A High-dimensional Convergence Theorem for U-statistics with Applications to Kernel-based Testing

We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the non-degenerate Gaussian limit to the degenerate limit, regardless of its degeneracy and depending only on a moment ratio. A surprising consequence is that a non-degenerate U-statistic in high dimensions can have a non-Gaussian limit with a larger variance and asymmetric distribution. Our bounds are valid for any finite $n$ and $d$, independent of individual eigenvalues of the underlying function, and dimension-independent under a mild assumption. As an application, we apply our theory to two popular kernel-based distribution tests, MMD and KSD, whose high-dimensional performance has been challenging to study. In a simple empirical setting, our results correctly predict how the test power at a fixed threshold scales with $d$ and the bandwidth.

Learning the Network of Graphs for Graph Neural Networks

Graph neural networks (GNNs) have achieved great success in many scenarios with graph-structured data. However, in many real applications, there are three issues when applying GNNs: graphs are unknown, nodes have noisy features, and graphs contain noisy connections. Aiming at solving these problems, we propose a new graph neural network named as GL-GNN. Our model includes multiple sub-modules, each sub-module selects important data features and learn the corresponding key relation graph of data samples when graphs are unknown. GL-GNN further obtains the network of graphs by learning the network of sub-modules. The learned graphs are further fused using an aggregation method over the network of graphs. Our model solves the first issue by simultaneously learning multiple relation graphs of data samples as well as a relation network of graphs, and solves the second and the third issue by selecting important data features as well as important data sample relations. We compare our method with 14 baseline methods on seven datasets when the graph is unknown and 11 baseline methods on two datasets when the graph is known. The results show that our method achieves better accuracies than the baseline methods and is capable of selecting important features and graph edges from the dataset. Our code will be publicly available at \url{https://github.com/Looomo/GL-GNN}.

SoccerNet 2022 Challenges Results

The SoccerNet 2022 challenges were the second annual video understanding challenges organized by the SoccerNet team. In 2022, the challenges were composed of 6 vision-based tasks: (1) action spotting, focusing on retrieving action timestamps in long untrimmed videos, (2) replay grounding, focusing on retrieving the live moment of an action shown in a replay, (3) pitch localization, focusing on detecting line and goal part elements, (4) camera calibration, dedicated to retrieving the intrinsic and extrinsic camera parameters, (5) player re-identification, focusing on retrieving the same players across multiple views, and (6) multiple object tracking, focusing on tracking players and the ball through unedited video streams. Compared to last year's challenges, tasks (1-2) had their evaluation metrics redefined to consider tighter temporal accuracies, and tasks (3-6) were novel, including their underlying data and annotations. More information on the tasks, challenges and leaderboards are available on https://www.soccer-net.org. Baselines and development kits are available on https://github.com/SoccerNet.

Instantaneous GNSS Ambiguity Resolution and Attitude Determination via Riemannian Manifold Optimization

We present an ambiguity resolution method for Global Navigation Satellite System (GNSS)-based attitude determination. A GNSS attitude model with nonlinear constraints is used to rigorously incorporate a priori information. Given the characteristics of the employed nonlinear constraints, we formulate GNSS attitude determination as an optimization problem on a manifold. Then, Riemannian manifold optimization algorithms are utilized to aid ambiguity resolution based on a proposed decomposition of the objective function. The application of manifold geometry enables high-quality float solutions that are critical to reinforcing search-based integer ambiguity resolution in terms of efficiency, availability, and reliability. The proposed approach is characterized by a low computational complexity and a high probability of resolving the ambiguities correctly. The performance of the proposed ambiguity resolution method is tested through a series of simulations and real experiments. Comparisons with the principal benchmarks indicate the superiority of the proposed method as reflected by the high ambiguity resolution success rates.

Grassmann Stein Variational Gradient Descent

Stein variational gradient descent (SVGD) is a deterministic particle inference algorithm that provides an efficient alternative to Markov chain Monte Carlo. However, SVGD has been found to suffer from variance underestimation when the dimensionality of the target distribution is high. Recent developments have advocated projecting both the score function and the data onto real lines to sidestep this issue, although this can severely overestimate the epistemic (model) uncertainty. In this work, we propose Grassmann Stein variational gradient descent (GSVGD) as an alternative approach, which permits projections onto arbitrary dimensional subspaces. Compared with other variants of SVGD that rely on dimensionality reduction, GSVGD updates the projectors simultaneously for the score function and the data, and the optimal projectors are determined through a coupled Grassmann-valued diffusion process which explores favourable subspaces. Both our theoretical and experimental results suggest that GSVGD enjoys efficient state-space exploration in high-dimensional problems that have an intrinsic low-dimensional structure.

Machine Learning in Heterogeneous Porous Materials

The "Workshop on Machine learning in heterogeneous porous materials" brought together international scientific communities of applied mathematics, porous media, and material sciences with experts in the areas of heterogeneous materials, machine learning (ML) and applied mathematics to identify how ML can advance materials research. Within the scope of ML and materials research, the goal of the workshop was to discuss the state-of-the-art in each community, promote crosstalk and accelerate multi-disciplinary collaborative research, and identify challenges and opportunities. As the end result, four topic areas were identified: ML in predicting materials properties, and discovery and design of novel materials, ML in porous and fractured media and time-dependent phenomena, Multi-scale modeling in heterogeneous porous materials via ML, and Discovery of materials constitutive laws and new governing equations. This workshop was part of the AmeriMech Symposium series sponsored by the National Academies of Sciences, Engineering and Medicine and the U.S. National Committee on Theoretical and Applied Mechanics.

Constrained Wrapped Least Squares: A Tool for High Accuracy GNSS Attitude Determination

Attitude determination is a popular application of Global Navigation Satellite Systems (GNSS). Many methods have been developed to solve the attitude determination problem with different performance offerings. We develop a constrained wrapped least-squares (C-WLS) method for high-accuracy attitude determination. This approach is built on an optimization model that leverages prior information related to the antenna array and the integer nature of the carrier-phase ambiguities in an innovative way. The proposed approach adopts an efficient search strategy to estimate the vehicle's attitude parameters using ambiguous carrier-phase observations directly, without requiring prior carrier-phase ambiguity fixing. The performance of the proposed method is evaluated via simulations and experimentally utilizing data collected using multiple GNSS receivers. The simulation and experimental results demonstrate excellent performance, with the proposed method outperforming the ambiguity function method, the constrained LAMBDA and multivariate constrained LAMBDA methods, three prominent attitude determination algorithms.

Matching in the Dark: A Dataset for Matching Image Pairs of Low-light Scenes

This paper considers matching images of low-light scenes, aiming to widen the frontier of SfM and visual SLAM applications. Recent image sensors can record the brightness of scenes with more than eight-bit precision, available in their RAW-format image. We are interested in making full use of such high-precision information to match extremely low-light scene images that conventional methods cannot handle. For extreme low-light scenes, even if some of their brightness information exists in the RAW format images' low bits, the standard raw image processing on cameras fails to utilize them properly. As was recently shown by Chen et al., CNNs can learn to produce images with a natural appearance from such RAW-format images. To consider if and how well we can utilize such information stored in RAW-format images for image matching, we have created a new dataset named MID (matching in the dark). Using it, we experimentally evaluated combinations of eight image-enhancing methods and eleven image matching methods consisting of classical/neural local descriptors and classical/neural initial point-matching methods. The results show the advantage of using the RAW-format images and the strengths and weaknesses of the above component methods. They also imply there is room for further research.

Cross-Region Domain Adaptation for Class-level Alignment

Semantic segmentation requires a lot of training data, which necessitates costly annotation. There have been many studies on unsupervised domain adaptation (UDA) from one domain to another, e.g., from computer graphics to real images. However, there is still a gap in accuracy between UDA and supervised training on native domain data. It is arguably attributable to class-level misalignment between the source and target domain data. To cope with this, we propose a method that applies adversarial training to align two feature distributions in the target domain. It uses a self-training framework to split the image into two regions (i.e., trusted and untrusted), which form two distributions to align in the feature space. We term this approach cross-region adaptation (CRA) to distinguish from the previous methods of aligning different domain distributions, which we call cross-domain adaptation (CDA). CRA can be applied after any CDA method. Experimental results show that this always improves the accuracy of the combined CDA method, having updated the state-of-the-art.

3D High-Fidelity Mask Face Presentation Attack Detection Challenge

The threat of 3D masks to face recognition systems is increasingly serious and has been widely concerned by researchers. To facilitate the study of the algorithms, a large-scale High-Fidelity Mask dataset, namely CASIA-SURF HiFiMask (briefly HiFiMask) has been collected. Specifically, it consists of a total amount of 54, 600 videos which are recorded from 75 subjects with 225 realistic masks under 7 new kinds of sensors. Based on this dataset and Protocol 3 which evaluates both the discrimination and generalization ability of the algorithm under the open set scenarios, we organized a 3D High-Fidelity Mask Face Presentation Attack Detection Challenge to boost the research of 3D mask-based attack detection. It attracted 195 teams for the development phase with a total of 18 teams qualifying for the final round. All the results were verified and re-run by the organizing team, and the results were used for the final ranking. This paper presents an overview of the challenge, including the introduction of the dataset used, the definition of the protocol, the calculation of the evaluation criteria, and the summary and publication of the competition results. Finally, we focus on introducing and analyzing the top ranking algorithms, the conclusion summary, and the research ideas for mask attack detection provided by this competition.