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Xiaolin Huang

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ICML Conference 2025 Conference Paper

Flat-LoRA: Low-Rank Adaptation over a Flat Loss Landscape

  • Tao Li
  • Zhengbao He
  • Yujun Li
  • Yasheng Wang
  • Lifeng Shang
  • Xiaolin Huang

Fine-tuning large-scale pre-trained models is prohibitively expensive in terms of computation and memory costs. Low-Rank Adaptation (LoRA), a popular Parameter-Efficient Fine-Tuning (PEFT) method, offers an efficient solution by optimizing only low-rank matrices. Despite recent progress in improving LoRA’s performance, the relationship between the LoRA optimization space and the full parameter space is often overlooked. A solution that appears flat in the loss landscape of the LoRA space may still exhibit sharp directions in the full parameter space, potentially compromising generalization. We introduce Flat-LoRA, which aims to identify a low-rank adaptation situated in a flat region of the full parameter space. Instead of adopting the well-established sharpness-aware minimization approach, which incurs significant computation and memory overheads, we employ a Bayesian expectation loss objective to preserve training efficiency. Further, we design a refined strategy for generating random perturbations to enhance performance and carefully manage memory overhead using random seeds. Experiments across diverse tasks—including mathematical reasoning, coding abilities, dialogue generation, instruction following, and text-to-image generation—demonstrate that Flat-LoRA improves both in-domain and out-of-domain generalization. Code is available at https: //github. com/nblt/Flat-LoRA.

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AAAI Conference 2025 Conference Paper

ParseCaps: An Interpretable Parsing Capsule Network for Medical Image Diagnosis

  • Xinyu Geng
  • Jiaming Wang
  • Xiaolin Huang
  • Fanglin Chen
  • Jun Xu

Deep learning has excelled in medical image classification, but its clinical application is limited by poor interpretability. Capsule networks, known for encoding hierarchical relationships and spatial features, show potential in addressing this issue. Nevertheless, traditional capsule networks often underperform due to their shallow structures, and deeper variants lack hierarchical architectures, thereby compromising interpretability. This paper introduces a novel capsule network, ParseCaps, which utilizes the sparse axial attention routing and parse convolutional capsule layer to form a parse-tree-like structure, enhancing both depth and interpretability. Firstly, sparse axial attention routing optimizes connections between child and parent capsules, as well as emphasizes the weight distribution across instantiation parameters of parent capsules. Secondly, the parse convolutional capsule layer generates capsule predictions aligning with the parse tree. Finally, based on the loss design that is effective whether concept ground truth exists or not, ParseCaps advances interpretability by associating each dimension of the global capsule with a comprehensible concept, thereby facilitating clinician trust and understanding of the model's classification results. Experimental results on three medical datasets show that ParseCaps not only outperforms other capsule network variants in classification accuracy and robustness, but also provides interpretable explanations, regardless of the availability of concept labels.

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ICML Conference 2025 Conference Paper

Primphormer: Efficient Graph Transformers with Primal Representations

  • Mingzhen He
  • Ruikai Yang
  • Hanling Tian
  • Youmei Qiu
  • Xiaolin Huang

Graph Transformers (GTs) have emerged as a promising approach for graph representation learning. Despite their successes, the quadratic complexity of GTs limits scalability on large graphs due to their pair-wise computations. To fundamentally reduce the computational burden of GTs, we propose a primal-dual framework that interprets the self-attention mechanism on graphs as a dual representation. Based on this framework, we develop Primphormer, an efficient GT that leverages a primal representation with linear complexity. Theoretical analysis reveals that Primphormer serves as a universal approximator for functions on both sequences and graphs, while also retaining its expressive power for distinguishing non-isomorphic graphs. Extensive experiments on various graph benchmarks demonstrate that Primphormer achieves competitive empirical results while maintaining a more user-friendly memory and computational costs.

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ICLR Conference 2025 Conference Paper

Pursuing Feature Separation based on Neural Collapse for Out-of-Distribution Detection

  • Yingwen Wu
  • Ruiji Yu
  • Xinwen Cheng
  • Zhengbao He
  • Xiaolin Huang

In the open world, detecting out-of-distribution (OOD) data, whose labels are disjoint with those of in-distribution (ID) samples, is important for reliable deep neural networks (DNNs). To achieve better detection performance, one type of approach proposes to fine-tune the model with auxiliary OOD datasets to amplify the difference between ID and OOD data through a separation loss defined on model outputs. However, none of these studies consider enlarging the feature disparity, which should be more effective compared to outputs. The main difficulty lies in the diversity of OOD samples, which makes it hard to describe their feature distribution, let alone design losses to separate them from ID features. In this paper, we neatly fence off the problem based on an aggregation property of ID features named Neural Collapse (NC). NC means that the penultimate features of ID samples within a class are nearly identical to the last layer weight of the corresponding class. Based on this property, we propose a simple but effective loss called Separation Loss, which binds the features of OOD data in a subspace orthogonal to the principal subspace of ID features formed by NC. In this way, the features of ID and OOD samples are separated by different dimensions. By optimizing the feature separation loss rather than purely enlarging output differences, our detection achieves SOTA performance on CIFAR10, CIFAR100 and ImageNet benchmarks without any additional data augmentation or sampling, demonstrating the importance of feature separation in OOD detection. Code is available at https://github.com/Wuyingwen/Pursuing-Feature-Separation-for-OOD-Detection.

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IROS Conference 2025 Conference Paper

SEB-Naver: A SE(2)-based Local Navigation Framework for Car-like Robots on Uneven Terrain

  • Xiaoying Li
  • Long Xu 0002
  • Xiaolin Huang
  • Donglai Xue
  • Zhihao Zhang
  • Zhichao Han 0002
  • Chao Xu 0001
  • Yanjun Cao

Autonomous navigation of car-like robots on uneven terrain poses unique challenges compared to flat terrain, particularly in traversability assessment and terrain-associated kinematic modelling for motion planning. This paper introduces SEB-Naver, a novel SE(2)-based local navigation framework designed to overcome these challenges. First, we propose an efficient traversability assessment method for SE(2) grids, leveraging GPU parallel computing to enable real-time updates and maintenance of local maps. Second, inspired by differential flatness, we present an optimization-based trajectory planning method that integrates terrain-associated kinematic models, significantly improving both planning efficiency and trajectory quality. Finally, we unify these components into SEB-Naver, achieving real-time terrain assessment and trajectory optimization. Extensive simulations and real-world experiments demonstrate the effectiveness and efficiency of our approach. The code is at https://github.com/ZJU-FAST-Lab/seb_naver.

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ICLR Conference 2025 Conference Paper

Simulating Training Dynamics to Reconstruct Training Data from Deep Neural Networks

  • Hanling Tian
  • Yuhang Liu 0003
  • Mingzhen He
  • Zhengbao He
  • Zhehao Huang
  • Ruikai Yang
  • Xiaolin Huang

Whether deep neural networks (DNNs) memorize the training data is a fundamental open question in understanding deep learning. A direct way to verify the memorization of DNNs is to reconstruct training data from DNNs’ parameters. Since parameters are gradually determined by data throughout training, characterizing training dynamics is important for reconstruction. Pioneering works rely on the linear training dynamics of shallow NNs with large widths, but cannot be extended to more practical DNNs which have non-linear dynamics. We propose Simulation of training Dynamics (SimuDy) to reconstruct training data from DNNs. Specifically, we simulate the training dynamics by training the model from the initial parameters with a dummy dataset, then optimize this dummy dataset so that the simulated dynamics reach the same final parameters as the true dynamics. By incorporating dummy parameters in the simulated dynamics, SimuDy effectively describes non-linear training dynamics. Experiments demonstrate that SimuDy significantly outperforms previous approaches when handling non-linear training dynamics, and for the first time, most training samples can be reconstructed from a trained ResNet’s parameters.

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NeurIPS Conference 2024 Conference Paper

Kernel PCA for Out-of-Distribution Detection

  • Kun Fang
  • Qinghua Tao
  • Kexin Lv
  • Mingzhen He
  • Xiaolin Huang
  • Jie Yang

Out-of-Distribution (OoD) detection is vital for the reliability of Deep Neural Networks (DNNs). Existing works have shown the insufficiency of Principal Component Analysis (PCA) straightforwardly applied on the features of DNNs in detecting OoD data from In-Distribution (InD) data. The failure of PCA suggests that the network features residing in OoD and InD are not well separated by simply proceeding in a linear subspace, which instead can be resolved through proper non-linear mappings. In this work, we leverage the framework of Kernel PCA (KPCA) for OoD detection, and seek suitable non-linear kernels that advocate the separability between InD and OoD data in the subspace spanned by the principal components. Besides, explicit feature mappings induced from the devoted task-specific kernels are adopted so that the KPCA reconstruction error for new test samples can be efficiently obtained with large-scale data. Extensive theoretical and empirical results on multiple OoD data sets and network structures verify the superiority of our KPCA detector in efficiency and efficacy with state-of-the-art detection performance.

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TMLR Journal 2024 Journal Article

Online Continual Learning via Logit Adjusted Softmax

  • Zhehao Huang
  • Tao Li
  • Chenhe Yuan
  • Yingwen Wu
  • Xiaolin Huang

Online continual learning is a challenging problem where models must learn from a non-stationary data stream while avoiding catastrophic forgetting. Inter-class imbalance during training has been identified as a major cause of forgetting, leading to model prediction bias towards recently learned classes. In this paper, we theoretically analyze that inter-class imbalance is entirely attributed to imbalanced class-priors, and the function learned from intra-class intrinsic distributions is the optimal classifier that minimizes the class-balanced error. To that end, we present that a simple adjustment of model logits during training can effectively resist prior class bias and pursue the corresponding optimum. Our proposed method, Logit Adjusted Softmax, can mitigate the impact of inter-class imbalance not only in class-incremental but also in realistic scenarios that sum up class and domain incremental learning, with little additional computational cost. We evaluate our approach on various benchmarks and demonstrate significant performance improvements compared to prior arts. For example, our approach improves the best baseline by 4.6% on CIFAR10.

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TMLR Journal 2024 Journal Article

Revisiting Random Weight Perturbation for Efficiently Improving Generalization

  • Tao Li
  • Qinghua Tao
  • Weihao Yan
  • Yingwen Wu
  • Zehao Lei
  • Kun Fang
  • Mingzhen He
  • Xiaolin Huang

Improving the generalization ability of modern deep neural networks (DNNs) is a fundamental challenge in machine learning. Two branches of methods have been proposed to seek flat minima and improve generalization: one led by sharpness-aware minimization (SAM) minimizes the worst-case neighborhood loss through adversarial weight perturbation (AWP), and the other minimizes the expected Bayes objective with random weight perturbation (RWP). While RWP offers advantages in computation and is closely linked to AWP on a mathematical basis, its empirical performance has consistently lagged behind that of AWP. In this paper, we revisit the use of RWP for improving generalization and propose improvements from two perspectives: i) the trade-off between generalization and convergence and ii) the random perturbation generation. Through extensive experimental evaluations, we demonstrate that our enhanced RWP methods achieve greater efficiency in enhancing generalization, particularly in large-scale problems, while also offering comparable or even superior performance to SAM. The code is released at https://github.com/nblt/mARWP.

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NeurIPS Conference 2024 Conference Paper

Unified Gradient-Based Machine Unlearning with Remain Geometry Enhancement

  • Zhehao Huang
  • Xinwen Cheng
  • JingHao Zheng
  • Haoran Wang
  • Zhengbao He
  • Tao Li
  • Xiaolin Huang

Machine unlearning (MU) has emerged to enhance the privacy and trustworthiness of deep neural networks. Approximate MU is a practical method for large-scale models. Our investigation into approximate MU starts with identifying the steepest descent direction, minimizing the output Kullback-Leibler divergence to exact MU inside a parameters' neighborhood. This probed direction decomposes into three components: weighted forgetting gradient ascent, fine-tuning retaining gradient descent, and a weight saliency matrix. Such decomposition derived from Euclidean metric encompasses most existing gradient-based MU methods. Nevertheless, adhering to Euclidean space may result in sub-optimal iterative trajectories due to the overlooked geometric structure of the output probability space. We suggest embedding the unlearning update into a manifold rendered by the remaining geometry, incorporating second-order Hessian from the remaining data. It helps prevent effective unlearning from interfering with the retained performance. However, computing the second-order Hessian for large-scale models is intractable. To efficiently leverage the benefits of Hessian modulation, we propose a fast-slow parameter update strategy to implicitly approximate the up-to-date salient unlearning direction. Free from specific modal constraints, our approach is adaptable across computer vision unlearning tasks, including classification and generation. Extensive experiments validate our efficacy and efficiency. Notably, our method successfully performs class-forgetting on ImageNet using DiT and forgets a class on CIFAR-10 using DDPM in just 50 steps, compared to thousands of steps required by previous methods. Code is available at Unified-Unlearning-w-Remain-Geometry.

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NeurIPS Conference 2023 Conference Paper

Diffusion Representation for Asymmetric Kernels via Magnetic Transform

  • Mingzhen He
  • FAN He
  • Ruikai Yang
  • Xiaolin Huang

As a nonlinear dimension reduction technique, the diffusion map (DM) has been widely used. In DM, kernels play an important role for capturing the nonlinear relationship of data. However, only symmetric kernels can be used now, which prevents the use of DM in directed graphs, trophic networks, and other real-world scenarios where the intrinsic and extrinsic geometries in data are asymmetric. A promising technique is the magnetic transform which converts an asymmetric matrix to a Hermitian one. However, we are facing essential problems, including how diffusion distance could be preserved and how divergence could be avoided during diffusion process. Via theoretical proof, we successfully establish a diffusion representation framework with the magnetic transform, named MagDM. The effectiveness and robustness for dealing data endowed with asymmetric proximity are demonstrated on three synthetic datasets and two trophic networks.

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ICLR Conference 2023 Conference Paper

One-Pixel Shortcut: On the Learning Preference of Deep Neural Networks

  • Shutong Wu
  • Sizhe Chen
  • Cihang Xie
  • Xiaolin Huang

Unlearnable examples (ULEs) aim to protect data from unauthorized usage for training DNNs. Existing work adds $\ell_\infty$-bounded perturbations to the original sample so that the trained model generalizes poorly. Such perturbations, however, are easy to eliminate by adversarial training and data augmentations. In this paper, we resolve this problem from a novel perspective by perturbing only one pixel in each image. Interestingly, such a small modification could effectively degrade model accuracy to almost an untrained counterpart. Moreover, our produced \emph{One-Pixel Shortcut (OPS)} could not be erased by adversarial training and strong augmentations. To generate OPS, we perturb in-class images at the same position to the same target value that could mostly and stably deviate from all the original images. Since such generation is only based on images, OPS needs significantly less computation cost than the previous methods using DNN generators. Based on OPS, we introduce an unlearnable dataset called CIFAR-10-S, which is indistinguishable from CIFAR-10 by humans but induces the trained model to extremely low accuracy. Even under adversarial training, a ResNet-18 trained on CIFAR-10-S has only 10.61% accuracy, compared to 83.02% by the existing error-minimizing method.

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ICLR Conference 2023 Conference Paper

Self-Ensemble Protection: Training Checkpoints Are Good Data Protectors

  • Sizhe Chen
  • Geng Yuan
  • Xinwen Cheng
  • Yifan Gong 0004
  • Minghai Qin
  • Yanzhi Wang 0001
  • Xiaolin Huang

As data becomes increasingly vital, a company would be very cautious about releasing data, because the competitors could use it to train high-performance models, thereby posing a tremendous threat to the company's commercial competence. To prevent training good models on the data, we could add imperceptible perturbations to it. Since such perturbations aim at hurting the entire training process, they should reflect the vulnerability of DNN training, rather than that of a single model. Based on this new idea, we seek perturbed examples that are always unrecognized (never correctly classified) in training. In this paper, we uncover them by model checkpoints' gradients, forming the proposed self-ensemble protection (SEP), which is very effective because (1) learning on examples ignored during normal training tends to yield DNNs ignoring normal examples; (2) checkpoints' cross-model gradients are close to orthogonal, meaning that they are as diverse as DNNs with different architectures. That is, our amazing performance of ensemble only requires the computation of training one model. By extensive experiments with 9 baselines on 3 datasets and 5 architectures, SEP is verified to be a new state-of-the-art, e.g., our small $\ell_\infty=2/255$ perturbations reduce the accuracy of a CIFAR-10 ResNet18 from 94.56% to 14.68%, compared to 41.35% by the best-known method. Code is available at https://github.com/Sizhe-Chen/SEP.

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ICLR Conference 2023 Conference Paper

Trainable Weight Averaging: Efficient Training by Optimizing Historical Solutions

  • Tao Li 0054
  • Zhehao Huang
  • Qinghua Tao
  • Yingwen Wu
  • Xiaolin Huang

Stochastic gradient descent (SGD) and its variants are considered as the de-facto methods to train deep neural networks (DNNs). While recent improvements to SGD mainly focus on the descent algorithm itself, few works pay attention to utilizing the historical solutions---as an iterative method, SGD has gone through substantial explorations before convergence. Recently, an interesting attempt is stochastic weight averaging (SWA), which significantly improves the generalization by simply averaging the solutions at the tail stage of training. In this paper, we realize that the averaging coefficients could be determined in a trainable manner and propose Trainable Weight Averaging (TWA), a novel optimization method in the reduced subspace spanned by historical solutions. TWA has much greater flexibility and can be applied to the head stage of training to achieve training efficiency while preserving good generalization capability. Further, we propose a distributed training scheme to resolve the memory burden of large-scale training with efficient parallel computation. In the extensive numerical experiments, (i) TWA achieves consistent improvements over SWA with less sensitivity to learning rate; (ii) applying TWA in the head stage of training largely speeds up the convergence, resulting in over $40\%$ time saving on CIFAR and $30\%$ on ImageNet with improved generalization compared with regular training.

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TIST Journal 2023 Journal Article

Unifying Gradients to Improve Real-World Robustness for Deep Networks

  • Yingwen Wu
  • Sizhe Chen
  • Kun Fang
  • Xiaolin Huang

The wide application of deep neural networks (DNNs) demands an increasing amount of attention to their real-world robustness, i.e., whether a DNN resists black-box adversarial attacks, among which score-based query attacks (SQAs) are the most threatening since they can effectively hurt a victim network with only access to model outputs. Defending against SQAs requires a slight but artful variation of outputs due to the service purpose for users, who share the same output information with SQAs. In this article, we propose a real-world defense by Unifying Gradients (UniG) of different data so that SQAs could only probe a much weaker attack direction that is similar for different samples. Since such universal attack perturbations have been validated as less aggressive than the input-specific perturbations, UniG protects real-world DNNs by indicating to attackers a twisted and less informative attack direction. We implement UniG efficiently by a Hadamard product module, which is plug-and-play. According to extensive experiments on 5 SQAs, 2 adaptive attacks and 7 defense baselines, UniG significantly improves real-world robustness without hurting clean accuracy on CIFAR10 and ImageNet. For instance, UniG maintains a model of 77.80% accuracy under a 2500-query Square attack while the state-of-the-art adversarially trained model only has 67.34% on CIFAR10. Simultaneously, UniG outperforms all compared baselines in terms of clean accuracy and achieves the smallest modification of the model output. The code is released at https://github.com/snowien/UniG-pytorch.

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NeurIPS Conference 2022 Conference Paper

Adversarial Attack on Attackers: Post-Process to Mitigate Black-Box Score-Based Query Attacks

  • Sizhe Chen
  • Zhehao Huang
  • Qinghua Tao
  • Yingwen Wu
  • Cihang Xie
  • Xiaolin Huang

The score-based query attacks (SQAs) pose practical threats to deep neural networks by crafting adversarial perturbations within dozens of queries, only using the model's output scores. Nonetheless, we note that if the loss trend of the outputs is slightly perturbed, SQAs could be easily misled and thereby become much less effective. Following this idea, we propose a novel defense, namely Adversarial Attack on Attackers (AAA), to confound SQAs towards incorrect attack directions by slightly modifying the output logits. In this way, (1) SQAs are prevented regardless of the model's worst-case robustness; (2) the original model predictions are hardly changed, i. e. , no degradation on clean accuracy; (3) the calibration of confidence scores can be improved simultaneously. Extensive experiments are provided to verify the above advantages. For example, by setting $\ell_\infty=8/255$ on CIFAR-10, our proposed AAA helps WideResNet-28 secure 80. 59% accuracy under Square attack (2500 queries), while the best prior defense (i. e. , adversarial training) only attains 67. 44%. Since AAA attacks SQA's general greedy strategy, such advantages of AAA over 8 defenses can be consistently observed on 8 CIFAR-10/ImageNet models under 6 SQAs, using different attack targets, bounds, norms, losses, and strategies. Moreover, AAA calibrates better without hurting the accuracy. Our code is available at https: //github. com/Sizhe-Chen/AAA.

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JMLR Journal 2021 Journal Article

Generalization Properties of hyper-RKHS and its Applications

  • Fanghui Liu
  • Lei Shi
  • Xiaolin Huang
  • Jie Yang
  • Johan A.K. Suykens

This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the introduced regression models in an approximation theory view. Algorithmically, we consider two regularized regression models with bivariate forms in this space, including kernel ridge regression (KRR) and support vector regression (SVR) endowed with hyper-RKHS, and further combine divide-and-conquer with Nystr\"{o}m approximation for scalability in large sample cases. This framework is general: the underlying kernel is learned from a broad class, and can be positive definite or not, which adapts to various requirements in kernel learning. Theoretically, we study the convergence behavior of regularized regression algorithms in hyper-RKHS and derive the learning rates, which goes beyond the classical analysis on RKHS due to the non-trivial independence of pairwise samples and the characterisation of hyper-RKHS. Experimentally, results on several benchmarks suggest that the employed framework is able to learn a general kernel function form an arbitrary similarity matrix, and thus achieves a satisfactory performance on classification tasks. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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AAAI Conference 2020 Conference Paper

A Generalized Framework for Edge-Preserving and Structure-Preserving Image Smoothing

  • Wei Liu
  • Pingping Zhang
  • Yinjie Lei
  • Xiaolin Huang
  • Jie Yang
  • Ian Reid

Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of one smoothing operator is usually fixed and thus cannot meet the various requirements of different applications. In this paper, a non-convex non-smooth optimization framework is proposed to achieve diverse smoothing natures where even contradictive smoothing behaviors can be achieved. To this end, we first introduce the truncated Huber penalty function which has seldom been used in image smoothing. A robust framework is then proposed. When combined with the strong flexibility of the truncated Huber penalty function, our framework is capable of a range of applications and can outperform the state-of-the-art approaches in several tasks. In addition, an efficient numerical solution is provided and its convergence is theoretically guaranteed even the optimization framework is non-convex and non-smooth. The effectiveness and superior performance of our approach are validated through comprehensive experimental results in a range of applications.

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JMLR Journal 2020 Journal Article

Learning Data-adaptive Non-parametric Kernels

  • Fanghui Liu
  • Xiaolin Huang
  • Chen Gong
  • Jie Yang
  • Li Li

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise scheme. Learning this data-adaptive matrix in a formulation-free strategy enlarges the margin between classes and thus improves the model flexibility. The introduced two constraints are imposed either exactly (on small data sets) or approximately (on large data sets) in our model, which provides a controllable trade-off between model flexibility and complexity with theoretical demonstration. In algorithm optimization, the objective function of our learning framework is proven to be gradient-Lipschitz continuous. Thereby, kernel and classifier/regressor learning can be efficiently optimized in a unified framework via Nesterov's acceleration. For the scalability issue, we study a decomposition-based approach to our model in the large sample case. The effectiveness of this approximation is illustrated by both empirical studies and theoretical guarantees. Experimental results on various classification and regression benchmark data sets demonstrate that our non-parametric kernel learning framework achieves good performance when compared with other representative kernel learning based algorithms. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

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AAAI Conference 2020 Conference Paper

Random Fourier Features via Fast Surrogate Leverage Weighted Sampling

  • Fanghui Liu
  • Xiaolin Huang
  • Yudong Chen
  • Jie Yang
  • Johan Suykens

In this paper, we propose a fast surrogate leverage weighted sampling strategy to generate refined random Fourier features for kernel approximation. Compared to the current state-ofthe-art method that uses the leverage weighted scheme (Li et al. 2019), our new strategy is simpler and more effective. It uses kernel alignment to guide the sampling process and it can avoid the matrix inversion operator when we compute the leverage function. Given n observations and s random features, our strategy can reduce the time complexity for sampling from O(ns2 +s3 ) to O(ns2 ), while achieving comparable (or even slightly better) prediction performance when applied to kernel ridge regression (KRR). In addition, we provide theoretical guarantees on the generalization performance of our approach, and in particular characterize the number of random features required to achieve statistical guarantees in KRR. Experiments on several benchmark datasets demonstrate that our algorithm achieves comparable prediction performance and takes less time cost when compared to (Li et al. 2019).

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AAAI Conference 2018 Conference Paper

Nonlinear Pairwise Layer and Its Training for Kernel Learning

  • Fanghui Liu
  • Xiaolin Huang
  • Chen Gong
  • Jie Yang
  • Li Li

Kernel learning is a fundamental technique that has been intensively studied in the past decades. For the complicated practical tasks, the traditional “shallow” kernels (e. g. , Gaussian kernel and sigmoid kernel) are not flexible enough to produce satisfactory performance. To address this shortcoming, this paper introduces a nonlinear layer in kernel learning to enhance the model flexibility. This layer is pairwise, which fully considers the coupling information among examples. So our model contains a fixed single mapping layer (i. e. a Gaussian kernel) as well as a nonlinear pairwise layer, thereby achieving better flexibility than the existing kernel structures. Moreover, the proposed structure can be seamlessly embedded to Support Vector Machines (SVM), of which the training process can be formulated as a joint optimization problem including nonlinear function learning and standard SVM optimization. We theoretically prove that the objective function is gradient-Lipschitz continuous, which further guides us how to accelerate the optimization process in a deep kernel architecture. Experimentally, we find that the proposed structure outperforms other state-ofthe-art kernel-based algorithms on various benchmark datasets, and thus the effectiveness of the incorporated pairwise layer with its training approach is demonstrated.

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EAAI Journal 2017 Journal Article

Robust kernel canonical correlation analysis with applications to information retrieval

  • Jia Cai
  • Xiaolin Huang

Canonical correlation analysis (CCA) is a powerful statistical tool quantifying correlations between two sets of multidimensional variables. CCA cannot detect nonlinear relationship, and it is costly to derive canonical variates for high-dimensional data. Kernel CCA, a nonlinear extension of the CCA method, can efficiently exploit nonlinear relations and reduce high dimensionality. However, kernel CCA yields the so called over-fitting phenomenon in the high-dimensional feature space. To handle the shortcomings of kernel CCA, this paper develops a novel robust kernel CCA algorithm (KCCA-ROB). The derived method begins with reformulating the traditional generalized eigenvalue–eigenvector problem into a new framework. Under this novel framework, we develop a stable and fast algorithm by means of singular value decomposition (SVD) method. Experimental results on both a simulated dataset and real-world datasets demonstrate the effectiveness of the developed method.

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JMLR Journal 2015 Journal Article

Learning with the Maximum Correntropy Criterion Induced Losses for Regression

  • Yunlong Feng
  • Xiaolin Huang
  • Lei Shi
  • Yuning Yang
  • Johan A.K. Suykens

Within the statistical learning framework, this paper studies the regression model associated with the correntropy induced losses. The correntropy, as a similarity measure, has been frequently employed in signal processing and pattern recognition. Motivated by its empirical successes, this paper aims at presenting some theoretical understanding towards the maximum correntropy criterion in regression problems. Our focus in this paper is two-fold: first, we are concerned with the connections between the regression model associated with the correntropy induced loss and the least squares regression model. Second, we study its convergence property. A learning theory analysis which is centered around the above two aspects is conducted. From our analysis, we see that the scale parameter in the loss function balances the convergence rates of the regression model and its robustness. We then make some efforts to sketch a general view on robust loss functions when being applied into the learning for regression problems. Numerical experiments are also implemented to verify the effectiveness of the model. [abs] [ pdf ][ bib ] &copy JMLR 2015. ( edit, beta )

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JMLR Journal 2014 Journal Article

Ramp Loss Linear Programming Support Vector Machine

  • Xiaolin Huang
  • Lei Shi
  • Johan A.K. Suykens

The ramp loss is a robust but non-convex loss for classification. Compared with other non-convex losses, a local minimum of the ramp loss can be effectively found. The effectiveness of local search comes from the piecewise linearity of the ramp loss. Motivated by the fact that the $\ell_1$-penalty is piecewise linear as well, the $\ell_1$-penalty is applied for the ramp loss, resulting in a ramp loss linear programming support vector machine (ramp- LPSVM). The proposed ramp-LPSVM is a piecewise linear minimization problem and the related optimization techniques are applicable. Moreover, the $\ell_1$-penalty can enhance the sparsity. In this paper, the corresponding misclassification error and convergence behavior are discussed. Generally, the ramp loss is a truncated hinge loss. Therefore ramp-LPSVM possesses some similar properties as hinge loss SVMs. A local minimization algorithm and a global search strategy are discussed. The good optimization capability of the proposed algorithms makes ramp-LPSVM perform well in numerical experiments: the result of ramp-LPSVM is more robust than that of hinge SVMs and is sparser than that of ramp-SVM, which consists of the $\|\cdot\|_{\mathcal{K}} $-penalty and the ramp loss. [abs] [ pdf ][ bib ] &copy JMLR 2014. ( edit, beta )

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