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Statistical inference based on lossy or incomplete samples is often needed in research areas such as signal/image processing, medical image storage, remote sensing, signal transmission. In this paper, we propose a nonparametric testing procedure based on samples quantized to $B$ bits through a computationally efficient algorithm. Under mild technical conditions, we establish the asymptotic properties of the proposed test statistic and investigate how the testing power changes as $B$ increases. In particular, we show that if $B$ exceeds a certain threshold, the proposed nonparametric testing procedure achieves the classical minimax rate of testing (Shang and Cheng, 2015) for spline models. We further extend our theoretical investigations to a nonparametric linearity test and an adaptive nonparametric test, expanding the applicability of the proposed methods. Extensive simulation studies {together with a real-data analysis} are used to demonstrate the validity and effectiveness of the proposed tests.

Graph Neural Networks (GNNs) have succeeded in various computer science applications, yet deep GNNs underperform their shallow counterparts despite deep learning's success in other domains. Over-smoothing and over-squashing are key challenges when stacking graph convolutional layers, hindering deep representation learning and information propagation from distant nodes. Our work reveals that over-smoothing and over-squashing are intrinsically related to the spectral gap of the graph Laplacian, resulting in an inevitable trade-off between these two issues, as they cannot be alleviated simultaneously. To achieve a suitable compromise, we propose adding and removing edges as a viable approach. We introduce the Stochastic Jost and Liu Curvature Rewiring (SJLR) algorithm, which is computationally efficient and preserves fundamental properties compared to previous curvature-based methods. Unlike existing approaches, SJLR performs edge addition and removal during GNN training while maintaining the graph unchanged during testing. Comprehensive comparisons demonstrate SJLR's competitive performance in addressing over-smoothing and over-squashing.

Despite the strong predictive performance of deep learning models for traffic prediction, their widespread deployment in real-world intelligent transportation systems has been restrained by a lack of interpretability. Uncertainty quantification (UQ) methods provide an approach to induce probabilistic reasoning, improve decision-making and enhance model deployment potential. To gain a comprehensive picture of the usefulness of existing UQ methods for traffic prediction and the relation between obtained uncertainties and city-wide traffic dynamics, we investigate their application to a large-scale image-based traffic dataset spanning multiple cities and time periods. We compare two epistemic and two aleatoric UQ methods on both temporal and spatio-temporal transfer tasks, and find that meaningful uncertainty estimates can be recovered. We further demonstrate how uncertainty estimates can be employed for unsupervised outlier detection on changes in city traffic dynamics. We find that our approach can capture both temporal and spatial effects on traffic behaviour in a representative case study for the city of Moscow. Our work presents a further step towards boosting uncertainty awareness in traffic prediction tasks, and aims to highlight the value contribution of UQ methods to a better understanding of city traffic dynamics.

In monocular depth estimation, uncertainty estimation approaches mainly target the data uncertainty introduced by image noise. In contrast to prior work, we address the uncertainty due to lack of knowledge, which is relevant for the detection of data not represented by the training distribution, the so-called out-of-distribution (OOD) data. Motivated by anomaly detection, we propose to detect OOD images from an encoder-decoder depth estimation model based on the reconstruction error. Given the features extracted with the fixed depth encoder, we train an image decoder for image reconstruction using only in-distribution data. Consequently, OOD images result in a high reconstruction error, which we use to distinguish between in- and out-of-distribution samples. We built our experiments on the standard NYU Depth V2 and KITTI benchmarks as in-distribution data. Our post hoc method performs astonishingly well on different models and outperforms existing uncertainty estimation approaches without modifying the trained encoder-decoder depth estimation model.

Monocular depth estimation is known as an ill-posed task in which objects in a 2D image usually do not contain sufficient information to predict their depth. Thus, it acts differently from other tasks (e.g., classification and segmentation) in many ways. In this paper, we find that self-supervised monocular depth estimation shows a direction sensitivity and environmental dependency in the feature representation. But the current backbones borrowed from other tasks pay less attention to handling different types of environmental information, limiting the overall depth accuracy. To bridge this gap, we propose a new Direction-aware Cumulative Convolution Network (DaCCN), which improves the depth feature representation in two aspects. First, we propose a direction-aware module, which can learn to adjust the feature extraction in each direction, facilitating the encoding of different types of information. Secondly, we design a new cumulative convolution to improve the efficiency for aggregating important environmental information. Experiments show that our method achieves significant improvements on three widely used benchmarks, KITTI, Cityscapes, and Make3D, setting a new state-of-the-art performance on the popular benchmarks with all three types of self-supervision.

Recent diffusion probabilistic models (DPMs) have shown remarkable abilities of generated content, however, they often suffer from complex forward processes, resulting in inefficient solutions for the reversed process and prolonged sampling times. In this paper, we aim to address the aforementioned challenges by focusing on the diffusion process itself that we propose to decouple the intricate diffusion process into two comparatively simpler process to improve the generative efficacy and speed. In particular, we present a novel diffusion paradigm named DDM (Decoupled Diffusion Models) based on the Ito diffusion process, in which the image distribution is approximated by an explicit transition probability while the noise path is controlled by the standard Wiener process. We find that decoupling the diffusion process reduces the learning difficulty and the explicit transition probability improves the generative speed significantly. We prove a new training objective for DPM, which enables the model to learn to predict the noise and image components separately. Moreover, given the novel forward diffusion equation, we derive the reverse denoising formula of DDM that naturally supports fewer steps of generation without ordinary differential equation (ODE) based accelerators. Our experiments demonstrate that DDM outperforms previous DPMs by a large margin in fewer function evaluations setting and gets comparable performances in long function evaluations setting. We also show that our framework can be applied to image-conditioned generation and high-resolution image synthesis, and that it can generate high-quality images with only 10 function evaluations.

We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a suitable notion of shift and convolution operators that we define. DAGs are the common model to capture causal relationships between data values and in this case our proposed Fourier analysis relates data with its causes under a linearity assumption that we define. The definition of the Fourier transform requires the transitive closure of the weighted DAG for which several forms are possible depending on the interpretation of the edge weights. Examples include level of influence, distance, or pollution distribution. Our framework is different from prior GSP: it is specific to DAGs and leverages, and extends, the classical theory of Moebius inversion from combinatorics. For a prototypical application we consider DAGs modeling dynamic networks in which edges change over time. Specifically, we model the spread of an infection on such a DAG obtained from real-world contact tracing data and learn the infection signal from samples assuming sparsity in the Fourier domain.

Video colorization, aiming at obtaining colorful and plausible results from grayish frames, has aroused a lot of interest recently. Nevertheless, how to maintain temporal consistency while keeping the quality of colorized results remains challenging. To tackle the above problems, we present a Histogram-guided Video Colorization with Spatial-Temporal connection structure (named ST-HVC). To fully exploit the chroma and motion information, the joint flow and histogram module is tailored to integrate the histogram and flow features. To manage the blurred and artifact, we design a combination scheme attending to temporal detail and flow feature combination. We further recombine the histogram, flow and sharpness features via a U-shape network. Extensive comparisons are conducted with several state-of-the-art image and video-based methods, demonstrating that the developed method achieves excellent performance both quantitatively and qualitatively in two video datasets.

Heterogeneous graph neural networks (HGNNs) as an emerging technique have shown superior capacity of dealing with heterogeneous information network (HIN). However, most HGNNs follow a semi-supervised learning manner, which notably limits their wide use in reality since labels are usually scarce in real applications. Recently, contrastive learning, a self-supervised method, becomes one of the most exciting learning paradigms and shows great potential when there are no labels. In this paper, we study the problem of self-supervised HGNNs and propose a novel co-contrastive learning mechanism for HGNNs, named HeCo. Different from traditional contrastive learning which only focuses on contrasting positive and negative samples, HeCo employs cross-viewcontrastive mechanism. Specifically, two views of a HIN (network schema and meta-path views) are proposed to learn node embeddings, so as to capture both of local and high-order structures simultaneously. Then the cross-view contrastive learning, as well as a view mask mechanism, is proposed, which is able to extract the positive and negative embeddings from two views. This enables the two views to collaboratively supervise each other and finally learn high-level node embeddings. Moreover, two extensions of HeCo are designed to generate harder negative samples with high quality, which further boosts the performance of HeCo. Extensive experiments conducted on a variety of real-world networks show the superior performance of the proposed methods over the state-of-the-arts.

Answering questions that require reading texts in an image is challenging for current models. One key difficulty of this task is that rare, polysemous, and ambiguous words frequently appear in images, e.g., names of places, products, and sports teams. To overcome this difficulty, only resorting to pre-trained word embedding models is far from enough. A desired model should utilize the rich information in multiple modalities of the image to help understand the meaning of scene texts, e.g., the prominent text on a bottle is most likely to be the brand. Following this idea, we propose a novel VQA approach, Multi-Modal Graph Neural Network (MM-GNN). It first represents an image as a graph consisting of three sub-graphs, depicting visual, semantic, and numeric modalities respectively. Then, we introduce three aggregators which guide the message passing from one graph to another to utilize the contexts in various modalities, so as to refine the features of nodes. The updated nodes have better features for the downstream question answering module. Experimental evaluations show that our MM-GNN represents the scene texts better and obviously facilitates the performances on two VQA tasks that require reading scene texts.