Spatiotemporal traffic data imputation (STDI), estimating the missing data from partially observed traffic data, is an inevitable and challenging task in data-driven intelligent transportation systems (ITS). Due to traffic data's multidimensional and spatiotemporal properties, we treat the missing data imputation as a tensor completion problem. Many studies have been on STDI based on tensor decomposition in the past decade. However, how to use spatiotemporal correlations and core tensor sparsity to improve the imputation performance still needs to be solved. This paper reshapes a 3rd/4th order Hankel tensor and proposes an innovative manifold regularized Tucker decomposition (ManiRTD) model for STDI. Expressly, we represent the sensory traffic state data as the 3rd/4th tensors by introducing Multiway Delay Embedding Transforms. Then, ManiRTD improves the sparsity of the Tucker core using a sparse regularization term and employs manifold regularization and temporal constraint terms of factor matrices to characterize the spatiotemporal correlations. Finally, we address the ManiRTD model through a block coordinate descent framework under alternating proximal gradient updating rules with convergence-guaranteed. Numerical experiments are conducted on real-world spatiotemporal traffic datasets (STDs). Our results demonstrate that the proposed model outperforms the other factorization approaches and reconstructs the STD more precisely under various missing scenarios.
相關內容
We present a new restricted SVD-based CUR (RSVD-CUR) factorization for matrix triplets $(A, B, G)$ that aims to extract meaningful information by providing a low-rank approximation of the three matrices using a subset of their rows and columns. The proposed method utilizes the discrete empirical interpolation method (DEIM) to select the subset of rows and columns from the orthogonal and nonsingular matrices obtained through a restricted singular value decomposition of the matrix triplet. We explore the relationships between a DEIM type RSVD-CUR factorization, a DEIM type CUR factorization, and a DEIM type generalized CUR decomposition, and provide an error analysis that establishes the accuracy of the RSVD-CUR decomposition within a factor of the approximation error of the restricted singular value decomposition of the given matrices. The RSVD-CUR factorization can be used in applications that require approximating one data matrix relative to two other given matrices. We discuss two such applications, namely multi-view dimension reduction and data perturbation problems where a correlated noise matrix is added to the input data matrix. Our numerical experiments demonstrate the advantages of the proposed method over the standard CUR approximation in these scenarios.
Multivariate time series (MTS) imputation is a widely studied problem in recent years. Existing methods can be divided into two main groups, including (1) deep recurrent or generative models that primarily focus on time series features, and (2) graph neural networks (GNNs) based models that utilize the topological information from the inherent graph structure of MTS as relational inductive bias for imputation. Nevertheless, these methods either neglect topological information or assume the graph structure is fixed and accurately known. Thus, they fail to fully utilize the graph dynamics for precise imputation in more challenging MTS data such as networked time series (NTS), where the underlying graph is constantly changing and might have missing edges. In this paper, we propose a novel approach to overcome these limitations. First, we define the problem of imputation over NTS which contains missing values in both node time series features and graph structures. Then, we design a new model named PoGeVon which leverages variational autoencoder (VAE) to predict missing values over both node time series features and graph structures. In particular, we propose a new node position embedding based on random walk with restart (RWR) in the encoder with provable higher expressive power compared with message-passing based graph neural networks (GNNs). We further design a decoder with 3-stage predictions from the perspective of multi-task learning to impute missing values in both time series and graph structures reciprocally. Experiment results demonstrate the effectiveness of our model over baselines.
We study the problem of learning with selectively labeled data, which arises when outcomes are only partially labeled due to historical decision-making. The labeled data distribution may substantially differ from the full population, especially when the historical decisions and the target outcome can be simultaneously affected by some unobserved factors. Consequently, learning with only the labeled data may lead to severely biased results when deployed to the full population. Our paper tackles this challenge by exploiting the fact that in many applications the historical decisions were made by a set of heterogeneous decision-makers. In particular, we analyze this setup in a principled instrumental variable (IV) framework. We establish conditions for the full-population risk of any given prediction rule to be point-identified from the observed data and provide sharp risk bounds when the point identification fails. We further propose a weighted learning approach that learns prediction rules robust to the label selection bias in both identification settings. Finally, we apply our proposed approach to a semi-synthetic financial dataset and demonstrate its superior performance in the presence of selection bias.
Data efficiency, or the ability to generalize from a few labeled data, remains a major challenge in deep learning. Semi-supervised learning has thrived in traditional recognition tasks alleviating the need for large amounts of labeled data, yet it remains understudied in image-to-image translation (I2I) tasks. In this work, we introduce the first semi-supervised (semi-paired) framework for label-to-image translation, a challenging subtask of I2I which generates photorealistic images from semantic label maps. In the semi-paired setting, the model has access to a small set of paired data and a larger set of unpaired images and labels. Instead of using geometrical transformations as a pretext task like previous works, we leverage an input reconstruction task by exploiting the conditional discriminator on the paired data as a reverse generator. We propose a training algorithm for this shared network, and we present a rare classes sampling algorithm to focus on under-represented classes. Experiments on 3 standard benchmarks show that the proposed model outperforms state-of-the-art unsupervised and semi-supervised approaches, as well as some fully supervised approaches while using a much smaller number of paired samples.
In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate (q) and momentum (p) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a generating function. To extend the prediction time period, we develop a new learning scheme by splitting the time series (q_i, p_i) into several partitions. We then train a large-step neural network (LSNN) to approximate the generating function between the first partition (i.e. the initial condition) and each one of the remaining partitions. This partition approach makes our LSNN effectively suppress the accumulative error when predicting the system evolution. Then we train the LSNN to learn the motions of the 2:3 resonant Kuiper belt objects for a long time period of 25000 yr. The results show that there are two significant improvements over the neural network constructed in our previous work (Li et al. 2022): (1) the conservation of the Jacobi integral, and (2) the highly accurate predictions of the orbital evolution. Overall, we propose that the designed LSNN has the potential to considerably improve predictions of the long-term evolution of more general Hamiltonian systems.
Many common types of data can be represented as functions that map coordinates to signal values, such as pixel locations to RGB values in the case of an image. Based on this view, data can be compressed by overfitting a compact neural network to its functional representation and then encoding the network weights. However, most current solutions for this are inefficient, as quantization to low-bit precision substantially degrades the reconstruction quality. To address this issue, we propose overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding instead of quantizing and entropy coding it. This strategy enables direct optimization of the rate-distortion performance by minimizing the $\beta$-ELBO, and target different rate-distortion trade-offs for a given network architecture by adjusting $\beta$. Moreover, we introduce an iterative algorithm for learning prior weight distributions and employ a progressive refinement process for the variational posterior that significantly enhances performance. Experiments show that our method achieves strong performance on image and audio compression while retaining simplicity.
This paper focuses on predicting the occurrence of grokking in neural networks, a phenomenon in which perfect generalization emerges long after signs of overfitting or memorization are observed. It has been reported that grokking can only be observed with certain hyper-parameters. This makes it critical to identify the parameters that lead to grokking. However, since grokking occurs after a large number of epochs, searching for the hyper-parameters that lead to it is time-consuming. In this paper, we propose a low-cost method to predict grokking without training for a large number of epochs. In essence, by studying the learning curve of the first few epochs, we show that one can predict whether grokking will occur later on. Specifically, if certain oscillations occur in the early epochs, one can expect grokking to occur if the model is trained for a much longer period of time. We propose using the spectral signature of a learning curve derived by applying the Fourier transform to quantify the amplitude of low-frequency components to detect the presence of such oscillations. We also present additional experiments aimed at explaining the cause of these oscillations and characterizing the loss landscape.
Deep Metric Learning (DML) models rely on strong representations and similarity-based measures with specific loss functions. Proxy-based losses have shown great performance compared to pair-based losses in terms of convergence speed. However, proxies that are assigned to different classes may end up being closely located in the embedding space and hence having a hard time to distinguish between positive and negative items. Alternatively, they may become highly correlated and hence provide redundant information with the model. To address these issues, we propose a novel approach that introduces Soft Orthogonality (SO) constraint on proxies. The constraint ensures the proxies to be as orthogonal as possible and hence control their positions in the embedding space. Our approach leverages Data-Efficient Image Transformer (DeiT) as an encoder to extract contextual features from images along with a DML objective. The objective is made of the Proxy Anchor loss along with the SO regularization. We evaluate our method on four public benchmarks for category-level image retrieval and demonstrate its effectiveness with comprehensive experimental results and ablation studies. Our evaluations demonstrate the superiority of our proposed approach over state-of-the-art methods by a significant margin.
With the extremely rapid advances in remote sensing (RS) technology, a great quantity of Earth observation (EO) data featuring considerable and complicated heterogeneity is readily available nowadays, which renders researchers an opportunity to tackle current geoscience applications in a fresh way. With the joint utilization of EO data, much research on multimodal RS data fusion has made tremendous progress in recent years, yet these developed traditional algorithms inevitably meet the performance bottleneck due to the lack of the ability to comprehensively analyse and interpret these strongly heterogeneous data. Hence, this non-negligible limitation further arouses an intense demand for an alternative tool with powerful processing competence. Deep learning (DL), as a cutting-edge technology, has witnessed remarkable breakthroughs in numerous computer vision tasks owing to its impressive ability in data representation and reconstruction. Naturally, it has been successfully applied to the field of multimodal RS data fusion, yielding great improvement compared with traditional methods. This survey aims to present a systematic overview in DL-based multimodal RS data fusion. More specifically, some essential knowledge about this topic is first given. Subsequently, a literature survey is conducted to analyse the trends of this field. Some prevalent sub-fields in the multimodal RS data fusion are then reviewed in terms of the to-be-fused data modalities, i.e., spatiospectral, spatiotemporal, light detection and ranging-optical, synthetic aperture radar-optical, and RS-Geospatial Big Data fusion. Furthermore, We collect and summarize some valuable resources for the sake of the development in multimodal RS data fusion. Finally, the remaining challenges and potential future directions are highlighted.
It is a common paradigm in object detection frameworks to treat all samples equally and target at maximizing the performance on average. In this work, we revisit this paradigm through a careful study on how different samples contribute to the overall performance measured in terms of mAP. Our study suggests that the samples in each mini-batch are neither independent nor equally important, and therefore a better classifier on average does not necessarily mean higher mAP. Motivated by this study, we propose the notion of Prime Samples, those that play a key role in driving the detection performance. We further develop a simple yet effective sampling and learning strategy called PrIme Sample Attention (PISA) that directs the focus of the training process towards such samples. Our experiments demonstrate that it is often more effective to focus on prime samples than hard samples when training a detector. Particularly, On the MSCOCO dataset, PISA outperforms the random sampling baseline and hard mining schemes, e.g. OHEM and Focal Loss, consistently by more than 1% on both single-stage and two-stage detectors, with a strong backbone ResNeXt-101.
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