Xiang Li

CV
h-index38
23papers
428citations
Novelty58%
AI Score47

23 Papers

8.3SDApr 12, 2022Code
Speech Emotion Recognition with Global-Aware Fusion on Multi-scale Feature Representation

Wenjing Zhu, Xiang Li

Speech Emotion Recognition (SER) is a fundamental task to predict the emotion label from speech data. Recent works mostly focus on using convolutional neural networks~(CNNs) to learn local attention map on fixed-scale feature representation by viewing time-varied spectral features as images. However, rich emotional feature at different scales and important global information are not able to be well captured due to the limits of existing CNNs for SER. In this paper, we propose a novel GLobal-Aware Multi-scale (GLAM) neural network (The code is available at https://github.com/lixiangucas01/GLAM) to learn multi-scale feature representation with global-aware fusion module to attend emotional information. Specifically, GLAM iteratively utilizes multiple convolutional kernels with different scales to learn multiple feature representation. Then, instead of using attention-based methods, a simple but effective global-aware fusion module is applied to grab most important emotional information globally. Experiments on the benchmark corpus IEMOCAP over four emotions demonstrates the superiority of our proposed model with 2.5% to 4.5% improvements on four common metrics compared to previous state-of-the-art approaches.

17.7OCJun 1, 2022
Nest Your Adaptive Algorithm for Parameter-Agnostic Nonconvex Minimax Optimization

Junchi Yang, Xiang Li, Niao He

Adaptive algorithms like AdaGrad and AMSGrad are successful in nonconvex optimization owing to their parameter-agnostic ability -- requiring no a priori knowledge about problem-specific parameters nor tuning of learning rates. However, when it comes to nonconvex minimax optimization, direct extensions of such adaptive optimizers without proper time-scale separation may fail to work in practice. We provide such an example proving that the simple combination of Gradient Descent Ascent (GDA) with adaptive stepsizes can diverge if the primal-dual stepsize ratio is not carefully chosen; hence, a fortiori, such adaptive extensions are not parameter-agnostic. To address the issue, we formally introduce a Nested Adaptive framework, NeAda for short, that carries an inner loop for adaptively maximizing the dual variable with controllable stopping criteria and an outer loop for adaptively minimizing the primal variable. Such mechanism can be equipped with off-the-shelf adaptive optimizers and automatically balance the progress in the primal and dual variables. Theoretically, for nonconvex-strongly-concave minimax problems, we show that NeAda can achieve the near-optimal $\tilde{O}(ε^{-2})$ and $\tilde{O}(ε^{-4})$ gradient complexities respectively in the deterministic and stochastic settings, without prior information on the problem's smoothness and strong concavity parameters. To the best of our knowledge, this is the first algorithm that simultaneously achieves near-optimal convergence rates and parameter-agnostic adaptation in the nonconvex minimax setting. Numerically, we further illustrate the robustness of the NeAda family with experiments on simple test functions and a real-world application.

11.2OCOct 31, 2022Code
TiAda: A Time-scale Adaptive Algorithm for Nonconvex Minimax Optimization

Xiang Li, Junchi Yang, Niao He

Adaptive gradient methods have shown their ability to adjust the stepsizes on the fly in a parameter-agnostic manner, and empirically achieve faster convergence for solving minimization problems. When it comes to nonconvex minimax optimization, however, current convergence analyses of gradient descent ascent (GDA) combined with adaptive stepsizes require careful tuning of hyper-parameters and the knowledge of problem-dependent parameters. Such a discrepancy arises from the primal-dual nature of minimax problems and the necessity of delicate time-scale separation between the primal and dual updates in attaining convergence. In this work, we propose a single-loop adaptive GDA algorithm called TiAda for nonconvex minimax optimization that automatically adapts to the time-scale separation. Our algorithm is fully parameter-agnostic and can achieve near-optimal complexities simultaneously in deterministic and stochastic settings of nonconvex-strongly-concave minimax problems. The effectiveness of the proposed method is further justified numerically for a number of machine learning applications.

12.4MLDec 19, 2022
Near-optimal Policy Identification in Active Reinforcement Learning

Xiang Li, Viraj Mehta, Johannes Kirschner et al.

Many real-world reinforcement learning tasks require control of complex dynamical systems that involve both costly data acquisition processes and large state spaces. In cases where the transition dynamics can be readily evaluated at specified states (e.g., via a simulator), agents can operate in what is often referred to as planning with a \emph{generative model}. We propose the AE-LSVI algorithm for best-policy identification, a novel variant of the kernelized least-squares value iteration (LSVI) algorithm that combines optimism with pessimism for active exploration (AE). AE-LSVI provably identifies a near-optimal policy \emph{uniformly} over an entire state space and achieves polynomial sample complexity guarantees that are independent of the number of states. When specialized to the recently introduced offline contextual Bayesian optimization setting, our algorithm achieves improved sample complexity bounds. Experimentally, we demonstrate that AE-LSVI outperforms other RL algorithms in a variety of environments when robustness to the initial state is required.

11.4CRNov 29, 2023Code
VA3: Virtually Assured Amplification Attack on Probabilistic Copyright Protection for Text-to-Image Generative Models

Xiang Li, Qianli Shen, Kenji Kawaguchi

The booming use of text-to-image generative models has raised concerns about their high risk of producing copyright-infringing content. While probabilistic copyright protection methods provide a probabilistic guarantee against such infringement, in this paper, we introduce Virtually Assured Amplification Attack (VA3), a novel online attack framework that exposes the vulnerabilities of these protection mechanisms. The proposed framework significantly amplifies the probability of generating infringing content on the sustained interactions with generative models and a non-trivial lower-bound on the success probability of each engagement. Our theoretical and experimental results demonstrate the effectiveness of our approach under various scenarios. These findings highlight the potential risk of implementing probabilistic copyright protection in practical applications of text-to-image generative models. Code is available at https://github.com/South7X/VA3.

2.6LGJul 14, 2024Code
Improving Graph Out-of-distribution Generalization Beyond Causality

Can Xu, Yao Cheng, Jianxiang Yu et al.

Existing methods for graph out-of-distribution (OOD) generalization primarily rely on empirical studies on synthetic datasets. Such approaches tend to overemphasize the causal relationships between invariant sub-graphs and labels, thereby neglecting the non-negligible role of environment in real-world scenarios. In contrast to previous studies that impose rigid independence assumptions on environments and invariant sub-graphs, this paper presents the theorems of environment-label dependency and mutable rationale invariance, where the former characterizes the usefulness of environments in determining graph labels while the latter refers to the mutable importance of graph rationales. Based on analytic investigations, a novel variational inference based method named ``Probability Dependency on Environments and Rationales for OOD Graphs on Real-world Data'' (DEROG) is introduced. To alleviate the adverse effect of unknown prior knowledge on environments and rationales, DEROG utilizes generalized Bayesian inference. Further, DEROG employs an EM-based algorithm for optimization. Finally, extensive experiments on real-world datasets under different distribution shifts are conducted to show the superiority of DEROG. Our code is publicly available at https://github.com/LEOXC1571/DEROG.

17.8CVMay 15, 2024Code
SARATR-X: Toward Building A Foundation Model for SAR Target Recognition

Weijie Li, Wei Yang, Yuenan Hou et al.

Despite the remarkable progress in synthetic aperture radar automatic target recognition (SAR ATR), recent efforts have concentrated on detecting and classifying a specific category, e.g., vehicles, ships, airplanes, or buildings. One of the fundamental limitations of the top-performing SAR ATR methods is that the learning paradigm is supervised, task-specific, limited-category, closed-world learning, which depends on massive amounts of accurately annotated samples that are expensively labeled by expert SAR analysts and have limited generalization capability and scalability. In this work, we make the first attempt towards building a foundation model for SAR ATR, termed SARATR-X. SARATR-X learns generalizable representations via self-supervised learning (SSL) and provides a cornerstone for label-efficient model adaptation to generic SAR target detection and classification tasks. Specifically, SARATR-X is trained on 0.18 M unlabelled SAR target samples, which are curated by combining contemporary benchmarks and constitute the largest publicly available dataset till now. Considering the characteristics of SAR images, a backbone tailored for SAR ATR is carefully designed, and a two-step SSL method endowed with multi-scale gradient features was applied to ensure the feature diversity and model scalability of SARATR-X. The capabilities of SARATR-X are evaluated on classification under few-shot and robustness settings and detection across various categories and scenes, and impressive performance is achieved, often competitive with or even superior to prior fully supervised, semi-supervised, or self-supervised algorithms. Our SARATR-X and the curated dataset are released at https://github.com/waterdisappear/SARATR-X to foster research into foundation models for SAR image interpretation.

3.8LGNov 14, 2023
Variational Graph Autoencoder for Heterogeneous Information Networks with Missing and Inaccurate Attributes

Yige Zhao, Jianxiang Yu, Yao Cheng et al.

Heterogeneous Information Networks (HINs), which consist of various types of nodes and edges, have recently demonstrated excellent performance in graph mining. However, most existing heterogeneous graph neural networks (HGNNs) ignore the problems of missing attributes, inaccurate attributes and scarce labels for nodes, which limits their expressiveness. In this paper, we propose a generative self-supervised model GraMI to address these issues simultaneously. Specifically, GraMI first initializes all the nodes in the graph with a low-dimensional representation matrix. After that, based on the variational graph autoencoder framework, GraMI learns both node-level and attribute-level embeddings in the encoder, which can provide fine-grained semantic information to construct node attributes. In the decoder, GraMI reconstructs both links and attributes. Instead of directly reconstructing raw features for attributed nodes, GraMI generates the initial low-dimensional representation matrix for all the nodes, based on which raw features of attributed nodes are further reconstructed to leverage accurate attributes. In this way, GraMI can not only complete informative features for non-attributed nodes, but rectify inaccurate ones for attributed nodes. Finally, we conduct extensive experiments to show the superiority of GraMI in tackling HINs with missing and inaccurate attributes.

2.6LGJul 16, 2024
Boosting drug-disease association prediction for drug repositioning via dual-feature extraction and cross-dual-domain decoding

Enqiang Zhu, Xiang Li, Chanjuan Liu et al.

The extraction of biomedical data has significant academic and practical value in contemporary biomedical sciences. In recent years, drug repositioning, a cost-effective strategy for drug development by discovering new indications for approved drugs, has gained increasing attention. However, many existing drug repositioning methods focus on mining information from adjacent nodes in biomedical networks without considering the potential inter-relationships between the feature spaces of drugs and diseases. This can lead to inaccurate encoding, resulting in biased mined drug-disease association information. To address this limitation, we propose a new model called Dual-Feature Drug Repurposing Neural Network (DFDRNN). DFDRNN allows the mining of two features (similarity and association) from the drug-disease biomedical networks to encode drugs and diseases. A self-attention mechanism is utilized to extract neighbor feature information. It incorporates two dual-feature extraction modules: the single-domain dual-feature extraction (SDDFE) module for extracting features within a single domain (drugs or diseases) and the cross-domain dual-feature extraction (CDDFE) module for extracting features across domains. By utilizing these modules, we ensure more appropriate encoding of drugs and diseases. A cross-dual-domain decoder is also designed to predict drug-disease associations in both domains. Our proposed DFDRNN model outperforms six state-of-the-art methods on four benchmark datasets, achieving an average AUROC of 0.946 and an average AUPR of 0.597. Case studies on two diseases show that the proposed DFDRNN model can be applied in real-world scenarios, demonstrating its significant potential in drug repositioning.

16.4CVDec 6, 2023Code
Diffusion Illusions: Hiding Images in Plain Sight

Ryan Burgert, Xiang Li, Abe Leite et al.

We explore the problem of computationally generating special `prime' images that produce optical illusions when physically arranged and viewed in a certain way. First, we propose a formal definition for this problem. Next, we introduce Diffusion Illusions, the first comprehensive pipeline designed to automatically generate a wide range of these illusions. Specifically, we both adapt the existing `score distillation loss' and propose a new `dream target loss' to optimize a group of differentially parametrized prime images, using a frozen text-to-image diffusion model. We study three types of illusions, each where the prime images are arranged in different ways and optimized using the aforementioned losses such that images derived from them align with user-chosen text prompts or images. We conduct comprehensive experiments on these illusions and verify the effectiveness of our proposed method qualitatively and quantitatively. Additionally, we showcase the successful physical fabrication of our illusions -- as they are all designed to work in the real world. Our code and examples are publicly available at our interactive project website: https://diffusionillusions.com

2.0LGNov 3, 2023
Resist Label Noise with PGM for Graph Neural Networks

Qingqing Ge, Jianxiang Yu, Zeyuan Zhao et al.

While robust graph neural networks (GNNs) have been widely studied for graph perturbation and attack, those for label noise have received significantly less attention. Most existing methods heavily rely on the label smoothness assumption to correct noisy labels, which adversely affects their performance on heterophilous graphs. Further, they generally perform poorly in high noise-rate scenarios. To address these problems, in this paper, we propose a novel probabilistic graphical model (PGM) based framework LNP. Given a noisy label set and a clean label set, our goal is to maximize the likelihood of labels in the clean set. We first present LNP-v1, which generates clean labels based on graphs only in the Bayesian network. To further leverage the information of clean labels in the noisy label set, we put forward LNP-v2, which incorporates the noisy label set into the Bayesian network to generate clean labels. The generative process can then be used to predict labels for unlabeled nodes. We conduct extensive experiments to show the robustness of LNP on varying noise types and rates, and also on graphs with different heterophilies. In particular, we show that LNP can lead to inspiring performance in high noise-rate situations.

6.2CVAug 19, 2025Code
Distilled-3DGS:Distilled 3D Gaussian Splatting

Lintao Xiang, Xinkai Chen, Jianhuang Lai et al.

3D Gaussian Splatting (3DGS) has exhibited remarkable efficacy in novel view synthesis (NVS). However, it suffers from a significant drawback: achieving high-fidelity rendering typically necessitates a large number of 3D Gaussians, resulting in substantial memory consumption and storage requirements. To address this challenge, we propose the first knowledge distillation framework for 3DGS, featuring various teacher models, including vanilla 3DGS, noise-augmented variants, and dropout-regularized versions. The outputs of these teachers are aggregated to guide the optimization of a lightweight student model. To distill the hidden geometric structure, we propose a structural similarity loss to boost the consistency of spatial geometric distributions between the student and teacher model. Through comprehensive quantitative and qualitative evaluations across diverse datasets, the proposed Distilled-3DGS, a simple yet effective framework without bells and whistles, achieves promising rendering results in both rendering quality and storage efficiency compared to state-of-the-art methods. Project page: https://distilled3dgs.github.io . Code: https://github.com/lt-xiang/Distilled-3DGS .

17.5IVJun 13, 2024Code
Blind Super-Resolution via Meta-learning and Markov Chain Monte Carlo Simulation

Jingyuan Xia, Zhixiong Yang, Shengxi Li et al.

Learning-based approaches have witnessed great successes in blind single image super-resolution (SISR) tasks, however, handcrafted kernel priors and learning based kernel priors are typically required. In this paper, we propose a Meta-learning and Markov Chain Monte Carlo (MCMC) based SISR approach to learn kernel priors from organized randomness. In concrete, a lightweight network is adopted as kernel generator, and is optimized via learning from the MCMC simulation on random Gaussian distributions. This procedure provides an approximation for the rational blur kernel, and introduces a network-level Langevin dynamics into SISR optimization processes, which contributes to preventing bad local optimal solutions for kernel estimation. Meanwhile, a meta-learning-based alternating optimization procedure is proposed to optimize the kernel generator and image restorer, respectively. In contrast to the conventional alternating minimization strategy, a meta-learning-based framework is applied to learn an adaptive optimization strategy, which is less-greedy and results in better convergence performance. These two procedures are iteratively processed in a plug-and-play fashion, for the first time, realizing a learning-based but plug-and-play blind SISR solution in unsupervised inference. Extensive simulations demonstrate the superior performance and generalization ability of the proposed approach when comparing with state-of-the-arts on synthesis and real-world datasets. The code is available at https://github.com/XYLGroup/MLMC.

12.1CVNov 8, 2021Code
Generative Dynamic Patch Attack

Xiang Li, Shihao Ji

Adversarial patch attack is a family of attack algorithms that perturb a part of image to fool a deep neural network model. Existing patch attacks mostly consider injecting adversarial patches at input-agnostic locations: either a predefined location or a random location. This attack setup may be sufficient for attack but has considerable limitations when using it for adversarial training. Thus, robust models trained with existing patch attacks cannot effectively defend other adversarial attacks. In this paper, we first propose an end-to-end patch attack algorithm, Generative Dynamic Patch Attack (GDPA), which generates both patch pattern and patch location adversarially for each input image. We show that GDPA is a generic attack framework that can produce dynamic/static and visible/invisible patches with a few configuration changes. Secondly, GDPA can be readily integrated for adversarial training to improve model robustness to various adversarial attacks. Extensive experiments on VGGFace, Traffic Sign and ImageNet show that GDPA achieves higher attack success rates than state-of-the-art patch attacks, while adversarially trained model with GDPA demonstrates superior robustness to adversarial patch attacks than competing methods. Our source code can be found at https://github.com/lxuniverse/gdpa.

8.0CVMay 19, 2021Code
An Orthogonal Classifier for Improving the Adversarial Robustness of Neural Networks

Cong Xu, Xiang Li, Min Yang

Neural networks are susceptible to artificially designed adversarial perturbations. Recent efforts have shown that imposing certain modifications on classification layer can improve the robustness of the neural networks. In this paper, we explicitly construct a dense orthogonal weight matrix whose entries have the same magnitude, thereby leading to a novel robust classifier. The proposed classifier avoids the undesired structural redundancy issue in previous work. Applying this classifier in standard training on clean data is sufficient to ensure the high accuracy and good robustness of the model. Moreover, when extra adversarial samples are used, better robustness can be further obtained with the help of a special worst-case loss. Experimental results show that our method is efficient and competitive to many state-of-the-art defensive approaches. Our code is available at \url{https://github.com/MTandHJ/roboc}.

14.1CVOct 28, 2024
Novel Object Synthesis via Adaptive Text-Image Harmony

Zeren Xiong, Zedong Zhang, Zikun Chen et al.

In this paper, we study an object synthesis task that combines an object text with an object image to create a new object image. However, most diffusion models struggle with this task, \textit{i.e.}, often generating an object that predominantly reflects either the text or the image due to an imbalance between their inputs. To address this issue, we propose a simple yet effective method called Adaptive Text-Image Harmony (ATIH) to generate novel and surprising objects. First, we introduce a scale factor and an injection step to balance text and image features in cross-attention and to preserve image information in self-attention during the text-image inversion diffusion process, respectively. Second, to better integrate object text and image, we design a balanced loss function with a noise parameter, ensuring both optimal editability and fidelity of the object image. Third, to adaptively adjust these parameters, we present a novel similarity score function that not only maximizes the similarities between the generated object image and the input text/image but also balances these similarities to harmonize text and image integration. Extensive experiments demonstrate the effectiveness of our approach, showcasing remarkable object creations such as colobus-glass jar. Project page: https://xzr52.github.io/ATIH/.

6.2CVAug 24, 2025
Performance is not All You Need: Sustainability Considerations for Algorithms

Xiang Li, Chong Zhang, Hongpeng Wang et al.

This work focuses on the high carbon emissions generated by deep learning model training, specifically addressing the core challenge of balancing algorithm performance and energy consumption. It proposes an innovative two-dimensional sustainability evaluation system. Different from the traditional single performance-oriented evaluation paradigm, this study pioneered two quantitative indicators that integrate energy efficiency ratio and accuracy: the sustainable harmonic mean (FMS) integrates accumulated energy consumption and performance parameters through the harmonic mean to reveal the algorithm performance under unit energy consumption; the area under the sustainability curve (ASC) constructs a performance-power consumption curve to characterize the energy efficiency characteristics of the algorithm throughout the cycle. To verify the universality of the indicator system, the study constructed benchmarks in various multimodal tasks, including image classification, segmentation, pose estimation, and batch and online learning. Experiments demonstrate that the system can provide a quantitative basis for evaluating cross-task algorithms and promote the transition of green AI research from theory to practice. Our sustainability evaluation framework code can be found here, providing methodological support for the industry to establish algorithm energy efficiency standards.

5.6OCJun 5, 2024
Achieving Near-Optimal Convergence for Distributed Minimax Optimization with Adaptive Stepsizes

Yan Huang, Xiang Li, Yipeng Shen et al.

In this paper, we show that applying adaptive methods directly to distributed minimax problems can result in non-convergence due to inconsistency in locally computed adaptive stepsizes. To address this challenge, we propose D-AdaST, a Distributed Adaptive minimax method with Stepsize Tracking. The key strategy is to employ an adaptive stepsize tracking protocol involving the transmission of two extra (scalar) variables. This protocol ensures the consistency among stepsizes of nodes, eliminating the steady-state error due to the lack of coordination of stepsizes among nodes that commonly exists in vanilla distributed adaptive methods, and thus guarantees exact convergence. For nonconvex-strongly-concave distributed minimax problems, we characterize the specific transient times that ensure time-scale separation of stepsizes and quasi-independence of networks, leading to a near-optimal convergence rate of $\tilde{\mathcal{O}} \left( ε^{-\left( 4+δ\right)} \right)$ for any small $δ> 0$, matching that of the centralized counterpart. To our best knowledge, D-AdaST is the first distributed adaptive method achieving near-optimal convergence without knowing any problem-dependent parameters for nonconvex minimax problems. Extensive experiments are conducted to validate our theoretical results.

14.7ROSep 23, 2021Code
Shape Control of Deformable Linear Objects with Offline and Online Learning of Local Linear Deformation Models

Mingrui Yu, Hanzhong Zhong, Xiang Li

The shape control of deformable linear objects (DLOs) is challenging, since it is difficult to obtain the deformation models. Previous studies often approximate the models in purely offline or online ways. In this paper, we propose a scheme for the shape control of DLOs, where the unknown model is estimated with both offline and online learning. The model is formulated in a local linear format, and approximated by a neural network (NN). First, the NN is trained offline to provide a good initial estimation of the model, which can directly migrate to the online phase. Then, an adaptive controller is proposed to achieve the shape control tasks, in which the NN is further updated online to compensate for any errors in the offline model caused by insufficient training or changes of DLO properties. The simulation and real-world experiments show that the proposed method can precisely and efficiently accomplish the DLO shape control tasks, and adapt well to new and untrained DLOs.

6.1AIApr 12, 2021
Deep Attributed Network Representation Learning via Attribute Enhanced Neighborhood

Cong Li, Min Shi, Bo Qu et al.

Attributed network representation learning aims at learning node embeddings by integrating network structure and attribute information. It is a challenge to fully capture the microscopic structure and the attribute semantics simultaneously, where the microscopic structure includes the one-step, two-step and multi-step relations, indicating the first-order, second-order and high-order proximity of nodes, respectively. In this paper, we propose a deep attributed network representation learning via attribute enhanced neighborhood (DANRL-ANE) model to improve the robustness and effectiveness of node representations. The DANRL-ANE model adopts the idea of the autoencoder, and expands the decoder component to three branches to capture different order proximity. We linearly combine the adjacency matrix with the attribute similarity matrix as the input of our model, where the attribute similarity matrix is calculated by the cosine similarity between the attributes based on the social homophily. In this way, we preserve the second-order proximity to enhance the robustness of DANRL-ANE model on sparse networks, and deal with the topological and attribute information simultaneously. Moreover, the sigmoid cross-entropy loss function is extended to capture the neighborhood character, so that the first-order proximity is better preserved. We compare our model with the state-of-the-art models on five real-world datasets and two network analysis tasks, i.e., link prediction and node classification. The DANRL-ANE model performs well on various networks, even on sparse networks or networks with isolated nodes given the attribute information is sufficient.

4.0OCJan 5, 2021
Delayed Projection Techniques for Linearly Constrained Problems: Convergence Rates, Acceleration, and Applications

Xiang Li, Zhihua Zhang

In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for LCPs call a projection after each (stochastic) gradient descent, resulting in that the required number of projections equals that of gradient descents (or total iterations). Motivated by the recent progress in distributed optimization, we propose the delayed projection technique that calls a projection once for a while, lowering the projection frequency and improving the projection efficiency. Accordingly, we devise a series of stochastic methods for LCPs using the technique, including a variance reduced method and an accelerated one. We theoretically show that it is feasible to improve projection efficiency in both strongly convex and generally convex cases. Our analysis is simple and unified and can be easily extended to other methods using delayed projections. When applying our new algorithms to federated optimization, a newfangled and privacy-preserving subfield in distributed optimization, we obtain not only a variance reduced federated algorithm with convergence rates better than previous works, but also the first accelerated method able to handle data heterogeneity inherent in federated optimization.

8.8MLFeb 13, 2019
Do Subsampled Newton Methods Work for High-Dimensional Data?

Xiang Li, Shusen Wang, Zhihua Zhang

Subsampled Newton methods approximate Hessian matrices through subsampling techniques, alleviating the cost of forming Hessian matrices but using sufficient curvature information. However, previous results require $Ω(d)$ samples to approximate Hessians, where $d$ is the dimension of data points, making it less practically feasible for high-dimensional data. The situation is deteriorated when $d$ is comparably as large as the number of data points $n$, which requires to take the whole dataset into account, making subsampling useless. This paper theoretically justifies the effectiveness of subsampled Newton methods on high dimensional data. Specifically, we prove only $\widetildeΘ(d^γ_{\rm eff})$ samples are needed in the approximation of Hessian matrices, where $d^γ_{\rm eff}$ is the $γ$-ridge leverage and can be much smaller than $d$ as long as $nγ\gg 1$. Additionally, we extend this result so that subsampled Newton methods can work for high-dimensional data on both distributed optimization problems and non-smooth regularized problems.

4.0MLNov 24, 2015
Statistical Properties of the Single Linkage Hierarchical Clustering Estimator

Dekang Zhu, Dan P. Guralnik, Xuezhi Wang et al.

Distance-based hierarchical clustering (HC) methods are widely used in unsupervised data analysis but few authors take account of uncertainty in the distance data. We incorporate a statistical model of the uncertainty through corruption or noise in the pairwise distances and investigate the problem of estimating the HC as unknown parameters from measurements. Specifically, we focus on single linkage hierarchical clustering (SLHC) and study its geometry. We prove that under fairly reasonable conditions on the probability distribution governing measurements, SLHC is equivalent to maximum partial profile likelihood estimation (MPPLE) with some of the information contained in the data ignored. At the same time, we show that direct evaluation of SLHC on maximum likelihood estimation (MLE) of pairwise distances yields a consistent estimator. Consequently, a full MLE is expected to perform better than SLHC in getting the correct HC results for the ground truth metric.