大型现代数据往往涉及评估和测试高维未知参数。所希望的是识别稀疏信号，``针在草堆“”，具有精度和错误发现控制。然而，在现代数据结构的空前复杂性和异质性需要新的机器学习工具来有效地利用共性和稳健地调整既稀疏和异质性。此外，对于高维参数的估计往往缺乏量化的不确定性。在本文中，我们提出了一个新颖的穗和 - 非参数混合物之前（SNP） - 尖峰，以促进稀疏和非参数结构，以捕获信号。在对比状态的最先进的方法中，所提出的方法解决了估计和在与几个优点一次测试的问题：1）精确稀疏估计; 2）的点估计与收缩/阈值处理软特性; 3）对于不确定性量化可信区间; 4）最佳的多个测试程序，其控制错误发现率。我们的方法表现出有前途的两个模拟数据和基因表达的案例研究经验性能。

Recent investigations on rotation invariance for 3D point clouds have been devoted to devising rotation-invariant feature descriptors or learning canonical spaces where objects are semantically aligned. Examinations of learning frameworks for invariance have seldom been looked into. In this work, we review rotation invariance in terms of point cloud registration and propose an effective framework for rotation invariance learning via three sequential stages, namely rotation-invariant shape encoding, aligned feature integration, and deep feature registration. We first encode shape descriptors constructed with respect to reference frames defined over different scales, e.g., local patches and global topology, to generate rotation-invariant latent shape codes. Within the integration stage, we propose Aligned Integration Transformer to produce a discriminative feature representation by integrating point-wise self- and cross-relations established within the shape codes. Meanwhile, we adopt rigid transformations between reference frames to align the shape codes for feature consistency across different scales. Finally, the deep integrated feature is registered to both rotation-invariant shape codes to maximize feature similarities, such that rotation invariance of the integrated feature is preserved and shared semantic information is implicitly extracted from shape codes. Experimental results on 3D shape classification, part segmentation, and retrieval tasks prove the feasibility of our work. Our project page is released at: https://rotation3d.github.io/.

With the attention mechanism, transformers achieve significant empirical successes. Despite the intuitive understanding that transformers perform relational inference over long sequences to produce desirable representations, we lack a rigorous theory on how the attention mechanism achieves it. In particular, several intriguing questions remain open: (a) What makes a desirable representation? (b) How does the attention mechanism infer the desirable representation within the forward pass? (c) How does a pretraining procedure learn to infer the desirable representation through the backward pass? We observe that, as is the case in BERT and ViT, input tokens are often exchangeable since they already include positional encodings. The notion of exchangeability induces a latent variable model that is invariant to input sizes, which enables our theoretical analysis. - To answer (a) on representation, we establish the existence of a sufficient and minimal representation of input tokens. In particular, such a representation instantiates the posterior distribution of the latent variable given input tokens, which plays a central role in predicting output labels and solving downstream tasks. - To answer (b) on inference, we prove that attention with the desired parameter infers the latent posterior up to an approximation error, which is decreasing in input sizes. In detail, we quantify how attention approximates the conditional mean of the value given the key, which characterizes how it performs relational inference over long sequences. - To answer (c) on learning, we prove that both supervised and self-supervised objectives allow empirical risk minimization to learn the desired parameter up to a generalization error, which is independent of input sizes. Particularly, in the self-supervised setting, we identify a condition number that is pivotal to solving downstream tasks.

In the new era of personalization, learning the heterogeneous treatment effect (HTE) becomes an inevitable trend with numerous applications. Yet, most existing HTE estimation methods focus on independently and identically distributed observations and cannot handle the non-stationarity and temporal dependency in the common panel data setting. The treatment evaluators developed for panel data, on the other hand, typically ignore the individualized information. To fill the gap, in this paper, we initialize the study of HTE estimation in panel data. Under different assumptions for HTE identifiability, we propose the corresponding heterogeneous one-side and two-side synthetic learner, namely H1SL and H2SL, by leveraging the state-of-the-art HTE estimator for non-panel data and generalizing the synthetic control method that allows flexible data generating process. We establish the convergence rates of the proposed estimators. The superior performance of the proposed methods over existing ones is demonstrated by extensive numerical studies.

The past few years have witnessed the prevalence of self-supervised representation learning within the language and 2D vision communities. However, such advancements have not been fully migrated to the community of 3D point cloud learning. Different from previous pre-training pipelines for 3D point clouds that generally fall into the scope of either generative modeling or contrastive learning, in this paper, we investigate a translative pre-training paradigm, namely PointVST, driven by a novel self-supervised pretext task of cross-modal translation from an input 3D object point cloud to its diverse forms of 2D rendered images (e.g., silhouette, depth, contour). Specifically, we begin with deducing view-conditioned point-wise embeddings via the insertion of the viewpoint indicator, and then adaptively aggregate a view-specific global codeword, which is further fed into the subsequent 2D convolutional translation heads for image generation. We conduct extensive experiments on common task scenarios of 3D shape analysis, where our PointVST shows consistent and prominent performance superiority over current state-of-the-art methods under diverse evaluation protocols. Our code will be made publicly available.

The high feature dimensionality is a challenge in music emotion recognition. There is no common consensus on a relation between audio features and emotion. The MER system uses all available features to recognize emotion; however, this is not an optimal solution since it contains irrelevant data acting as noise. In this paper, we introduce a feature selection approach to eliminate redundant features for MER. We created a Selected Feature Set (SFS) based on the feature selection algorithm (FSA) and benchmarked it by training with two models, Support Vector Regression (SVR) and Random Forest (RF) and comparing them against with using the Complete Feature Set (CFS). The result indicates that the performance of MER has improved for both Random Forest (RF) and Support Vector Regression (SVR) models by using SFS. We found using FSA can improve performance in all scenarios, and it has potential benefits for model efficiency and stability for MER task.

A general, {\em rectangular} kernel matrix may be defined as $K_{ij} = \kappa(x_i,y_j)$ where $\kappa(x,y)$ is a kernel function and where $X=\{x_i\}_{i=1}^m$ and $Y=\{y_i\}_{i=1}^n$ are two sets of points. In this paper, we seek a low-rank approximation to a kernel matrix where the sets of points $X$ and $Y$ are large and are not well-separated (e.g., the points in $X$ and $Y$ may be ``intermingled''). Such rectangular kernel matrices may arise, for example, in Gaussian process regression where $X$ corresponds to the training data and $Y$ corresponds to the test data. In this case, the points are often high-dimensional. Since the point sets are large, we must exploit the fact that the matrix arises from a kernel function, and avoid forming the matrix, and thus ruling out most algebraic techniques. In particular, we seek methods that can scale linearly, i.e., with computational complexity $O(m)$ or $O(n)$ for a fixed accuracy or rank. The main idea in this paper is to {\em geometrically} select appropriate subsets of points to construct a low rank approximation. An analysis in this paper guides how this selection should be performed.

We propose a new neural network design paradigm Reversible Column Network (RevCol). The main body of RevCol is composed of multiple copies of subnetworks, named columns respectively, between which multi-level reversible connections are employed. Such architectural scheme attributes RevCol very different behavior from conventional networks: during forward propagation, features in RevCol are learned to be gradually disentangled when passing through each column, whose total information is maintained rather than compressed or discarded as other network does. Our experiments suggest that CNN-style RevCol models can achieve very competitive performances on multiple computer vision tasks such as image classification, object detection and semantic segmentation, especially with large parameter budget and large dataset. For example, after ImageNet-22K pre-training, RevCol-XL obtains 88.2% ImageNet-1K accuracy. Given more pre-training data, our largest model RevCol-H reaches 90.0% on ImageNet-1K, 63.8% APbox on COCO detection minival set, 61.0% mIoU on ADE20k segmentation. To our knowledge, it is the best COCO detection and ADE20k segmentation result among pure (static) CNN models. Moreover, as a general macro architecture fashion, RevCol can also be introduced into transformers or other neural networks, which is demonstrated to improve the performances in both computer vision and NLP tasks. We release code and models at https://github.com/megvii-research/RevCol

We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints and actuator saturation. The planned trajectory of flat output is transformed to state trajectory in real-time with consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally-parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The effectiveness of the proposed framework is demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10m/s, typical tail-sitter maneuvers (transition, level flight and loiter) with speed up to 20m/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight and Cuban Eight) with acceleration up to 2.5g.

Deep learning-based 3D object detectors have made significant progress in recent years and have been deployed in a wide range of applications. It is crucial to understand the robustness of detectors against adversarial attacks when employing detectors in security-critical applications. In this paper, we make the first attempt to conduct a thorough evaluation and analysis of the robustness of 3D detectors under adversarial attacks. Specifically, we first extend three kinds of adversarial attacks to the 3D object detection task to benchmark the robustness of state-of-the-art 3D object detectors against attacks on KITTI and Waymo datasets, subsequently followed by the analysis of the relationship between robustness and properties of detectors. Then, we explore the transferability of cross-model, cross-task, and cross-data attacks. We finally conduct comprehensive experiments of defense for 3D detectors, demonstrating that simple transformations like flipping are of little help in improving robustness when the strategy of transformation imposed on input point cloud data is exposed to attackers. Our findings will facilitate investigations in understanding and defending the adversarial attacks against 3D object detectors to advance this field.