Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRecursive Least Squares Based Refinement Network for the Rollout Trajectory Prediction Methods
85
0
0.0
(
0
)
Added by
Qifan Xue
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Trajectory prediction plays a pivotal role in the field of intelligent vehicles. It currently suffers from several challenges,e.g., accumulative error in rollout process and weak adaptability in various scenarios. This paper proposes a parametric-learning recursive least squares (RLS) estimation based on deep neural network for trajectory prediction. We design a flexible plug-in module which can be readily implanted into rollout approaches. Goal points are proposed to capture the long-term prediction stability from the global perspective. We carried experiments out on the NGSIM dataset. The promising results indicate that our method could improve rollout trajectory prediction methods effectively.
rate research
Read More
Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they have high computational complexity and too many preconditions. In this paper, to overcome these drawbacks, we propose three novel RLS optimization algorithms for training feedforward neural networks, convolutional neural networks and recurrent neural networks (including long short-term memory networks), by using the error backpropagation and our average-approximation RLS method, together with the equivalent gradients of the linear least squares loss function with respect to the linear outputs of hidden layers. Compared with previous RLS optimization algorithms, our algorithms are simple and elegant. They can be viewed as an improved stochastic gradient descent (SGD) algorithm, which uses the inverse autocorrelation matrix of each layer as the adaptive learning rate. Their time and space complexities are only several times those of SGD. They only require the loss function to be the mean squared error and the activation function of the output layer to be invertible. In fact, our algorithms can be also used in combination with other first-order optimization algorithms without requiring these two preconditions. In addition, we present two improved methods for our algorithms. Finally, we demonstrate their effectiveness compared to the Adam algorithm on MNIST, CIFAR-10 and IMDB datasets, and investigate the influences of their hyperparameters experimentally.
This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and employs least-squares functionals as loss functions to determine parameters of the deep neural network. There are various least-squares functionals for a partial differential equation. This paper focuses on the so-called first-order system least-squares (FOSLS) functional studied in [3], which is based on a first-order system of scalar second-order elliptic PDEs. Numerical results for second-order elliptic PDEs in one dimension are presented.
With the increasing deployment of diverse positioning devices and location-based services, a huge amount of spatial and temporal information has been collected and accumulated as trajectory data. Among many applications, trajectory-based location prediction is gaining increasing attention because of its potential to improve the performance of many applications in multiple domains. This research focuses on trajectory sequence prediction methods using trajectory data obtained from the vehicles in urban traffic network. As Recurrent Neural Network(RNN) model is previously proposed, we propose an improved method of Attention-based Recurrent Neural Network model(ARNN) for urban vehicle trajectory prediction. We introduce attention mechanism into urban vehicle trajectory prediction to explain the impact of network-level traffic state information. The model is evaluated using the Bluetooth data of private vehicles collected in Brisbane, Australia with 5 metrics which are widely used in the sequence modeling. The proposed ARNN model shows significant performance improvement compared to the existing RNN models considering not only the cells to be visited but also the alignment of the cells in sequence.
Updating a linear least squares solution can be critical for near real-time signalprocessing applications. The Greville algorithm proposes a simple formula for updating the pseudoinverse of a matrix A $in$ R nxm with rank r. In this paper, we explicitly derive a similar formula by maintaining a general rank factorization, which we call rank-Greville. Based on this formula, we implemented a recursive least squares algorithm exploiting the rank-deficiency of A, achieving the update of the minimum-norm least-squares solution in O(mr) operations and, therefore, solving the linear least-squares problem from scratch in O(nmr) operations. We empirically confirmed that this algorithm displays a better asymptotic time complexity than LAPACK solvers for rank-deficient matrices. The numerical stability of rank-Greville was found to be comparable to Cholesky-based solvers. Nonetheless, our implementation supports exact numerical representations of rationals, due to its remarkable algebraic simplicity.
Most multilayer least squares (LS)-based neural networks are structured with two separate stages: unsupervised feature encoding and supervised pattern classification. Once the unsupervised learning is finished, the latent encoding would be fixed without supervised fine-tuning. However, in complex tasks such as handling the ImageNet dataset, there are often many more clues that can be directly encoded, while the unsupervised learning, by definition cannot know exactly what is useful for a certain task. This serves as the motivation to retrain the latent space representations to learn some clues that unsupervised learning has not yet learned. In particular, the error matrix from the output layer is pulled back to each hidden layer, and the parameters of the hidden layer are recalculated with Moore-Penrose (MP) inverse for more generalized representations. In this paper, a recomputation-based multilayer network using MP inverse (RML-MP) is developed. A sparse RML-MP (SRML-MP) model to boost the performance of RML-MP is then proposed. The experimental results with varying training samples (from 3 K to 1.8 M) show that the proposed models provide better generalization performance than most representation learning algorithms.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
