStaF increases the performance of PointPillars in NDS by a large margin from 57.7% to 61.6%. When combined with CenterPoint, our framework achieves 61.0% mAP and 67.7% NDS, leading to state-of-the-art performance without bells and whistles.

Incrementally recovering 3D dense structures from monocular videos is of paramount importance since it enables various robotics and AR applications. Feature volumes have recently been shown to enable efficient and accurate incremental dense reconstruction without the need to first estimate depth, but they are not able to achieve as high of a resolution as depth-based methods due to the large memory consumption of high-resolution feature volumes. This letter proposes a real-time feature volume-based dense reconstruction method that predicts TSDF (Truncated Signed Distance Function) values from a novel sparsified deep feature volume, which is able to achieve higher resolutions than previous feature volume-based methods, and is favorable in large-scale outdoor scenarios where the majority of voxels are empty. An uncertainty-aware multi-view stereo (MVS) network is leveraged to infer initial voxel locations of the physical surface in a sparse feature volume. Then for refining the recovered 3D geometry, deep features are attentively aggregated from multiview images at potential surface locations, and temporally fused. Besides achieving higher resolutions than before, our method is shown to produce more complete reconstructions with finer detail in many cases. Extensive evaluations on both public and self-collected datasets demonstrate a very competitive real-time reconstruction result for our method compared to state-of-the-art reconstruction methods in both indoor and outdoor settings.

We study the change point detection problem for high-dimensional linear regression models. The existing literature mainly focused on the change point estimation with stringent sub-Gaussian assumptions on the errors. In practice, however, there is no prior knowledge about the existence of a change point or the tail structures of errors. To address these issues, in this paper, we propose a novel tail-adaptive approach for simultaneous change point testing and estimation. The method is built on a new loss function which is a weighted combination between the composite quantile and least squared losses, allowing us to borrow information of the possible change points from both the conditional mean and quantiles. For the change point testing, based on the adjusted $L_2$-norm aggregation of a weighted score CUSUM process, we propose a family of individual testing statistics with different weights to account for the unknown tail structures. Combining the individual tests, a tail-adaptive test is further constructed that is powerful for sparse alternatives of regression coefficients' changes under various tail structures. For the change point estimation, a family of argmax-based individual estimators is proposed once a change point is detected. In theory, for both individual and tail-adaptive tests, the bootstrap procedures are proposed to approximate their limiting null distributions. Under some mild conditions, we justify the validity of the new tests in terms of size and power under the high-dimensional setup. The corresponding change point estimators are shown to be rate optimal up to a logarithm factor. Moreover, combined with the wild binary segmentation technique, a new algorithm is proposed to detect multiple change points in a tail-adaptive manner. Extensive numerical results are conducted to illustrate the appealing performance of the proposed method.

Stein Variational Gradient Descent (SVGD) is a nonparametric particle-based deterministic sampling algorithm. Despite its wide usage, understanding the theoretical properties of SVGD has remained a challenging problem. For sampling from a Gaussian target, the SVGD dynamics with a bilinear kernel will remain Gaussian as long as the initializer is Gaussian. Inspired by this fact, we undertake a detailed theoretical study of the Gaussian-SVGD, i.e., SVGD projected to the family of Gaussian distributions via the bilinear kernel, or equivalently Gaussian variational inference (GVI) with SVGD. We present a complete picture by considering both the mean-field PDE and discrete particle systems. When the target is strongly log-concave, the mean-field Gaussian-SVGD dynamics is proven to converge linearly to the Gaussian distribution closest to the target in KL divergence. In the finite-particle setting, there is both uniform in time convergence to the mean-field limit and linear convergence in time to the equilibrium if the target is Gaussian. In the general case, we propose a density-based and a particle-based implementation of the Gaussian-SVGD, and show that several recent algorithms for GVI, proposed from different perspectives, emerge as special cases of our unified framework. Interestingly, one of the new particle-based instance from this framework empirically outperforms existing approaches. Our results make concrete contributions towards obtaining a deeper understanding of both SVGD and GVI.

Conventional methods for object detection typically require a substantial amount of training data and preparing such high-quality training data is very labor-intensive. In this paper, we propose a novel few-shot object detection network that aims at detecting objects of unseen categories with only a few annotated examples. Central to our method are our Attention-RPN, Multi-Relation Detector and Contrastive Training strategy, which exploit the similarity between the few shot support set and query set to detect novel objects while suppressing false detection in the background. To train our network, we contribute a new dataset that contains 1000 categories of various objects with high-quality annotations. To the best of our knowledge, this is one of the first datasets specifically designed for few-shot object detection. Once our few-shot network is trained, it can detect objects of unseen categories without further training or fine-tuning. Our method is general and has a wide range of potential applications. We produce a new state-of-the-art performance on different datasets in the few-shot setting. The dataset link is //github.com/fanq15/Few-Shot-Object-Detection-Dataset.

This paper introduces an online model for object detection in videos designed to run in real-time on low-powered mobile and embedded devices. Our approach combines fast single-image object detection with convolutional long short term memory (LSTM) layers to create an interweaved recurrent-convolutional architecture. Additionally, we propose an efficient Bottleneck-LSTM layer that significantly reduces computational cost compared to regular LSTMs. Our network achieves temporal awareness by using Bottleneck-LSTMs to refine and propagate feature maps across frames. This approach is substantially faster than existing detection methods in video, outperforming the fastest single-frame models in model size and computational cost while attaining accuracy comparable to much more expensive single-frame models on the Imagenet VID 2015 dataset. Our model reaches a real-time inference speed of up to 15 FPS on a mobile CPU.

Object detection is an important and challenging problem in computer vision. Although the past decade has witnessed major advances in object detection in natural scenes, such successes have been slow to aerial imagery, not only because of the huge variation in the scale, orientation and shape of the object instances on the earth's surface, but also due to the scarcity of well-annotated datasets of objects in aerial scenes. To advance object detection research in Earth Vision, also known as Earth Observation and Remote Sensing, we introduce a large-scale Dataset for Object deTection in Aerial images (DOTA). To this end, we collect $2806$ aerial images from different sensors and platforms. Each image is of the size about 4000-by-4000 pixels and contains objects exhibiting a wide variety of scales, orientations, and shapes. These DOTA images are then annotated by experts in aerial image interpretation using $15$ common object categories. The fully annotated DOTA images contains $188,282$ instances, each of which is labeled by an arbitrary (8 d.o.f.) quadrilateral To build a baseline for object detection in Earth Vision, we evaluate state-of-the-art object detection algorithms on DOTA. Experiments demonstrate that DOTA well represents real Earth Vision applications and are quite challenging.