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Accurate pedestrian trajectory prediction is of great importance for downstream tasks such as autonomous driving and mobile robot navigation. Fully investigating the social interactions within the crowd is crucial for accurate pedestrian trajectory prediction. However, most existing methods do not capture group level interactions well, focusing only on pairwise interactions and neglecting group-wise interactions. In this work, we propose a hierarchical graph convolutional network, HGCN-GJS, for trajectory prediction which well leverages group level interactions within the crowd. Furthermore, we introduce a novel joint sampling scheme for modeling the joint distribution of multiple pedestrians in the future trajectories. Based on the group information, this scheme associates the trajectory of one person with the trajectory of other people in the group, but maintains the independence of the trajectories of outsiders. We demonstrate the performance of our network on several trajectory prediction datasets, achieving state-of-the-art results on all datasets considered.

The parallel alternating direction method of multipliers (ADMM) algorithms have gained popularity in statistics and machine learning for their efficient handling of large sample data problems. However, the parallel structure of these algorithms is based on the consensus problem, which can lead to an excessive number of auxiliary variables for high-dimensional data. In this paper, we propose a partition-insensitive parallel framework based on the linearized ADMM (LADMM) algorithm and apply it to solve nonconvex penalized smooth quantile regression problems. Compared to existing parallel ADMM algorithms, our algorithm does not rely on the consensus problem, resulting in a significant reduction in the number of variables that need to be updated at each iteration. It is worth noting that the solution of our algorithm remains unchanged regardless of how the total sample is divided, which is also known as partition-insensitivity. Furthermore, under some mild assumptions, we prove that the iterative sequence generated by the parallel LADMM algorithm converges to a critical point of the nonconvex optimization problem. Numerical experiments on synthetic and real datasets demonstrate the feasibility and validity of the proposed algorithm.

Optimization-based methods are commonly applied in autonomous driving trajectory planners, which transform the continuous-time trajectory planning problem into a finite nonlinear program with constraints imposed at finite collocation points. However, potential violations between adjacent collocation points can occur. To address this issue thoroughly, we propose a safety-guaranteed collision-avoidance model to mitigate collision risks within optimization-based trajectory planners. This model introduces an embodied footprint, an enlarged representation of the vehicle's nominal footprint. If the embodied footprints do not collide with obstacles at finite collocation points, then the ego vehicle's nominal footprint is guaranteed to be collision-free at any of the infinite moments between adjacent collocation points. According to our theoretical analysis, we define the geometric size of an embodied footprint as a simple function of vehicle velocity and curvature. Particularly, we propose a trajectory optimizer with the embodied footprints that can theoretically set an appropriate number of collocation points prior to the optimization process. We conduct this research to enhance the foundation of optimization-based planners in robotics. Comparative simulations and field tests validate the completeness, solution speed, and solution quality of our proposal.

We present VAPOR, a novel method for autonomous legged robot navigation in unstructured, densely vegetated outdoor environments using Offline Reinforcement Learning (RL). Our method trains a novel RL policy from unlabeled data collected in real outdoor vegetation. This policy uses height and intensity-based cost maps derived from 3D LiDAR point clouds, a goal cost map, and processed proprioception data as state inputs, and learns the physical and geometric properties of the surrounding vegetation such as height, density, and solidity/stiffness for navigation. Instead of using end-to-end policy actions, the fully-trained RL policy's Q network is used to evaluate dynamically feasible robot actions generated from a novel adaptive planner capable of navigating through dense narrow passages and preventing entrapment in vegetation such as tall grass and bushes. We demonstrate our method's capabilities on a legged robot in complex outdoor vegetation. We observe an improvement in success rates, a decrease in average power consumption, and decrease in normalized trajectory length compared to both existing end-to-end offline RL and outdoor navigation methods.

We introduce a new debiasing framework for high-dimensional linear regression that bypasses the restrictions on covariate distributions imposed by modern debiasing technology. We study the prevalent setting where the number of features and samples are both large and comparable. In this context, state-of-the-art debiasing technology uses a degrees-of-freedom correction to remove shrinkage bias of regularized estimators and conduct inference. However, this method requires that the observed samples are i.i.d., the covariates follow a mean zero Gaussian distribution, and reliable covariance matrix estimates for observed features are available. This approach struggles when (i) covariates are non-Gaussian with heavy tails or asymmetric distributions, (ii) rows of the design exhibit heterogeneity or dependencies, and (iii) reliable feature covariance estimates are lacking. To address these, we develop a new strategy where the debiasing correction is a rescaled gradient descent step (suitably initialized) with step size determined by the spectrum of the sample covariance matrix. Unlike prior work, we assume that eigenvectors of this matrix are uniform draws from the orthogonal group. We show this assumption remains valid in diverse situations where traditional debiasing fails, including designs with complex row-column dependencies, heavy tails, asymmetric properties, and latent low-rank structures. We establish asymptotic normality of our proposed estimator (centered and scaled) under various convergence notions. Moreover, we develop a consistent estimator for its asymptotic variance. Lastly, we introduce a debiased Principal Component Regression (PCR) technique using our Spectrum-Aware approach. In varied simulations and real data experiments, we observe that our method outperforms degrees-of-freedom debiasing by a margin.

Despite the remarkable success of deep learning systems over the last decade, a key difference still remains between neural network and human decision-making: As humans, we cannot only form a decision on the spot, but also ponder, revisiting an initial guess from different angles, distilling relevant information, arriving at a better decision. Here, we propose RecycleNet, a latent feature recycling method, instilling the pondering capability for neural networks to refine initial decisions over a number of recycling steps, where outputs are fed back into earlier network layers in an iterative fashion. This approach makes minimal assumptions about the neural network architecture and thus can be implemented in a wide variety of contexts. Using medical image segmentation as the evaluation environment, we show that latent feature recycling enables the network to iteratively refine initial predictions even beyond the iterations seen during training, converging towards an improved decision. We evaluate this across a variety of segmentation benchmarks and show consistent improvements even compared with top-performing segmentation methods. This allows trading increased computation time for improved performance, which can be beneficial, especially for safety-critical applications.

The myriad complex systems with multiway interactions motivate the extension of graph-based pairwise connections to higher-order relations. In particular, the simplicial complex has inspired generalizations of graph neural networks (GNNs) to simplicial complex-based models. Learning on such systems requires large amounts of data, which can be expensive or impossible to obtain. We propose data augmentation of simplicial complexes through both linear and nonlinear mixup mechanisms that return mixtures of existing labeled samples. In addition to traditional pairwise mixup, we present a convex clustering mixup approach for a data-driven relationship among several simplicial complexes. We theoretically demonstrate that the resultant synthetic simplicial complexes interpolate among existing data with respect to homomorphism densities. Our method is demonstrated on both synthetic and real-world datasets for simplicial complex classification.

Self-supervised learning methods are gaining increasing traction in computer vision due to their recent success in reducing the gap with supervised learning. In natural language processing (NLP) self-supervised learning and transformers are already the methods of choice. The recent literature suggests that the transformers are becoming increasingly popular also in computer vision. So far, the vision transformers have been shown to work well when pretrained either using a large scale supervised data or with some kind of co-supervision, e.g. in terms of teacher network. These supervised pretrained vision transformers achieve very good results in downstream tasks with minimal changes. In this work we investigate the merits of self-supervised learning for pretraining image/vision transformers and then using them for downstream classification tasks. We propose Self-supervised vIsion Transformers (SiT) and discuss several self-supervised training mechanisms to obtain a pretext model. The architectural flexibility of SiT allows us to use it as an autoencoder and work with multiple self-supervised tasks seamlessly. We show that a pretrained SiT can be finetuned for a downstream classification task on small scale datasets, consisting of a few thousand images rather than several millions. The proposed approach is evaluated on standard datasets using common protocols. The results demonstrate the strength of the transformers and their suitability for self-supervised learning. We outperformed existing self-supervised learning methods by large margin. We also observed that SiT is good for few shot learning and also showed that it is learning useful representation by simply training a linear classifier on top of the learned features from SiT. Pretraining, finetuning, and evaluation codes will be available under: //github.com/Sara-Ahmed/SiT.

The cross-domain recommendation technique is an effective way of alleviating the data sparsity in recommender systems by leveraging the knowledge from relevant domains. Transfer learning is a class of algorithms underlying these techniques. In this paper, we propose a novel transfer learning approach for cross-domain recommendation by using neural networks as the base model. We assume that hidden layers in two base networks are connected by cross mappings, leading to the collaborative cross networks (CoNet). CoNet enables dual knowledge transfer across domains by introducing cross connections from one base network to another and vice versa. CoNet is achieved in multi-layer feedforward networks by adding dual connections and joint loss functions, which can be trained efficiently by back-propagation. The proposed model is evaluated on two real-world datasets and it outperforms baseline models by relative improvements of 3.56\% in MRR and 8.94\% in NDCG, respectively.