Yun Yang

Yifan Chen, Tianning Xu, Dilek Hakkani-Tur et al.

Multiple sampling-based methods have been developed for approximating and accelerating node embedding aggregation in graph convolutional networks (GCNs) training. Among them, a layer-wise approach recursively performs importance sampling to select neighbors jointly for existing nodes in each layer. This paper revisits the approach from a matrix approximation perspective, and identifies two issues in the existing layer-wise sampling methods: suboptimal sampling probabilities and estimation biases induced by sampling without replacement. To address these issues, we accordingly propose two remedies: a new principle for constructing sampling probabilities and an efficient debiasing algorithm. The improvements are demonstrated by extensive analyses of estimation variance and experiments on common benchmarks. Code and algorithm implementations are publicly available at https://github.com/ychen-stat-ml/GCN-layer-wise-sampling .

Yifan Chen, Rentian Yao, Yun Yang et al.

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel $K$-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

Tencent Hunyuan Team, Ao Liu, Botong Zhou et al. · tencent-ai

As Large Language Models (LLMs) rapidly advance, we introduce Hunyuan-TurboS, a novel large hybrid Transformer-Mamba Mixture of Experts (MoE) model. It synergistically combines Mamba's long-sequence processing efficiency with Transformer's superior contextual understanding. Hunyuan-TurboS features an adaptive long-short chain-of-thought (CoT) mechanism, dynamically switching between rapid responses for simple queries and deep "thinking" modes for complex problems, optimizing computational resources. Architecturally, this 56B activated (560B total) parameter model employs 128 layers (Mamba2, Attention, FFN) with an innovative AMF/MF block pattern. Faster Mamba2 ensures linear complexity, Grouped-Query Attention minimizes KV cache, and FFNs use an MoE structure. Pre-trained on 16T high-quality tokens, it supports a 256K context length and is the first industry-deployed large-scale Mamba model. Our comprehensive post-training strategy enhances capabilities via Supervised Fine-Tuning (3M instructions), a novel Adaptive Long-short CoT Fusion method, Multi-round Deliberation Learning for iterative improvement, and a two-stage Large-scale Reinforcement Learning process targeting STEM and general instruction-following. Evaluations show strong performance: overall top 7 rank on LMSYS Chatbot Arena with a score of 1356, outperforming leading models like Gemini-2.0-Flash-001 (1352) and o4-mini-2025-04-16 (1345). TurboS also achieves an average of 77.9% across 23 automated benchmarks. Hunyuan-TurboS balances high performance and efficiency, offering substantial capabilities at lower inference costs than many reasoning models, establishing a new paradigm for efficient large-scale pre-trained models.

Zhichao Lu, Chuntao Ding, Felix Juefei-Xu et al.

Deploying high-performance vision transformer (ViT) models on ubiquitous Internet of Things (IoT) devices to provide high-quality vision services will revolutionize the way we live, work, and interact with the world. Due to the contradiction between the limited resources of IoT devices and resource-intensive ViT models, the use of cloud servers to assist ViT model training has become mainstream. However, due to the larger number of parameters and floating-point operations (FLOPs) of the existing ViT models, the model parameters transmitted by cloud servers are large and difficult to run on resource-constrained IoT devices. To this end, this paper proposes a transmission-friendly ViT model, TFormer, for deployment on resource-constrained IoT devices with the assistance of a cloud server. The high performance and small number of model parameters and FLOPs of TFormer are attributed to the proposed hybrid layer and the proposed partially connected feed-forward network (PCS-FFN). The hybrid layer consists of nonlearnable modules and a pointwise convolution, which can obtain multitype and multiscale features with only a few parameters and FLOPs to improve the TFormer performance. The PCS-FFN adopts group convolution to reduce the number of parameters. The key idea of this paper is to propose TFormer with few model parameters and FLOPs to facilitate applications running on resource-constrained IoT devices to benefit from the high performance of the ViT models. Experimental results on the ImageNet-1K, MS COCO, and ADE20K datasets for image classification, object detection, and semantic segmentation tasks demonstrate that the proposed model outperforms other state-of-the-art models. Specifically, TFormer-S achieves 5% higher accuracy on ImageNet-1K than ResNet18 with 1.4$\times$ fewer parameters and FLOPs.

Anirban Bhattacharya, Debdeep Pati, Yun Yang

As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable efficacy and superior efficiency. Several recent works provide theoretical justifications of VI by proving its statistical optimality for parameter estimation under various settings; meanwhile, formal analysis on the algorithmic convergence aspects of VI is still largely lacking. In this paper, we consider the common coordinate ascent variational inference (CAVI) algorithm for implementing the mean-field (MF) VI towards optimizing a Kullback--Leibler divergence objective functional over the space of all factorized distributions. Focusing on the two-block case, we analyze the convergence of CAVI by leveraging the extensive toolbox from functional analysis and optimization. We provide general conditions for certifying global or local exponential convergence of CAVI. Specifically, a new notion of generalized correlation for characterizing the interaction between the constituting blocks in influencing the VI objective functional is introduced, which according to the theory, quantifies the algorithmic contraction rate of two-block CAVI. As illustrations, we apply the developed theory to a number of examples, and derive explicit problem-dependent upper bounds on the algorithmic contraction rate.

Honghao Li, Qiuze Ru, Yiwen Zhang et al.

Effective feature interaction modeling is critical for enhancing the accuracy of click-through rate (CTR) prediction in industrial recommender systems. Most of the current deep CTR models resort to building complex network architectures to better capture intricate feature interactions or user behaviors. However, we identify two limitations in these models: (1) the samples given to the model are undifferentiated, which may lead the model to learn a larger number of easy samples in a single-minded manner while ignoring a smaller number of hard samples, thus reducing the model's generalization ability; (2) differentiated feature interaction encoders are designed to capture different interactions information but receive consistent supervision signals, thereby limiting the effectiveness of the encoder. To bridge the identified gaps, this paper introduces a novel CTR prediction framework by integrating the plug-and-play Twin Focus (TF) Loss, Sample Selection Embedding Module (SSEM), and Dynamic Fusion Module (DFM), named the Twin Focus Framework for CTR (TF4CTR). Specifically, the framework employs the SSEM at the bottom of the model to differentiate between samples, thereby assigning a more suitable encoder for each sample. Meanwhile, the TF Loss provides tailored supervision signals to both simple and complex encoders. Moreover, the DFM dynamically fuses the feature interaction information captured by the encoders, resulting in more accurate predictions. Experiments on five real-world datasets confirm the effectiveness and compatibility of the framework, demonstrating its capacity to enhance various representative baselines in a model-agnostic manner. To facilitate reproducible research, our open-sourced code and detailed running logs will be made available at: https://github.com/salmon1802/TF4CTR.

Yubo Zhuang, Xiaohui Chen, Yun Yang

Clustering is an important exploratory data analysis technique to group objects based on their similarity. The widely used $K$-means clustering method relies on some notion of distance to partition data into a fewer number of groups. In the Euclidean space, centroid-based and distance-based formulations of the $K$-means are equivalent. In modern machine learning applications, data often arise as probability distributions and a natural generalization to handle measure-valued data is to use the optimal transport metric. Due to non-negative Alexandrov curvature of the Wasserstein space, barycenters suffer from regularity and non-robustness issues. The peculiar behaviors of Wasserstein barycenters may make the centroid-based formulation fail to represent the within-cluster data points, while the more direct distance-based $K$-means approach and its semidefinite program (SDP) relaxation are capable of recovering the true cluster labels. In the special case of clustering Gaussian distributions, we show that the SDP relaxed Wasserstein $K$-means can achieve exact recovery given the clusters are well-separated under the $2$-Wasserstein metric. Our simulation and real data examples also demonstrate that distance-based $K$-means can achieve better classification performance over the standard centroid-based $K$-means for clustering probability distributions and images.

Yubo Zhuang, Xiaohui Chen, Yun Yang

Clustering is a widely deployed unsupervised learning tool. Model-based clustering is a flexible framework to tackle data heterogeneity when the clusters have different shapes. Likelihood-based inference for mixture distributions often involves non-convex and high-dimensional objective functions, imposing difficult computational and statistical challenges. The classic expectation-maximization (EM) algorithm is a computationally thrifty iterative method that maximizes a surrogate function minorizing the log-likelihood of observed data in each iteration, which however suffers from bad local maxima even in the special case of the standard Gaussian mixture model with common isotropic covariance matrices. On the other hand, recent studies reveal that the unique global solution of a semidefinite programming (SDP) relaxed $K$-means achieves the information-theoretically sharp threshold for perfectly recovering the cluster labels under the standard Gaussian mixture model. In this paper, we extend the SDP approach to a general setting by integrating cluster labels as model parameters and propose an iterative likelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact observed likelihood in the presence of data heterogeneity. By lifting the cluster assignment to group-specific membership matrices, iLA-SDP avoids centroids estimation -- a key feature that allows exact recovery under well-separateness of centroids without being trapped by their adversarial configurations. Thus iLA-SDP is less sensitive than EM to initialization and more stable on high-dimensional data. Our numeric experiments demonstrate that iLA-SDP can achieve lower mis-clustering errors over several widely used clustering methods including $K$-means, SDP and EM algorithms.

Xiong Zhang, Hong Peng, Changlong Fu et al.

A significant number of anomalous nodes in the real world, such as fake news, noncompliant users, malicious transactions, and malicious posts, severely compromises the health of the graph data ecosystem and urgently requires effective identification and processing. With anomalies that span multiple data domains yet exhibit vast differences in features, cross-domain detection models face severe domain shift issues, which limit their generalizability across all domains. This study identifies and quantitatively analyzes a specific feature mismatch pattern exhibited by domain shift in graph anomaly detection, which we define as the \emph{Anomaly Disassortativity} issue ($\mathcal{AD}$). Based on the modeling of the issue $\mathcal{AD}$, we introduce a novel graph foundation model for anomaly detection. It achieves cross-domain generalization in different graphs, requiring only a single training phase to perform effectively across diverse domains. The experimental findings, based on fourteen diverse real-world graphs, confirm a breakthrough in the model's cross-domain adaptation, achieving a pioneering state-of-the-art (SOTA) level in terms of detection accuracy. In summary, the proposed theory of $\mathcal{AD}$ provides a novel theoretical perspective and a practical route for future research in generalist graph anomaly detection (GGAD). The code is available at https://anonymous.4open.science/r/Anonymization-TA-GGAD/.

Delin Ma, Menghui Zhou, Jun Qi et al.

Alzheimer's disease (AD) is the most prevalent form of dementia, and its early diagnosis is essential for slowing disease progression. Recent studies on multimodal neuroimaging fusion using MRI and PET have achieved promising results by integrating multi-scale complementary features. However, most existing approaches primarily emphasize cross-modal complementarity while overlooking the diagnostic importance of modality-specific features. In addition, the inherent distributional differences between modalities often lead to biased and noisy representations, degrading classification performance. To address these challenges, we propose a Collaborative Attention and Consistent-Guided Fusion framework for MRI and PET based AD diagnosis. The proposed model introduces a learnable parameter representation (LPR) block to compensate for missing modality information, followed by a shared encoder and modality-independent encoders to preserve both shared and specific representations. Furthermore, a consistency-guided mechanism is employed to explicitly align the latent distributions across modalities. Experimental results on the ADNI dataset demonstrate that our method achieves superior diagnostic performance compared with existing fusion strategies.

Chenglong Wang, Canjia Li, Xingzhao Zhu et al.

Due to the dynamically evolving nature of real-world query streams, relevance models struggle to generalize to practical search scenarios. A sophisticated solution is self-evolution techniques. However, in large-scale industrial settings with massive query streams, this technique faces two challenges: (1) informative samples are often sparse and difficult to identify, and (2) pseudo-labels generated by the current model could be unreliable. To address these challenges, in this work, we propose a Self-Evolving Relevance Model approach (SERM), which comprises two complementary multi-agent modules: a multi-agent sample miner, designed to detect distributional shifts and identify informative training samples, and a multi-agent relevance annotator, which provides reliable labels through a two-level agreement framework. We evaluate SERM in a large-scale industrial setting, which serves billions of user requests daily. Experimental results demonstrate that SERM can achieve significant performance gains through iterative self-evolution, as validated by extensive offline multilingual evaluations and online testing.

Mingchen Jiang, Peng Xu, Xichen Ye et al.

Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT methods predominantly focused on the efficient computation of a single map between two distributions. To address this challenge, we introduce a novel approach to learning transport maps for new empirical distributions. Specifically, we employ the transformer architecture to produce embeddings from distributional data of varying length; these embeddings are then fed into a hypernetwork to generate neural OT maps. Various numerical experiments were conducted to validate the embeddings and the generated OT maps. The model implementation and the code are provided on https://github.com/jiangmingchen/HOTET.

Zixiang Xu, Menghui Zhou, Jun Qi et al.

Alzheimer's Disease (AD) is the most prevalent neurodegenerative disorder in aging populations, posing a significant and escalating burden on global healthcare systems. While Multi-Tusk Learning (MTL) has emerged as a powerful computational paradigm for modeling longitudinal AD data, existing frameworks do not account for the time-varying nature of feature correlations. To address this limitation, we propose a novel MTL framework, named Feature Similarity Laplacian graph Multi-Task Learning (MTL-FSL). Our framework introduces a novel Feature Similarity Laplacian (FSL) penalty that explicitly models the time-varying relationships between features. By simultaneously considering temporal smoothness among tasks and the dynamic correlations among features, our model enhances both predictive accuracy and biological interpretability. To solve the non-smooth optimization problem arising from our proposed penalty terms, we adopt the Alternating Direction Method of Multipliers (ADMM) algorithm. Experiments conducted on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that our proposed MTL-FSL framework achieves state-of-the-art performance, outperforming various baseline methods. The implementation source can be found at https://github.com/huatxxx/MTL-FSL.

Jie Zhang, Haoyu Bu, Hui Wen et al.

The rapid development of large language models (LLMs) has opened new avenues across various fields, including cybersecurity, which faces an evolving threat landscape and demand for innovative technologies. Despite initial explorations into the application of LLMs in cybersecurity, there is a lack of a comprehensive overview of this research area. This paper addresses this gap by providing a systematic literature review, covering the analysis of over 300 works, encompassing 25 LLMs and more than 10 downstream scenarios. Our comprehensive overview addresses three key research questions: the construction of cybersecurity-oriented LLMs, the application of LLMs to various cybersecurity tasks, the challenges and further research in this area. This study aims to shed light on the extensive potential of LLMs in enhancing cybersecurity practices and serve as a valuable resource for applying LLMs in this field. We also maintain and regularly update a list of practical guides on LLMs for cybersecurity at https://github.com/tmylla/Awesome-LLM4Cybersecurity.

Fei Du, Peng Yang, Qi Jia et al.

In this paper, our goal is to design a simple learning paradigm for long-tail visual recognition, which not only improves the robustness of the feature extractor but also alleviates the bias of the classifier towards head classes while reducing the training skills and overhead. We propose an efficient one-stage training strategy for long-tailed visual recognition called Global and Local Mixture Consistency cumulative learning (GLMC). Our core ideas are twofold: (1) a global and local mixture consistency loss improves the robustness of the feature extractor. Specifically, we generate two augmented batches by the global MixUp and local CutMix from the same batch data, respectively, and then use cosine similarity to minimize the difference. (2) A cumulative head tail soft label reweighted loss mitigates the head class bias problem. We use empirical class frequencies to reweight the mixed label of the head-tail class for long-tailed data and then balance the conventional loss and the rebalanced loss with a coefficient accumulated by epochs. Our approach achieves state-of-the-art accuracy on CIFAR10-LT, CIFAR100-LT, and ImageNet-LT datasets. Additional experiments on balanced ImageNet and CIFAR demonstrate that GLMC can significantly improve the generalization of backbones. Code is made publicly available at https://github.com/ynu-yangpeng/GLMC.

Chenyang Wang, Yun Yang

We derive explicit non-asymptotic PAC-Bayes generalization bounds for Gibbs posteriors, that is, data-dependent distributions over model parameters obtained by exponentially tilting a prior with the empirical risk. Unlike classical worst-case complexity bounds based on uniform laws of large numbers, which require explicit control of the model space in terms of metric entropy (integrals), our analysis yields posterior-averaged risk bounds that can be applied to overparameterized models and adapt to the data structure and the intrinsic model complexity. The bound involves a marginal-type integral over the parameter space, which we analyze using tools from singular learning theory to obtain explicit and practically meaningful characterizations of the posterior risk. Applications to low-rank matrix completion and ReLU neural network regression and classification show that the resulting bounds are analytically tractable and substantially tighter than classical complexity-based bounds. Our results highlight the potential of PAC-Bayes analysis for precise finite-sample generalization guarantees in modern overparameterized and singular models.

Zhiyuan Fan, Tinghao Yu, Yuanjun Cai et al.

Terminal agents have demonstrated strong potential for autonomous command-line execution, yet their training remains constrained by the scarcity of high-quality and diverse execution trajectories. Existing approaches mitigate this bottleneck by synthesizing large-scale terminal task instances for trajectory sampling. However, they primarily focus on scaling the number of tasks while providing limited control over the diversity of execution trajectories that agents actually experience during training. In this paper, we present SkillSynth, an automated framework for terminal task synthesis built on a scenario-mediated skill graph. SkillSynth first constructs a large-scale skill graph, where scenarios serve as intermediate transition nodes that connect diverse command-line skills. It then samples paths from this graph as abstractions of real-world workflows, and uses a multi-agent harness to instantiate them into executable task instances. By grounding task synthesis in graph-sampled workflow paths, SkillSynth explicitly controls the diversity of minimal execution trajectories required to solve the synthesized tasks. Experiments on Terminal-Bench demonstrate the effectiveness of SkillSynth. Moreover, task instances synthesized by SkillSynth have been adopted to train Hy3 Preview, contributing to its enhanced agentic capabilities in terminal-based settings.

Yi Zhang, Linjun Huang, Yun Yang et al.

Conditional mean independence (CMI) testing is crucial for statistical tasks including model determination and variable importance evaluation. In this work, we introduce a novel population CMI measure and a bootstrap-based testing procedure that utilizes deep generative neural networks to estimate the conditional mean functions involved in the population measure. The test statistic is thoughtfully constructed to ensure that even slowly decaying nonparametric estimation errors do not affect the asymptotic accuracy of the test. Our approach demonstrates strong empirical performance in scenarios with high-dimensional covariates and response variable, can handle multivariate responses, and maintains nontrivial power against local alternatives outside an $n^{-1/2}$ neighborhood of the null hypothesis. We also use numerical simulations and real-world imaging data applications to highlight the efficacy and versatility of our testing procedure.

Quanjun Zhang, Chunrong Fang, Haichuan Hu et al.

Automated program repair (APR) attempts to generate correct patches and has drawn wide attention from both academia and industry in the past decades. However, APR is continuously struggling with the patch overfitting issue due to the weak test suites. Thus, to address the overfitting problem, the community has proposed an increasing number of approaches to predict patch correctness (APCA approaches). Among them, locally deep learning approaches aimed at automatically match designs has been emerging strongly. Such approaches typically encode input code snippets into well-designed representations and build a binary model for correctness prediction. Despite being fundamental in reason about patch correctness, code representation has not been systematically investigated. To bridge this gap, we perform the first extensive study to evaluate the performance of different code representations on predicting patch correctness from more than 500 trained APCA models. The experimental results on 15 benchmarks with four categories and 11 classifiers show that the graph-based code representation which is ill-explored in the literature, consistently outperforms other representations, e.g., an average accuracy of 82.6% for CPG across three GNN models. Moreover, we demonstrate that such representations can achieve comparable or better performance for three different previous APCA approaches, e.g., filtering out 87.09% overfitting patches by TREETRAIN with AST. We further find that integrating sequence-based representation into heuristic-based representation is able to yield an average improvement of 13.5% on five metrics. Overall, our study highlights the potential and challenges of utilizing code representation to reason about patch correctness, thus increasing the usability of off-the-shelf APR tools and reducing the manual debugging effort of developers in practice.

Weiming Zhao, Xulong Wang, Jun Qi et al.

Severity assessment of Parkinson's disease (PD) using wearable sensors offers an effective, objective basis for clinical management. However, general-purpose time series models often lack pathological specificity in feature extraction, making it difficult to capture subtle signals highly correlated with PD.Furthermore, the temporal sparsity of PD symptoms causes key diagnostic features to be easily "diluted" by traditional aggregation methods, further complicating assessment. To address these issues, we propose the Multi-scale Frequency-Aware Adversarial Multi-Instance Network (MFAM). This model enhances feature specificity through a frequency decomposition module guided by medical prior knowledge. Furthermore, by introducing an attention-based multi-instance learning (MIL) framework, the model can adaptively focus on the most diagnostically valuable sparse segments.We comprehensively validated MFAM on both the public PADS dataset for PD versus differential diagnosis (DD) binary classification and a private dataset for four-class severity assessment. Experimental results demonstrate that MFAM outperforms general-purpose time series models in handling complex clinical time series with specificity, providing a promising solution for automated assessment of PD severity.

Ziteng Wei, Qiang He, Bing Li et al.

Vision Transformers (ViTs) excel in computer vision tasks but lack flexibility for edge devices' diverse needs. A vital issue is that ViTs pre-trained to cover a broad range of tasks are \textit{over-qualified} for edge devices that usually demand only part of a ViT's knowledge for specific tasks. Their task-specific accuracy on these edge devices is suboptimal. We discovered that small ViTs that focus on device-specific tasks can improve model accuracy and in the meantime, accelerate model inference. This paper presents NuWa, an approach that derives small ViTs from the base ViT for edge devices with specific task requirements. NuWa can transfer task-specific knowledge extracted from the base ViT into small ViTs that fully leverage constrained resources on edge devices to maximize model accuracy with inference latency assurance. Experiments with three base ViTs on three public datasets demonstrate that compared with state-of-the-art solutions, NuWa improves model accuracy by up to $\text{11.83}\%$ and accelerates model inference by 1.29$\times$ - 2.79$\times$. Code for reproduction is available at https://anonymous.4open.science/r/Task_Specific-3A5E.

Ziming Zhao, Zhenwei Wang, Tiehua Zhang et al.

In recent years, the widespread adoption of distributed microservice architectures within the industry has significantly increased the demand for enhanced system availability and robustness. Due to the complex service invocation paths and dependencies in enterprise-level microservice systems, it is challenging to locate the anomalies promptly during service invocations, thus causing intractable issues for normal system operations and maintenance. In this paper, we propose a Causal Heterogeneous grAph baSed framEwork for root cause analysis, namely CHASE, for microservice systems with multimodal data, including traces, logs, and system monitoring metrics. Specifically, related information is encoded into representative embeddings and further modeled by a multimodal invocation graph. Following that, anomaly detection is performed on each instance node with attentive heterogeneous message passing from its adjacent metric and log nodes. Finally, CHASE learns from the constructed hypergraph with hyperedges representing the flow of causality and performs root cause localization. We evaluate the proposed framework on two public microservice datasets with distinct attributes and compare with the state-of-the-art methods. The results show that CHASE achieves the average performance gain up to 36.2%(A@1) and 29.4%(Percentage@1), respectively to its best counterpart.

Yudi Li, Min Tang, Yun Yang et al.

We present a novel learning method to predict the cloth deformation for skeleton-based characters with a two-stream network. The characters processed in our approach are not limited to humans, and can be other skeletal-based representations of non-human targets such as fish or pets. We use a novel network architecture which consists of skeleton-based and mesh-based residual networks to learn the coarse and wrinkle features as the overall residual from the template cloth mesh. Our network is used to predict the deformation for loose or tight-fitting clothing or dresses. We ensure that the memory footprint of our network is low, and thereby result in reduced storage and computational requirements. In practice, our prediction for a single cloth mesh for the skeleton-based character takes about 7 milliseconds on an NVIDIA GeForce RTX 3090 GPU. Compared with prior methods, our network can generate fine deformation results with details and wrinkles.

Yubo Zhuang, Xiaohui Chen, Yun Yang et al.

$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Recently, semidefinite programming (SDP) relaxations have been proposed for solving the $K$-means optimization problem, which enjoy strong statistical optimality guarantees. However, the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. In contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm widely used by machine learning practitioners, but it lacks a solid statistical underpinning and theoretical guarantees. In this paper, we consider an NMF-like algorithm that solves a nonnegative low-rank restriction of the SDP-relaxed $K$-means formulation using a nonconvex Burer--Monteiro factorization approach. The resulting algorithm is as simple and scalable as state-of-the-art NMF algorithms while also enjoying the same strong statistical optimality guarantees as the SDP. In our experiments, we observe that our algorithm achieves significantly smaller mis-clustering errors compared to the existing state-of-the-art while maintaining scalability.

Yubo Zhuang, Xiaohui Chen, Yun Yang

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large (or even moderate) datasets. In this paper, we introduce a linear time complexity algorithm for approximating an SDP relaxed $K$-means clustering. The proposed sketch-and-lift (SL) approach solves an SDP on a subsampled dataset and then propagates the solution to all data points by a nearest-centroid rounding procedure. It is shown that the SL approach enjoys a similar exact recovery threshold as the $K$-means SDP on the full dataset, which is known to be information-theoretically tight under the Gaussian mixture model. The SL method can be made adaptive with enhanced theoretic properties when the cluster sizes are unbalanced. Our simulation experiments demonstrate that the statistical accuracy of the proposed method outperforms state-of-the-art fast clustering algorithms without sacrificing too much computational efficiency, and is comparable to the original $K$-means SDP with substantially reduced runtime.

Yudi Li, Min Tang, Yun Yang et al.

We present a novel mesh-based learning approach (N-Cloth) for plausible 3D cloth deformation prediction. Our approach is general and can handle cloth or obstacles represented by triangle meshes with arbitrary topologies. We use graph convolution to transform the cloth and object meshes into a latent space to reduce the non-linearity in the mesh space. Our network can predict the target 3D cloth mesh deformation based on the initial state of the cloth mesh template and the target obstacle mesh. Our approach can handle complex cloth meshes with up to 100K triangles and scenes with various objects corresponding to SMPL humans, non-SMPL humans or rigid bodies. In practice, our approach can be used to generate plausible cloth simulation at 30-45 fps on an NVIDIA GeForce RTX 3090 GPU. We highlight its benefits over prior learning-based methods and physically-based cloth simulators.

Yifan Chen, Qi Zeng, Dilek Hakkani-Tur et al.

Transformer-based models are not efficient in processing long sequences due to the quadratic space and time complexity of the self-attention modules. To address this limitation, Linformer and Informer are proposed to reduce the quadratic complexity to linear (modulo logarithmic factors) via low-dimensional projection and row selection respectively. These two models are intrinsically connected, and to understand their connection, we introduce a theoretical framework of matrix sketching. Based on the theoretical analysis, we propose Skeinformer to accelerate self-attention and further improve the accuracy of matrix approximation to self-attention with three carefully designed components: column sampling, adaptive row normalization and pilot sampling reutilization. Experiments on the Long Range Arena (LRA) benchmark demonstrate that our methods outperform alternatives with a consistently smaller time/space footprint.

Yifan Chen, Qi Zeng, Heng Ji et al.

Transformers are expensive to train due to the quadratic time and space complexity in the self-attention mechanism. On the other hand, although kernel machines suffer from the same computation bottleneck in pairwise dot products, several approximation schemes have been successfully incorporated to considerably reduce their computational cost without sacrificing too much accuracy. In this work, we leverage the computation methods for kernel machines to alleviate the high computational cost and introduce Skyformer, which replaces the softmax structure with a Gaussian kernel to stabilize the model training and adapts the Nyström method to a non-positive semidefinite matrix to accelerate the computation. We further conduct theoretical analysis by showing that the matrix approximation error of our proposed method is small in the spectral norm. Experiments on Long Range Arena benchmark show that the proposed method is sufficient in getting comparable or even better performance than the full self-attention while requiring fewer computation resources.

Yinyin Chen, Shishuang He, Yun Yang et al.

Topic models provide a useful text-mining tool for learning, extracting, and discovering latent structures in large text corpora. Although a plethora of methods have been proposed for topic modeling, lacking in the literature is a formal theoretical investigation of the statistical identifiability and accuracy of latent topic estimation. In this paper, we propose a maximum likelihood estimator (MLE) of latent topics based on a specific integrated likelihood that is naturally connected to the concept, in computational geometry, of volume minimization. Our theory introduces a new set of geometric conditions for topic model identifiability, conditions that are weaker than conventional separability conditions, which typically rely on the existence of pure topic documents or of anchor words. Weaker conditions allow a wider and thus potentially more fruitful investigation. We conduct finite-sample error analysis for the proposed estimator and discuss connections between our results and those of previous investigations. We conclude with empirical studies employing both simulated and real datasets.

Ke Li, Yun Yang, Naveen N. Narisetty

In this paper, we consider the multi-armed bandit problem with high-dimensional features. First, we prove a minimax lower bound, $\mathcal{O}\big((\log d)^{\frac{α+1}{2}}T^{\frac{1-α}{2}}+\log T\big)$, for the cumulative regret, in terms of horizon $T$, dimension $d$ and a margin parameter $α\in[0,1]$, which controls the separation between the optimal and the sub-optimal arms. This new lower bound unifies existing regret bound results that have different dependencies on T due to the use of different values of margin parameter $α$ explicitly implied by their assumptions. Second, we propose a simple and computationally efficient algorithm inspired by the general Upper Confidence Bound (UCB) strategy that achieves a regret upper bound matching the lower bound. The proposed algorithm uses a properly centered $\ell_1$-ball as the confidence set in contrast to the commonly used ellipsoid confidence set. In addition, the algorithm does not require any forced sampling step and is thereby adaptive to the practically unknown margin parameter. Simulations and a real data analysis are conducted to compare the proposed method with existing ones in the literature.

Ranjie Duan, Yuefeng Chen, Dantong Niu et al.

Human can easily recognize visual objects with lost information: even losing most details with only contour reserved, e.g. cartoon. However, in terms of visual perception of Deep Neural Networks (DNNs), the ability for recognizing abstract objects (visual objects with lost information) is still a challenge. In this work, we investigate this issue from an adversarial viewpoint: will the performance of DNNs decrease even for the images only losing a little information? Towards this end, we propose a novel adversarial attack, named \textit{AdvDrop}, which crafts adversarial examples by dropping existing information of images. Previously, most adversarial attacks add extra disturbing information on clean images explicitly. Opposite to previous works, our proposed work explores the adversarial robustness of DNN models in a novel perspective by dropping imperceptible details to craft adversarial examples. We demonstrate the effectiveness of \textit{AdvDrop} by extensive experiments, and show that this new type of adversarial examples is more difficult to be defended by current defense systems.

Dengcheng Yan, Wenxin Xie, Yiwen Zhang et al.

Network dismantling aims to degrade the connectivity of a network by removing an optimal set of nodes. It has been widely adopted in many real-world applications such as epidemic control and rumor containment. However, conventional methods usually focus on simple network modeling with only pairwise interactions, while group-wise interactions modeled by hypernetwork are ubiquitous and critical. In this work, we formulate the hypernetwork dismantling problem as a node sequence decision problem and propose a deep reinforcement learning (DRL)-based hypernetwork dismantling framework. Besides, we design a novel inductive hypernetwork embedding method to ensure the transferability to various real-world hypernetworks. Our framework first generates small-scale synthetic hypernetworks and embeds the nodes and hypernetworks into a low dimensional vector space to represent the action and state space in DRL, respectively. Then trial-and-error dismantling tasks are conducted by an agent on these synthetic hypernetworks, and the dismantling strategy is continuously optimized. Finally, the well-optimized strategy is applied to real-world hypernetwork dismantling tasks. Experimental results on five real-world hypernetworks demonstrate the effectiveness of our proposed framework.

Ranjie Duan, Xiaofeng Mao, A. K. Qin et al.

Though it is well known that the performance of deep neural networks (DNNs) degrades under certain light conditions, there exists no study on the threats of light beams emitted from some physical source as adversarial attacker on DNNs in a real-world scenario. In this work, we show by simply using a laser beam that DNNs are easily fooled. To this end, we propose a novel attack method called Adversarial Laser Beam ($AdvLB$), which enables manipulation of laser beam's physical parameters to perform adversarial attack. Experiments demonstrate the effectiveness of our proposed approach in both digital- and physical-settings. We further empirically analyze the evaluation results and reveal that the proposed laser beam attack may lead to some interesting prediction errors of the state-of-the-art DNNs. We envisage that the proposed $AdvLB$ method enriches the current family of adversarial attacks and builds the foundation for future robustness studies for light.

Yifan Chen, Yun Yang

Nyström approximation is a fast randomized method that rapidly solves kernel ridge regression (KRR) problems through sub-sampling the n-by-n empirical kernel matrix appearing in the objective function. However, the performance of such a sub-sampling method heavily relies on correctly estimating the statistical leverage scores for forming the sampling distribution, which can be as costly as solving the original KRR. In this work, we propose a linear time (modulo poly-log terms) algorithm to accurately approximate the statistical leverage scores in the stationary-kernel-based KRR with theoretical guarantees. Particularly, by analyzing the first-order condition of the KRR objective, we derive an analytic formula, which depends on both the input distribution and the spectral density of stationary kernels, for capturing the non-uniformity of the statistical leverage scores. Numerical experiments demonstrate that with the same prediction accuracy our method is orders of magnitude more efficient than existing methods in selecting the representative sub-samples in the Nyström approximation.

Yifan Chen, Yun Yang

With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However, computing optimal sampling probabilities is often itself expensive, and in practice one typically resorts to suboptimal schemes. This generally leads to increased time and space costs, as more subsamples are required and the resulting projection matrices become larger, thereby making the inference procedure more computationally demanding. In this paper, we extend the framework of sampling-based random projection and propose a new projection method, \emph{accumulative sub-sampling}. By carefully accumulating multiple such projections, accumulative sub-sampling improves statistical efficiency while controlling the effective matrix size throughout the statistical computation. On the theoretical side, we quantify how the quality of the subsampling scheme affects the error in approximating matrix products and positive semidefinite matrices, and show how the proposed accumulation strategy mitigates this effect. Moreover, we apply our method to statistical models involving intensive matrix operations, such as eigendecomposition in spectral clustering and matrix inversion in kernel ridge regression, and demonstrate that reducing the effective matrix size leads to substantial computational savings. Numerical experiments across a range of problems further show that our approach consistently improves computational efficiency compared to existing random projection baselines under suboptimal sampling schemes.

Cheng Xie, Ting Zeng, Hongxin Xiang et al.

New categories can be discovered by transforming semantic features into synthesized visual features without corresponding training samples in zero-shot image classification. Although significant progress has been made in generating high-quality synthesized visual features using generative adversarial networks, guaranteeing semantic consistency between the semantic features and visual features remains very challenging. In this paper, we propose a novel zero-shot learning approach, GAN-CST, based on class knowledge to visual feature learning to tackle the problem. The approach consists of three parts, class knowledge overlay, semi-supervised learning and triplet loss. It applies class knowledge overlay (CKO) to obtain knowledge not only from the corresponding class but also from other classes that have the knowledge overlay. It ensures that the knowledge-to-visual learning process has adequate information to generate synthesized visual features. The approach also applies a semi-supervised learning process to re-train knowledge-to-visual model. It contributes to reinforcing synthesized visual features generation as well as new category prediction. We tabulate results on a number of benchmark datasets demonstrating that the proposed model delivers superior performance over state-of-the-art approaches.

Hongxin Xiang, Cheng Xie, Ting Zeng et al.

Suffering from the semantic insufficiency and domain-shift problems, most of existing state-of-the-art methods fail to achieve satisfactory results for Zero-Shot Learning (ZSL). In order to alleviate these problems, we propose a novel generative ZSL method to learn more generalized features from multi-knowledge with continuously generated new semantics in semantic-to-visual embedding. In our approach, the proposed Multi-Knowledge Fusion Network (MKFNet) takes different semantic features from multi-knowledge as input, which enables more relevant semantic features to be trained for semantic-to-visual embedding, and finally generates more generalized visual features by adaptively fusing visual features from different knowledge domain. The proposed New Feature Generator (NFG) with adaptive genetic strategy is used to enrich semantic information on the one hand, and on the other hand it greatly improves the intersection of visual feature generated by MKFNet and unseen visual faetures. Empirically, we show that our approach can achieve significantly better performance compared to existing state-of-the-art methods on a large number of benchmarks for several ZSL tasks, including traditional ZSL, generalized ZSL and zero-shot retrieval.

Xuejun Li, Ran Ding, Xiao Liu et al.

Current cloud-based smart systems suffer from weaknesses such as high response latency, limited network bandwidth and the restricted computing power of smart end devices which seriously affect the system's QoS (Quality of Service). Recently, given its advantages of low latency, high bandwidth and location awareness, edge computing has become a promising solution for smart systems. However, the development of edge computing based smart systems is a very challenging job for software developers who do not have the skills for the creation of edge computing environments. The management of edge computing resources and computing tasks is also very challenging. Workflow technology has been widely used in smart systems to automate task and resource management, but there does not yet exist a real-world deployable edge computing based workflow execution engine. To fill this gap, we present EdgeWorkflowReal, an edge computing based workflow execution engine for smart systems. EdgeWorkflowReal supports: 1) automatic creation of a real edge computing environment according to user settings; 2) visualized modelling of edge workflow applications; and 3) automatic deployment, monitoring and performance evaluation of edge workflow applications in a smart system.

Cheng Xie, Hongxin Xiang, Ting Zeng et al.

Although zero-shot learning (ZSL) has an inferential capability of recognizing new classes that have never been seen before, it always faces two fundamental challenges of the cross modality and crossdomain challenges. In order to alleviate these problems, we develop a generative network-based ZSL approach equipped with the proposed Cross Knowledge Learning (CKL) scheme and Taxonomy Regularization (TR). In our approach, the semantic features are taken as inputs, and the output is the synthesized visual features generated from the corresponding semantic features. CKL enables more relevant semantic features to be trained for semantic-to-visual feature embedding in ZSL, while Taxonomy Regularization (TR) significantly improves the intersections with unseen images with more generalized visual features generated from generative network. Extensive experiments on several benchmark datasets (i.e., AwA1, AwA2, CUB, NAB and aPY) show that our approach is superior to these state-of-the-art methods in terms of ZSL image classification and retrieval.

Po Yang, Jun Qi, Xulong Wang et al.

Recent outbreak of COVID-19 has led a rapid global spread around the world. Many countries have implemented timely intensive suppression to minimize the infections, but resulted in high case fatality rate (CFR) due to critical demand of health resources. Other country-based factors such as sociocultural issues, ageing population etc., has also influenced practical effectiveness of taking interventions to improve morality in early phase. To better understand the relationship of these factors across different countries with COVID-19 CFR is of primary importance to prepare for potentially second wave of COVID-19 infections. In the paper, we propose a novel regularized multi-task learning based factor analysis approach for quantifying country-based factors affecting CFR in early phase of COVID-19 epidemic. We formulate the prediction of CFR progression as a ML regression problem with observed CFR and other countries-based factors. In this formulation, all CFR related factors were categorized into 6 sectors with 27 indicators. We proposed a hybrid feature selection method combining filter, wrapper and tree-based models to calibrate initial factors for a preliminary feature interaction. Then we adopted two typical single task model (Ridge and Lasso regression) and one state-of-the-art MTFL method (fused sparse group lasso) in our formulation. The fused sparse group Lasso (FSGL) method allows the simultaneous selection of a common set of country-based factors for multiple time points of COVID-19 epidemic and also enables incorporating temporal smoothness of each factor over the whole early phase period. Finally, we proposed one novel temporal voting feature selection scheme to balance the weight instability of multiple factors in our MTFL model.

Xiangdong Zhang, Tengjun Wang, Yun Yang

Because hyperspectral remote sensing images contain a lot of redundant information and the data structure is highly non-linear, leading to low classification accuracy of traditional machine learning methods. The latest research shows that hyperspectral image classification based on deep convolutional neural network has high accuracy. However, when a small amount of data is used for training, the classification accuracy of deep learning methods is greatly reduced. In order to solve the problem of low classification accuracy of existing algorithms on small samples of hyperspectral images, a multi-scale residual network is proposed. The multi-scale extraction and fusion of spatial and spectral features is realized by adding a branch structure into the residual block and using convolution kernels of different sizes in the branch. The spatial and spectral information contained in hyperspectral images are fully utilized to improve the classification accuracy. In addition, in order to improve the speed and prevent overfitting, the model uses dynamic learning rate, BN and Dropout strategies. The experimental results show that the overall classification accuracy of this method is 99.07% and 99.96% respectively in the data set of Indian Pines and Pavia University, which is better than other algorithms.

Xi Chen, Jason D. Lee, He Li et al.

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine learning problem, principal component analysis (PCA). Despite the massive literature on top eigenvector estimation, much less is presented for the top-$L$-dim ($L>1$) eigenspace estimation, especially in a distributed manner. We propose a novel multi-round algorithm for constructing top-$L$-dim eigenspace for distributed data. Our algorithm takes advantage of shift-and-invert preconditioning and convex optimization. Our estimator is communication-efficient and achieves a fast convergence rate. In contrast to the existing divide-and-conquer algorithm, our approach has no restriction on the number of machines. Theoretically, the traditional Davis-Kahan theorem requires the explicit eigengap assumption to estimate the top-$L$-dim eigenspace. To abandon this eigengap assumption, we consider a new route in our analysis: instead of exactly identifying the top-$L$-dim eigenspace, we show that our estimator is able to cover the targeted top-$L$-dim population eigenspace. Our distributed algorithm can be applied to a wide range of statistical problems based on PCA, such as principal component regression and single index model. Finally, We provide simulation studies to demonstrate the performance of the proposed distributed estimator.

Ranjie Duan, Xingjun Ma, Yisen Wang et al.

Deep neural networks (DNNs) are known to be vulnerable to adversarial examples. Existing works have mostly focused on either digital adversarial examples created via small and imperceptible perturbations, or physical-world adversarial examples created with large and less realistic distortions that are easily identified by human observers. In this paper, we propose a novel approach, called Adversarial Camouflage (\emph{AdvCam}), to craft and camouflage physical-world adversarial examples into natural styles that appear legitimate to human observers. Specifically, \emph{AdvCam} transfers large adversarial perturbations into customized styles, which are then "hidden" on-target object or off-target background. Experimental evaluation shows that, in both digital and physical-world scenarios, adversarial examples crafted by \emph{AdvCam} are well camouflaged and highly stealthy, while remaining effective in fooling state-of-the-art DNN image classifiers. Hence, \emph{AdvCam} is a flexible approach that can help craft stealthy attacks to evaluate the robustness of DNNs. \emph{AdvCam} can also be used to protect private information from being detected by deep learning systems.

Xiaohui Chen, Yun Yang

We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the $K$-means clustering method achieves such sharp threshold for exact recovery without assuming the symmetry of cluster centers.

Wei Han, Yun Yang

We conduct non-asymptotic analysis on the mean-field variational inference for approximating posterior distributions in complex Bayesian models that may involve latent variables. We show that the mean-field approximation to the posterior can be well-approximated relative to the Kullback-Leibler divergence discrepancy measure by a normal distribution whose center is the maximum likelihood estimator (MLE). In particular, our results imply that the center of the mean-field approximation matches the MLE up to higher-order terms and there is essentially no loss of efficiency in using it as a point estimator for the parameter in any regular parametric model with latent variables. We also propose a new class of variational weighted likelihood bootstrap (VWLB) methods for quantifying the uncertainty in the mean-field variational inference. The proposed VWLB can be viewed as a new sampling scheme that produces independent samples for approximating the posterior. Comparing with traditional sampling algorithms such Markov Chain Monte Carlo, VWLB can be implemented in parallel and is free of tuning.

Dongwei Li, Shuliang Wang, Nan Gao et al.

Clustering big data often requires tremendous computational resources where cloud computing is undoubtedly one of the promising solutions. However, the computation cost in the cloud can be unexpectedly high if it cannot be managed properly. The long tail phenomenon has been observed widely in the big data clustering area, which indicates that the majority of time is often consumed in the middle to late stages in the clustering process. In this research, we try to cut the unnecessary long tail in the clustering process to achieve a sufficiently satisfactory accuracy at the lowest possible computation cost. A novel approach is proposed to achieve cost-effective big data clustering in the cloud. By training the regression model with the sampling data, we can make widely used k-means and EM (Expectation-Maximization) algorithms stop automatically at an early point when the desired accuracy is obtained. Experiments are conducted on four popular data sets and the results demonstrate that both k-means and EM algorithms can achieve high cost-effectiveness in the cloud with our proposed approach. For example, in the case studies with the much more efficient k-means algorithm, we find that achieving a 99% accuracy needs only 47.71%-71.14% of the computation cost required for achieving a 100% accuracy while the less efficient EM algorithm needs 16.69%-32.04% of the computation cost. To put that into perspective, in the United States land use classification example, our approach can save up to $94,687.49 for the government in each use.

Peng Zhao, Yun Yang, Qiao-Chu He

Many statistical estimators for high-dimensional linear regression are M-estimators, formed through minimizing a data-dependent square loss function plus a regularizer. This work considers a new class of estimators implicitly defined through a discretized gradient dynamic system under overparameterization. We show that under suitable restricted isometry conditions, overparameterization leads to implicit regularization: if we directly apply gradient descent to the residual sum of squares with sufficiently small initial values, then under some proper early stopping rule, the iterates converge to a nearly sparse rate-optimal solution that improves over explicitly regularized approaches. In particular, the resulting estimator does not suffer from extra bias due to explicit penalties, and can achieve the parametric root-n rate when the signal-to-noise ratio is sufficiently high. We also perform simulations to compare our methods with high dimensional linear regression with explicit regularization. Our results illustrate the advantages of using implicit regularization via gradient descent after overparameterization in sparse vector estimation.

Xiaohui Chen, Yun Yang

We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity graph with vertices as data points randomly sampled on the manifolds and edges as similarities given by a kernel that captures the local geometry of manifolds. The diffusion $K$-means is a multi-scale clustering tool that is suitable for data with non-linear and non-Euclidean geometric features in mixed dimensions. Given the number of clusters, we propose a polynomial-time convex relaxation algorithm via the semidefinite programming (SDP) to solve the diffusion $K$-means. In addition, we also propose a nuclear norm regularized SDP that is adaptive to the number of clusters. In both cases, we show that exact recovery of the SDPs for diffusion $K$-means can be achieved under suitable between-cluster separability and within-cluster connectedness of the submanifolds, which together quantify the hardness of the manifold clustering problem. We further propose the {\it localized diffusion $K$-means} by using the local adaptive bandwidth estimated from the nearest neighbors. We show that exact recovery of the localized diffusion $K$-means is fully adaptive to the local probability density and geometric structures of the underlying submanifolds.

Debdeep Pati, Anirban Bhattacharya, Yun Yang

The article addresses a long-standing open problem on the justification of using variational Bayes methods for parameter estimation. We provide general conditions for obtaining optimal risk bounds for point estimates acquired from mean-field variational Bayesian inference. The conditions pertain to the existence of certain test functions for the distance metric on the parameter space and minimal assumptions on the prior. A general recipe for verification of the conditions is outlined which is broadly applicable to existing Bayesian models with or without latent variables. As illustrations, specific applications to Latent Dirichlet Allocation and Gaussian mixture models are discussed.

Yun Yang, Debdeep Pati, Anirban Bhattacharya

We propose a family of variational approximations to Bayesian posterior distributions, called $α$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $α$-VB with $α=1$. When $α\in(0,1]$, a novel class of variational inequalities are developed for linking the Bayes risk under the variational approximation to the objective function in the variational optimization problem, implying that maximizing the evidence lower bound in variational inference has the effect of minimizing the Bayes risk within the variational density family. Operating in a frequentist setup, the variational inequalities imply that point estimates constructed from the $α$-VB procedure converge at an optimal rate to the true parameter in a wide range of problems. We illustrate our general theory with a number of examples, including the mean-field variational approximation to (low)-high-dimensional Bayesian linear regression with spike and slab priors, mixture of Gaussian models, latent Dirichlet allocation, and (mixture of) Gaussian variational approximation in regular parametric models.