arXiv subjects

Wei Qian

Publications and source records attributed to Wei Qian.

At least 55 records · Page 3Linked to original sources

arXiv2023

Geodesics in the Brownian map: Strong confluence and geometric structure

We study geodesics in the Brownian map $(\mathcal{S},d,ν)$, the random metric measure space which arises as the Gromov-Hausdorff scaling limit of uniformly random planar maps. Our results apply to all geodesics including those between exceptional points. First, we prove a strong and quantitative form of the confluence of geodesics phenomenon which states that any pair of geodesics which are sufficiently close in the Hausdorff distance must coincide with each other except near their endpoints. Then, we show that the intersection of any two geodesics minus their endpoints is connected, the number of geodesics which emanate from a single point and are disjoint except at their starting point is at most $5$, and the maximal number of geodesics which connect any pair of points is $9$. For each $1\le k \le 9$, we obtain the Hausdorff dimension of the pairs of points connected by exactly $k$ geodesics. For $k=7,8,9$, such pairs have dimension zero and are countably infinite. Further, we classify the (finite number of) possible configurations of geodesics between any pair of points in $\mathcal{S}$, up to homeomorphism, and give a dimension upper bound for the set of endpoints in each case. Finally, we show that every geodesic can be approximated arbitrarily well and in a strong sense by a geodesic connecting $ν$-typical points. In particular, this gives an affirmative answer to a conjecture of Angel, Kolesnik, and Miermont that the geodesic frame of $\mathcal{S}$, the union of all of the geodesics in $\mathcal{S}$ minus their endpoints, has dimension one, the dimension of a single geodesic.

math.PR↗

arXiv2023

Exploiting Diverse Feature for Multimodal Sentiment Analysis

In this paper, we present our solution to the MuSe-Personalisation sub-challenge in the MuSe 2023 Multimodal Sentiment Analysis Challenge. The task of MuSe-Personalisation aims to predict the continuous arousal and valence values of a participant based on their audio-visual, language, and physiological signal modalities data. Considering different people have personal characteristics, the main challenge of this task is how to build robustness feature presentation for sentiment prediction. To address this issue, we propose exploiting diverse features. Specifically, we proposed a series of feature extraction methods to build a robust representation and model ensemble. We empirically evaluate the performance of the utilized method on the officially provided dataset. \textbf{As a result, we achieved 3rd place in the MuSe-Personalisation sub-challenge.} Specifically, we achieve the results of 0.8492 and 0.8439 for MuSe-Personalisation in terms of arousal and valence CCC.

cs.CV↗

arXiv2023

Dual-path TokenLearner for Remote Photoplethysmography-based Physiological Measurement with Facial Videos

Remote photoplethysmography (rPPG) based physiological measurement is an emerging yet crucial vision task, whose challenge lies in exploring accurate rPPG prediction from facial videos accompanied by noises of illumination variations, facial occlusions, head movements, \etc, in a non-contact manner. Existing mainstream CNN-based models make efforts to detect physiological signals by capturing subtle color changes in facial regions of interest (ROI) caused by heartbeats. However, such models are constrained by the limited local spatial or temporal receptive fields in the neural units. Unlike them, a native Transformer-based framework called Dual-path TokenLearner (Dual-TL) is proposed in this paper, which utilizes the concept of learnable tokens to integrate both spatial and temporal informative contexts from the global perspective of the video. Specifically, the proposed Dual-TL uses a Spatial TokenLearner (S-TL) to explore associations in different facial ROIs, which promises the rPPG prediction far away from noisy ROI disturbances. Complementarily, a Temporal TokenLearner (T-TL) is designed to infer the quasi-periodic pattern of heartbeats, which eliminates temporal disturbances such as head movements. The two TokenLearners, S-TL and T-TL, are executed in a dual-path mode. This enables the model to reduce noise disturbances for final rPPG signal prediction. Extensive experiments on four physiological measurement benchmark datasets are conducted. The Dual-TL achieves state-of-the-art performances in both intra- and cross-dataset testings, demonstrating its immense potential as a basic backbone for rPPG measurement. The source code is available at \href{https://github.com/VUT-HFUT/Dual-TL}{https://github.com/VUT-HFUT/Dual-TL}

cs.CV↗

arXiv2023

Crossing exponent in the Brownian loop soup

We study the clusters of loops in a Brownian loop soup in some bounded two-dimensional domain with subcritical intensity $θ\in (0,1/2]$. We obtain an exact expression for the asymptotic probability of the existence of a cluster crossing a given annulus of radii $r$ and $r^s$ as $r \to 0$ ($s >1$ fixed). Relying on this result, we then show that the probability for a macroscopic cluster to hit a given disc of radius $r$ decays like $|\log r|^{-1+θ+ o(1)}$ as $r \to 0$. Finally, we characterise the polar sets of clusters, i.e. sets that are not hit by the closure of any cluster, in terms of $\log^α$-capacity. This paper reveals a connection between the 1D and 2D Brownian loop soups. This connection in turn implies the existence of a second critical intensity $θ= 1$ that describes a phase transition in the percolative behaviour of large loops on a logarithmic scale targeting an interior point of the domain.

math.PR↗

arXiv2023

Learning Occupancy for Monocular 3D Object Detection

Monocular 3D detection is a challenging task due to the lack of accurate 3D information. Existing approaches typically rely on geometry constraints and dense depth estimates to facilitate the learning, but often fail to fully exploit the benefits of three-dimensional feature extraction in frustum and 3D space. In this paper, we propose \textbf{OccupancyM3D}, a method of learning occupancy for monocular 3D detection. It directly learns occupancy in frustum and 3D space, leading to more discriminative and informative 3D features and representations. Specifically, by using synchronized raw sparse LiDAR point clouds, we define the space status and generate voxel-based occupancy labels. We formulate occupancy prediction as a simple classification problem and design associated occupancy losses. Resulting occupancy estimates are employed to enhance original frustum/3D features. As a result, experiments on KITTI and Waymo open datasets demonstrate that the proposed method achieves a new state of the art and surpasses other methods by a significant margin. Codes and pre-trained models will be available at \url{https://github.com/SPengLiang/OccupancyM3D}.

cs.CV↗

arXiv2023

Multi-Target Landmark Detection with Incomplete Images via Reinforcement Learning and Shape Prior

Medical images are generally acquired with limited field-of-view (FOV), which could lead to incomplete regions of interest (ROI), and thus impose a great challenge on medical image analysis. This is particularly evident for the learning-based multi-target landmark detection, where algorithms could be misleading to learn primarily the variation of background due to the varying FOV, failing the detection of targets. Based on learning a navigation policy, instead of predicting targets directly, reinforcement learning (RL)-based methods have the potential totackle this challenge in an efficient manner. Inspired by this, in this work we propose a multi-agent RL framework for simultaneous multi-target landmark detection. This framework is aimed to learn from incomplete or (and) complete images to form an implicit knowledge of global structure, which is consolidated during the training stage for the detection of targets from either complete or incomplete test images. To further explicitly exploit the global structural information from incomplete images, we propose to embed a shape model into the RL process. With this prior knowledge, the proposed RL model can not only localize dozens of targetssimultaneously, but also work effectively and robustly in the presence of incomplete images. We validated the applicability and efficacy of the proposed method on various multi-target detection tasks with incomplete images from practical clinics, using body dual-energy X-ray absorptiometry (DXA), cardiac MRI and head CT datasets. Results showed that our method could predict whole set of landmarks with incomplete training images up to 80% missing proportion (average distance error 2.29 cm on body DXA), and could detect unseen landmarks in regions with missing image information outside FOV of target images (average distance error 6.84 mm on 3D half-head CT).

cs.CV↗

arXiv2023

Generalized disconnection exponents

We introduce and compute the generalized disconnection exponents $η_κ(β)$ which depend on $κ\in(0,4]$ and another real parameter $β$, extending the Brownian disconnection exponents (corresponding to $κ=8/3$) computed by Lawler, Schramm and Werner 2001 (conjectured by Duplantier and Kwon 1988). For $κ\in(8/3,4]$, the generalized disconnection exponents have a physical interpretation in terms of planar Brownian loop-soups with intensity $c\in (0,1]$, which allows us to obtain the first prediction of the dimension of multiple points on the cluster boundaries of these loop-soups. In particular, according to our prediction, the dimension of double points on the cluster boundaries is strictly positive for $c\in(0,1)$ and equal to zero for the critical intensity $c=1$, leading to an interesting open question of whether such points exist for the critical loop-soup. Our definition of the exponents is based on a certain general version of radial restriction measures that we construct and study. As an important tool, we introduce a new family of radial SLEs depending on $κ$ and two additional parameters $μ, ν$, that we call radial hypergeometric SLEs. This is a natural but substantial extension of the family of radial SLE$_κ(ρ)s$.

math.PR↗

arXiv2022

Two-stage Contextual Transformer-based Convolutional Neural Network for Airway Extraction from CT Images

Accurate airway extraction from computed tomography (CT) images is a critical step for planning navigation bronchoscopy and quantitative assessment of airway-related chronic obstructive pulmonary disease (COPD). The existing methods are challenging to sufficiently segment the airway, especially the high-generation airway, with the constraint of the limited label and cannot meet the clinical use in COPD. We propose a novel two-stage 3D contextual transformer-based U-Net for airway segmentation using CT images. The method consists of two stages, performing initial and refined airway segmentation. The two-stage model shares the same subnetwork with different airway masks as input. Contextual transformer block is performed both in the encoder and decoder path of the subnetwork to finish high-quality airway segmentation effectively. In the first stage, the total airway mask and CT images are provided to the subnetwork, and the intrapulmonary airway mask and corresponding CT scans to the subnetwork in the second stage. Then the predictions of the two-stage method are merged as the final prediction. Extensive experiments were performed on in-house and multiple public datasets. Quantitative and qualitative analysis demonstrate that our proposed method extracted much more branches and lengths of the tree while accomplishing state-of-the-art airway segmentation performance. The code is available at https://github.com/zhaozsq/airway_segmentation.

eess.IV↗

arXiv2022

SPATL: Salient Parameter Aggregation and Transfer Learning for Heterogeneous Clients in Federated Learning

Federated learning~(FL) facilitates the training and deploying AI models on edge devices. Preserving user data privacy in FL introduces several challenges, including expensive communication costs, limited resources, and data heterogeneity. In this paper, we propose SPATL, an FL method that addresses these issues by: (a) introducing a salient parameter selection agent and communicating selected parameters only; (b) splitting a model into a shared encoder and a local predictor, and transferring its knowledge to heterogeneous clients via the locally customized predictor. Additionally, we leverage a gradient control mechanism to further speed up model convergence and increase robustness of training processes. Experiments demonstrate that SPATL reduces communication overhead, accelerates model inference, and enables stable training processes with better results compared to state-of-the-art methods. Our approach reduces communication cost by up to $86.45\%$, accelerates local inference by reducing up to $39.7\%$ FLOPs on VGG-11, and requires $7.4 \times$ less communication overhead when training ResNet-20.

cs.LG↗

arXiv2022

Graph R-CNN: Towards Accurate 3D Object Detection with Semantic-Decorated Local Graph

Two-stage detectors have gained much popularity in 3D object detection. Most two-stage 3D detectors utilize grid points, voxel grids, or sampled keypoints for RoI feature extraction in the second stage. Such methods, however, are inefficient in handling unevenly distributed and sparse outdoor points. This paper solves this problem in three aspects. 1) Dynamic Point Aggregation. We propose the patch search to quickly search points in a local region for each 3D proposal. The dynamic farthest voxel sampling is then applied to evenly sample the points. Especially, the voxel size varies along the distance to accommodate the uneven distribution of points. 2) RoI-graph Pooling. We build local graphs on the sampled points to better model contextual information and mine point relations through iterative message passing. 3) Visual Features Augmentation. We introduce a simple yet effective fusion strategy to compensate for sparse LiDAR points with limited semantic cues. Based on these modules, we construct our Graph R-CNN as the second stage, which can be applied to existing one-stage detectors to consistently improve the detection performance. Extensive experiments show that Graph R-CNN outperforms the state-of-the-art 3D detection models by a large margin on both the KITTI and Waymo Open Dataset. And we rank first place on the KITTI BEV car detection leaderboard. Code will be available at \url{https://github.com/Nightmare-n/GraphRCNN}.

cs.CV↗

arXiv2022

Golfer: Trajectory Prediction with Masked Goal Conditioning MnM Network

Transformers have enabled breakthroughs in NLP and computer vision, and have recently began to show promising performance in trajectory prediction for Autonomous Vehicle (AV). How to efficiently model the interactive relationships between the ego agent and other road and dynamic objects remains challenging for the standard attention module. In this work we propose a general Transformer-like architectural module MnM network equipped with novel masked goal conditioning training procedures for AV trajectory prediction. The resulted model, named golfer, achieves state-of-the-art performance, winning the 2nd place in the 2022 Waymo Open Dataset Motion Prediction Challenge and ranked 1st place according to minADE.

cs.CV↗

arXiv2021

Conformal invariance of double random currents II: tightness and properties in the discrete

This is the second of two papers devoted to the proof of conformal invariance of the critical double random current on the square lattice. More precisely, we show convergence of loop ensembles obtained by taking the cluster boundaries in the sum of two independent critical currents (both for free and wired boundary conditions). The strategy is first to prove convergence of the associated height function to the continuum Gaussian free field, and then to characterize the scaling limit of the loop ensembles as certain local sets of this Gaussian Free Field. In this paper, we derive crossing properties of the discrete model required to prove this characterization.

math.PR↗

arXiv2021

Free boundary dimers: random walk representation and scaling limit

We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplicative weight $z>0$ to the total weight of the configuration. A bijection described by Giuliani, Jauslin and Lieb relates this model to a standard dimer model but on a non-bipartite graph. The Kasteleyn matrix of this dimer model describes a walk with transition weights that are negative along the free boundary. Yet under certain assumptions, which are in particular satisfied in the infinite volume limit in the upper half-plane, we prove an effective, true random walk representation for the inverse Kasteleyn matrix. In this case we further show that, independently of the value of $z>0$, the scaling limit of the height function is the Gaussian free field with Neumann (or free) boundary conditions, thereby answering a question of Giuliani et al.

math.PR↗

arXiv2021

Variable selection for longitudinal survey data

In this article we propose a new variable selection method for analyzing data collected from longitudinal sample surveys. The procedure is based on the survey-weighted quadratic inference function, which was recently introduced as an alternative to the survey-weighted generalized estimating function. Under the joint model-design framework, we introduce the penalized survey-weighted quadratic inference estimator and obtain sufficient conditions for the existence, weak consistency, sparsity and asymptotic normality. To illustrate the finite sample performance of the model selection procedure, we include a limited simulation study.

math.ST↗

arXiv2020

Structures of Spurious Local Minima in $k$-means

$k$-means clustering is a fundamental problem in unsupervised learning. The problem concerns finding a partition of the data points into $k$ clusters such that the within-cluster variation is minimized. Despite its importance and wide applicability, a theoretical understanding of the $k$-means problem has not been completely satisfactory. Existing algorithms with theoretical performance guarantees often rely on sophisticated (sometimes artificial) algorithmic techniques and restricted assumptions on the data. The main challenge lies in the non-convex nature of the problem; in particular, there exist additional local solutions other than the global optimum. Moreover, the simplest and most popular algorithm for $k$-means, namely Lloyd's algorithm, generally converges to such spurious local solutions both in theory and in practice. In this paper, we approach the $k$-means problem from a new perspective, by investigating the structures of these spurious local solutions under a probabilistic generative model with $k$ ground truth clusters. As soon as $k=3$, spurious local minima provably exist, even for well-separated and balanced clusters. One such local minimum puts two centers at one true cluster, and the third center in the middle of the other two true clusters. For general $k$, one local minimum puts multiple centers at a true cluster, and one center in the middle of multiple true clusters. Perhaps surprisingly, we prove that this is essentially the only type of spurious local minima under a separation condition. Our results pertain to the $k$-means formulation for mixtures of Gaussians or bounded distributions. Our theoretical results corroborate existing empirical observations and provide justification for several improved algorithms for $k$-means clustering.

stat.ML↗

arXiv2019

Tweedie Gradient Boosting for Extremely Unbalanced Zero-inflated Data

Tweedie's compound Poisson model is a popular method to model insurance claims with probability mass at zero and nonnegative, highly right-skewed distribution. In particular, it is not uncommon to have extremely unbalanced data with excessively large proportion of zero claims, and even traditional Tweedie model may not be satisfactory for fitting the data. In this paper, we propose a boosting-assisted zero-inflated Tweedie model, called EMTboost, that allows zero probability mass to exceed a traditional model. We makes a nonparametric assumption on its Tweedie model component, that unlike a linear model, is able to capture nonlinearities, discontinuities, and complex higher order interactions among predictors. A specialized Expectation-Maximization algorithm is developed that integrates a blockwise coordinate descent strategy and a gradient tree-boosting algorithm to estimate key model parameters. We use extensive simulation and data analysis on synthetic zero-inflated auto-insurance claim data to illustrate our method's prediction performance.

stat.CO↗

arXiv2019

Conformal invariance of CLE$_κ$ on the Riemann sphere for $κ\in (4,8)$

The conformal loop ensemble (CLE) is the canonical conformally invariant probability measure on non-crossing loops in a simply connected domain in $\mathbb C$ and is indexed by a parameter $κ\in (8/3,8)$. We consider CLE$_κ$ on the whole-plane in the regime in which the loops are self-intersecting ($κ\in (4,8)$) and show that it is invariant under the inversion map $z \mapsto 1/z$. This shows that whole-plane CLE$_κ$ for $κ\in (4,8)$ defines a conformally invariant measure on loops on the Riemann sphere. The analogous statement in the regime in which the loops are simple ($κ\in (8/3,4]$) was proven by Kemppainen and Werner and together with the present work covers the entire range $κ\in (8/3,8)$ for which CLE$_κ$ is defined. As an intermediate step in the proof, we show that CLE$_κ$ for $κ\in (4,8)$ on an annulus, with any specified number of inner-boundary-surrounding loops, is well-defined and conformally invariant.

math.PR↗

arXiv2019

The geodesics in Liouville quantum gravity are not Schramm-Loewner evolutions

We prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of SLE$_κ$. These hypotheses are satisfied by the LQG metric for $γ=\sqrt{8/3}$ constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each $γ\in (0,2)$. As a consequence of our analysis, we also establish certain regularity properties of LQG geodesics which imply, among other things, that they are conformally removable.

math.PR↗