arXiv subjects
Publications and source records attributed to Hui Xiao.
We prove a non-arithmeticity property for the complex eigenvalues of a Zariski dense subsemigroups of real reductive algebraic groups. This property will be used in [7] in order to establish a local limit theorem for the operator norm of products of random matrices.
We prove a local limit theorem for the quantity $\| g_n \cdots g_1 \|$, where $g_1, g_2, \ldots$ is a sequence of independent and identically distributed random invertible square matrices. The norm $\| \cdot \|$ is arbitrary and we make no proximality assumption.
Semi-Supervised Domain Adaptation (SSDA) leverages knowledge from a fully labeled source domain to classify data in a partially labeled target domain. Due to the limited number of labeled samples in the target domain, there can be intrinsic similarity of classes in the feature space, which may result in biased predictions, even when the model is trained on a balanced dataset. To overcome this limitation, we introduce a multi-view consistency framework, which includes two views for training strongly augmented data. One is a debiasing strategy for correcting class-wise prediction probabilities according to the prediction performance of the model. The other involves leveraging pseudo-negative labels derived from the model predictions. Furthermore, we introduce a cross-domain affinity learning aimed at aligning features of the same class across different domains, thereby enhancing overall performance. Experimental results demonstrate that our method outperforms the competing methods on two standard domain adaptation datasets, DomainNet and Office-Home. Combining unsupervised domain adaptation and semi-supervised learning offers indispensable contributions to the industrial sector by enhancing model adaptability, reducing annotation costs, and improving performance.
We study the random walk $(S_n)_{n\geq 1}$ with independent and identically distributed real-valued increments having zero mean and an absolute moment of order $2 + \delta$ for some $\delta > 0$. For any starting point $x \in \mathbb{R}$, let $\tau_x = \inf\{k \geq 1 : x + S_k < 0\}$ denote the first exit time of the random walk $x + S_n$ from the half-line $[0, \infty)$. In the previous work [25], we established a Gaussian heat kernel approximation for both the persistence probability $\mathbb{P}(\tau_x > n)$ and the joint distribution $\mathbb{P}(x + S_n \leq \cdot, \tau_x > n)$, uniformly over $x \in \mathbb{R}$ as $n \to \infty$. In this paper, we leverage these results to establish a novel conditioned local limit theorem for the walk $(x + S_n)_{n \geq 1}$. For $\mathbb{Z}$-valued random walks, we prove that the joint probability $\mathbb{P}(x + S_n = y, \tau_x > n)$ is uniformly approximated by a distribution governed by the Gaussian heat kernel over all $x, y \in \mathbb{Z}$ as $n \to \infty$. Our new asymptotic unifies into a single comprehensive formula the classical local limit theorem by Caravenna [6], as well as various results relying on specific assumptions on $x$ and $y$. As a corollary, we obtain a new uniform-in-$x$ asymptotic formula for the local probability $\mathbb{P}(\tau_x = n)$. We also extend our analysis to non-lattice random walks.
Previously, mathematicians Steven Krantz and Jeffery McNeal studied a type of positive numbers permutation called $\lambda$-permutation. This type of permutation, when applied to the index of terms of a series, is defined to be both convergence-preserving and "fixing" at least one divergent series, that is, rearranging the terms of any convergent series will result in a convergent series, while rearranging the terms of some divergent series will result in a convergent series. In general, if a divergent series can be fixed to converge in some way (it does not need to be by $\lambda$-permutation), it is called a "conditionally divergent series". In 2006, another mathematician Daniel Velleman raised an open problem related to $\lambda$-permutation: for a conditionally divergent series $\sum_{n=0}^{\infty}a_n,n\in \mathbb{N},a_n\in \mathbb{R}$, let $S=\{L \in \mathbb{R} \colon L = \sum_{n=0}^{\infty}{a_{\sigma\left(n\right)}}$ $\text{for some } \lambda\text{-permutation } \sigma\}$, can $S$ ever be something between $\emptyset$ and $\mathbb{R}$? This paper is devoted to partially answering this open problem by considering a subset of $\lambda$-permutation constraint by how we can permute, named type R $\lambda$-permutation. Then we answer the analogous question about a subset of S with respect to type R $\lambda$-permutation, named $Z_{R}=\{L \in \mathbb{R} \colon L = \sum_{n=0}^{\infty}{a_{\sigma\left(n\right)}}$ $\text{for some type R } \lambda \text{-permutation } \sigma\}$. We show that $Z_R$ is either $\emptyset$, a singleton or $\mathbb{R}$. We also provide sufficient conditions on the conditionally divergent series $\sum_{n=0}^{\infty}a_n$ for $Z_R$ to be a singleton or $\mathbb{R}$, by introducing a "substantial property" on the series.
We consider a matrix branching random walk on the semi-group of nonnegative matrices, where we are able to derive, under general assumptions, an analogue of Biggins' martingale convergence theorem for the additive martingale $W_n$, a spinal decomposition theorem, convergence of the derivative martingale $D_n$, and finally, the Seneta-Heyde scaling stating that in the boundary case $c \sqrt{n} W_n \to D_\infty$ a.s., where $D_\infty$ is the limit of the derivative martingale and $c$ is a positive constant. As an important tool that is of interest in its own right, we provide explicit duality results for the renewal measure of centered Markov random walks, relating the renewal measure of the process, killed when the random walk component becomes negative, to the renewal measure of the ascending ladder process.
Automatic personality recognition is a research hotspot in the intersection of computer science and psychology, and in human-computer interaction, personalised has a wide range of applications services and other scenarios. In this paper, an end-to-end multimodal performance personality is established for both visual and auditory modal datarecognition network , and the through feature-level fusion , which effectively of the two modalities is carried out the cross-attention mechanismfuses the features of the two modal data; and a is proposed multiscale feature enhancement modalitiesmodule , which enhances for visual and auditory boththe expression of the information of effective the features and suppresses the interference of the redundant information. In addition, during the training process, this paper proposes a modal enhancement training strategy to simulate non-ideal such as modal loss and noise interferencedata situations , which enhances the adaptability ofand the model to non-ideal data scenarios improves the robustness of the model. Experimental results show that the method proposed in this paper is able to achieve an average Big Five personality accuracy of , which outperforms existing 0.916 on the personality analysis dataset ChaLearn First Impressionother methods based on audiovisual and audio-visual both modalities. The ablation experiments also validate our proposed , respectivelythe contribution of module and modality enhancement strategy to the model performance. Finally, we simulate in the inference phase multi-scale feature enhancement six non-ideal data scenarios to verify the modal enhancement strategy's improvement in model robustness.
Consider a random walk $S_n=\sum_{i=1}^n X_i$ with independent and identically distributed real-valued increments with zero mean, finite variance and moment of order $2 + \delta$ for some $\delta>0$. For any starting point $x\in \mathbb R$, let $\tau_x = \inf \left\{ k\geq 1: x+S_{k} < 0 \right\}$ denote the first time when the random walk $x+S_n$ exits the half-line $[0,\infty)$. We investigate the uniform asymptotic behavior over $x\in \mathbb R$ of the persistence probability $\mathbb P (\tau_x >n)$ and the joint distribution $\mathbb{P} \left( x + S_n \leq u, \tau_x > n \right)$, for $u\geq 0$, as $n \to \infty$. New limit theorems for these probabilities are established based on the heat kernel approximations. Additionally, we evaluate the rate of convergence by proving Berry-Esseen type bounds.
Annotation ambiguity caused by the inherent subjectivity of visual judgment has always been a major challenge for Facial Expression Recognition (FER) tasks, particularly for largescale datasets from in-the-wild scenarios. A potential solution is the evaluation of relatively objective emotional distributions to help mitigate the ambiguity of subjective annotations. To this end, this paper proposes a novel Prior-based Objective Inference (POI) network. This network employs prior knowledge to derive a more objective and varied emotional distribution and tackles the issue of subjective annotation ambiguity through dynamic knowledge transfer. POI comprises two key networks: Firstly, the Prior Inference Network (PIN) utilizes the prior knowledge of AUs and emotions to capture intricate motion details. To reduce over-reliance on priors and facilitate objective emotional inference, PIN aggregates inferential knowledge from various key facial subregions, encouraging mutual learning. Secondly, the Target Recognition Network (TRN) integrates subjective emotion annotations and objective inference soft labels provided by the PIN, fostering an understanding of inherent facial expression diversity, thus resolving annotation ambiguity. Moreover, we introduce an uncertainty estimation module to quantify and balance facial expression confidence. This module enables a flexible approach to dealing with the uncertainties of subjective annotations. Extensive experiments show that POI exhibits competitive performance on both synthetic noisy datasets and multiple real-world datasets. All codes and training logs will be publicly available at https://github.com/liuhw01/POI.
Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper represents the first step toward achieving this goal, specifically entailing the construction of a novel entity -- the target harmonic measure. This measure, together with the harmonic function, serves as a pivotal component in establishing the conditioned local limit theorem. Using a reversal identity, we introduce a reversed sequence characterized as a dual random walk with a perturbation depending on future observations. The investigation of such walks, which rely on future information, lies at the heart of this paper. To carry out this study, we develop an approach grounded in the finite-size approximation of perturbations, enabling us to simplify the investigation to an array of Markov chains with increasing dimensions.
We investigate random walks on the general linear group constrained within a specific domain, with a focus on their asymptotic behavior. In a previous work [38], we constructed the associated harmonic measure, a key element in formulating the local limit theorem for conditioned random walks on groups. The primary aim of this paper is to prove this theorem. The main challenge arises from studying the conditioned reverse walk, whose increments, in the context of random walks on groups, depend on the entire future. To achieve our goal, we combine a Caravenna-type conditioned local limit theorem with the conditioned version of the central limit theorem for the reversed walk. The resulting local limit theorem is then applied to derive the local behavior of the exit time.
In fine-grained road scene understanding, semantic segmentation plays a crucial role in enabling vehicles to perceive and comprehend their surroundings. By assigning a specific class label to each pixel in an image, it allows for precise identification and localization of detailed road features, which is vital for high-quality scene understanding and downstream perception tasks. A key challenge in this domain lies in improving the recognition performance of minority classes while mitigating the dominance of majority classes, which is essential for achieving balanced and robust overall performance. However, traditional semi-supervised learning methods often train models overlooking the imbalance between classes. To address this issue, firstly, we propose a general training module that learns from all the pseudo-labels without a conventional filtering strategy. Secondly, we propose a professional training module to learn specifically from reliable minority-class pseudo-labels identified by a novel mismatch score metric. The two modules are crossly supervised by each other so that it reduces model coupling which is essential for semi-supervised learning. During contrastive learning, to avoid the dominance of the majority classes in the feature space, we propose a strategy to assign evenly distributed anchors for different classes in the feature space. Experimental results on multiple public benchmarks show that our method surpasses traditional approaches in recognizing tail classes.
Semi-supervised semantic segmentation relieves the reliance on large-scale labeled data by leveraging unlabeled data. Recent semi-supervised semantic segmentation approaches mainly resort to pseudo-labeling methods to exploit unlabeled data. However, unreliable pseudo-labeling can undermine the semi-supervision processes. In this paper, we propose an algorithm called Multi-Level Label Correction (MLLC), which aims to use graph neural networks to capture structural relationships in Semantic-Level Graphs (SLGs) and Class-Level Graphs (CLGs) to rectify erroneous pseudo-labels. Specifically, SLGs represent semantic affinities between pairs of pixel features, and CLGs describe classification consistencies between pairs of pixel labels. With the support of proximate pattern information from graphs, MLLC can rectify incorrectly predicted pseudo-labels and can facilitate discriminative feature representations. We design an end-to-end network to train and perform this effective label corrections mechanism. Experiments demonstrate that MLLC can significantly improve supervised baselines and outperforms state-of-the-art approaches in different scenarios on Cityscapes and PASCAL VOC 2012 datasets. Specifically, MLLC improves the supervised baseline by at least 5% and 2% with DeepLabV2 and DeepLabV3+ respectively under different partition protocols.
In decision-making, individuals often rely on intuition, which can occasionally yield suboptimal outcomes. This study examines the impact of intuitive decision-making on individuals who are confronted with limited position information in the job application process. We propose a measure, the mismatch index, that gauges allocation efficiency by comparing the final application rate to the preset admission rate. By simulation and analytical results, we counter-intuitively find that under the intuitive strategy, acquiring more information does not always lead to more efficient allocation. Additionally, a shift from despondency to a bandwagon effect occurs when the initial application rate surpasses the admission rate, which can be observed in our field experiments. Meanwhile, experimental data also unveil variations in individuals' reliance on intuition, indicating the presence of inherent adventurous and conservative inclinations. To account for these effects, we introduce an enhancement factor into our model. The improved results align well with these real data, showing that compared to mediate competitive scenarios, individuals exhibit a stronger conservative tendency in fierce or less competitive scenarios. These findings offer significant insights into resource allocation, especially in the competitive job market context.
We present PD-REAL, a novel large-scale dataset for unsupervised anomaly detection (AD) in the 3D domain. It is motivated by the fact that 2D-only representations in the AD task may fail to capture the geometric structures of anomalies due to uncertainty in lighting conditions or shooting angles. PD-REAL consists entirely of Play-Doh models for 15 object categories and focuses on the analysis of potential benefits from 3D information in a controlled environment. Specifically, objects are first created with six types of anomalies, such as \textit{dent}, \textit{crack}, or \textit{perforation}, and then photographed under different lighting conditions to mimic real-world inspection scenarios. To demonstrate the usefulness of 3D information, we use a commercially available RealSense camera to capture RGB and depth images. Compared to the existing 3D dataset for AD tasks, the data acquisition of PD-REAL is significantly cheaper, easily scalable, and easier to control variables. Furthermore, we introduce a multi-scale teacher--student framework with hierarchical distillation for multimodal anomaly detection. This architecture overcomes the inherent limitation of single-scale distillation approaches, which often struggle to reconcile global context with local features. Leveraging multi-level guidance from the teacher network, the student network can effectively capture richer features for anomaly detection. Extensive evaluations with our method and state-of-the-art AD algorithms on our dataset qualitatively and quantitatively demonstrate the higher detection accuracy of our method. Our dataset can be downloaded from https://github.com/Andy-cs008/PD-REAL
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed positive random $d\times d$ matrices, where $d\geq 2$ is an integer. For any starting point $x \in \mathbb{R}_+^d$ with $|x| = 1$ and $y \in \mathbb R$, we define the exit time $\tau_{x, y} = \inf \{ k \geq 1: y + \log |g_k \cdots g_1 x| < 0 \}$. In this paper, we investigate the conditioned local probability $\mathbb{P} (y + \log |g_n \cdots g_1 x| \in z + [0, \Delta], \tau_{x, y} > n)$ under various assumptions on $y$, $z$ and $\Delta$. For the case where $z = O(\sqrt{n})$, we establish an exact asymptotic result as $n \to \infty$, uniformly in $y$ and $\Delta$, which extends the classical Caravenna conditioned local limit theorem to the case of products of positive random matrices. Our proof does not rely on the reversibility techniques. Furthermore, for arbitrary $z \in \mathbb R_+$, we deduce a uniform upper bound with rate $n^{-3/2}$.
In ecological and environmental contexts, management actions must sometimes be chosen urgently. Value of information (VoI) analysis provides a quantitative toolkit for projecting the improved management outcomes expected after making additional measurements. However, traditional VoI analysis reports metrics as expected values (i.e. risk-neutral). This can be problematic because expected values hide uncertainties in projections. The true value of a measurement will only be known after the measurement's outcome is known, leaving large uncertainty in the measurement's value before it is performed. As a result, the expected value metrics produced in traditional VoI analysis may not align with the priorities of a risk-averse decision-maker who wants to avoid low-value measurement outcomes. In the present work, we introduce four new VoI metrics that can address a decision-maker's risk-aversion to different measurement outcomes. We demonstrate the benefits of the new metrics with two ecological case studies for which traditional VoI analysis has been previously applied. Using the new metrics, we also demonstrate a clear mathematical link between the often-separated environmental decision-making disciplines of VoI and optimal design of experiments. This mathematical link has the potential to catalyse future collaborations between ecologists and statisticians to work together to quantitatively address environmental decision-making questions of fundamental importance. Overall, the introduced VoI metrics complement existing metrics to provide decision-makers with a comprehensive view of the value of, and risks associated with, a proposed monitoring or measurement activity. This is critical for improved environmental outcomes when decisions must be urgently made.
Software vulnerabilities pose significant risks to computer systems, impacting our daily lives, productivity, and even our health. Identifying and addressing security vulnerabilities in a timely manner is crucial to prevent hacking and data breaches. Unfortunately, current vulnerability identification methods, including classical and deep learning-based approaches, exhibit critical drawbacks that prevent them from meeting the demands of the contemporary software industry. To tackle these issues, we present JFinder, a novel architecture for Java vulnerability identification that leverages quad self-attention and pre-training mechanisms to combine structural information and semantic representations. Experimental results demonstrate that JFinder outperforms all baseline methods, achieving an accuracy of 0.97 on the CWE dataset and an F1 score of 0.84 on the PROMISE dataset. Furthermore, a case study reveals that JFinder can accurately identify four cases of vulnerabilities after patching.