MAJun 1, 2022
Policy Diagnosis via Measuring Role Diversity in Cooperative Multi-agent RLSiyi Hu, Chuanlong Xie, Xiaodan Liang et al.
Cooperative multi-agent reinforcement learning (MARL) is making rapid progress for solving tasks in a grid world and real-world scenarios, in which agents are given different attributes and goals, resulting in different behavior through the whole multi-agent task. In this study, we quantify the agent's behavior difference and build its relationship with the policy performance via {\bf Role Diversity}, a metric to measure the characteristics of MARL tasks. We define role diversity from three perspectives: action-based, trajectory-based, and contribution-based to fully measure a multi-agent task. Through theoretical analysis, we find that the error bound in MARL can be decomposed into three parts that have a strong relation to the role diversity. The decomposed factors can significantly impact policy optimization on three popular directions including parameter sharing, communication mechanism, and credit assignment. The main experimental platforms are based on {\bf Multiagent Particle Environment (MPE)} and {\bf The StarCraft Multi-Agent Challenge (SMAC). Extensive experiments} clearly show that role diversity can serve as a robust measurement for the characteristics of a multi-agent cooperation task and help diagnose whether the policy fits the current multi-agent system for a better policy performance.
LGOct 17, 2022
ZooD: Exploiting Model Zoo for Out-of-Distribution GeneralizationQishi Dong, Awais Muhammad, Fengwei Zhou et al.
Recent advances on large-scale pre-training have shown great potentials of leveraging a large set of Pre-Trained Models (PTMs) for improving Out-of-Distribution (OoD) generalization, for which the goal is to perform well on possible unseen domains after fine-tuning on multiple training domains. However, maximally exploiting a zoo of PTMs is challenging since fine-tuning all possible combinations of PTMs is computationally prohibitive while accurate selection of PTMs requires tackling the possible data distribution shift for OoD tasks. In this work, we propose ZooD, a paradigm for PTMs ranking and ensemble with feature selection. Our proposed metric ranks PTMs by quantifying inter-class discriminability and inter-domain stability of the features extracted by the PTMs in a leave-one-domain-out cross-validation manner. The top-K ranked models are then aggregated for the target OoD task. To avoid accumulating noise induced by model ensemble, we propose an efficient variational EM algorithm to select informative features. We evaluate our paradigm on a diverse model zoo consisting of 35 models for various OoD tasks and demonstrate: (i) model ranking is better correlated with fine-tuning ranking than previous methods and up to 9859x faster than brute-force fine-tuning; (ii) OoD generalization after model ensemble with feature selection outperforms the state-of-the-art methods and the accuracy on most challenging task DomainNet is improved from 46.5\% to 50.6\%. Furthermore, we provide the fine-tuning results of 35 PTMs on 7 OoD datasets, hoping to help the research of model zoo and OoD generalization. Code will be available at https://gitee.com/mindspore/models/tree/master/research/cv/zood.
CVOct 9, 2022
Boosting Out-of-distribution Detection with Typical FeaturesYao Zhu, YueFeng Chen, Chuanlong Xie et al.
Out-of-distribution (OOD) detection is a critical task for ensuring the reliability and safety of deep neural networks in real-world scenarios. Different from most previous OOD detection methods that focus on designing OOD scores or introducing diverse outlier examples to retrain the model, we delve into the obstacle factors in OOD detection from the perspective of typicality and regard the feature's high-probability region of the deep model as the feature's typical set. We propose to rectify the feature into its typical set and calculate the OOD score with the typical features to achieve reliable uncertainty estimation. The feature rectification can be conducted as a {plug-and-play} module with various OOD scores. We evaluate the superiority of our method on both the commonly used benchmark (CIFAR) and the more challenging high-resolution benchmark with large label space (ImageNet). Notably, our approach outperforms state-of-the-art methods by up to 5.11$\%$ in the average FPR95 on the ImageNet benchmark.
LGDec 24, 2022
Boosting Out-of-Distribution Detection with Multiple Pre-trained ModelsFeng Xue, Zi He, Chuanlong Xie et al.
Out-of-Distribution (OOD) detection, i.e., identifying whether an input is sampled from a novel distribution other than the training distribution, is a critical task for safely deploying machine learning systems in the open world. Recently, post hoc detection utilizing pre-trained models has shown promising performance and can be scaled to large-scale problems. This advance raises a natural question: Can we leverage the diversity of multiple pre-trained models to improve the performance of post hoc detection methods? In this work, we propose a detection enhancement method by ensembling multiple detection decisions derived from a zoo of pre-trained models. Our approach uses the p-value instead of the commonly used hard threshold and leverages a fundamental framework of multiple hypothesis testing to control the true positive rate of In-Distribution (ID) data. We focus on the usage of model zoos and provide systematic empirical comparisons with current state-of-the-art methods on various OOD detection benchmarks. The proposed ensemble scheme shows consistent improvement compared to single-model detectors and significantly outperforms the current competitive methods. Our method substantially improves the relative performance by 65.40% and 26.96% on the CIFAR10 and ImageNet benchmarks.
LGApr 1, 2023
Fair-CDA: Continuous and Directional Augmentation for Group FairnessRui Sun, Fengwei Zhou, Zhenhua Dong et al.
In this work, we propose {\it Fair-CDA}, a fine-grained data augmentation strategy for imposing fairness constraints. We use a feature disentanglement method to extract the features highly related to the sensitive attributes. Then we show that group fairness can be achieved by regularizing the models on transition paths of sensitive features between groups. By adjusting the perturbation strength in the direction of the paths, our proposed augmentation is controllable and auditable. To alleviate the accuracy degradation caused by fairness constraints, we further introduce a calibrated model to impute labels for the augmented data. Our proposed method does not assume any data generative model and ensures good generalization for both accuracy and fairness. Experimental results show that Fair-CDA consistently outperforms state-of-the-art methods on widely-used benchmarks, e.g., Adult, CelebA and MovieLens. Especially, Fair-CDA obtains an 86.3\% relative improvement for fairness while maintaining the accuracy on the Adult dataset. Moreover, we evaluate Fair-CDA in an online recommendation system to demonstrate the effectiveness of our method in terms of accuracy and fairness.
MLApr 6, 2023
Heavy-Tailed Regularization of Weight Matrices in Deep Neural NetworksXuanzhe Xiao, Zeng Li, Chuanlong Xie et al.
Unraveling the reasons behind the remarkable success and exceptional generalization capabilities of deep neural networks presents a formidable challenge. Recent insights from random matrix theory, specifically those concerning the spectral analysis of weight matrices in deep neural networks, offer valuable clues to address this issue. A key finding indicates that the generalization performance of a neural network is associated with the degree of heavy tails in the spectrum of its weight matrices. To capitalize on this discovery, we introduce a novel regularization technique, termed Heavy-Tailed Regularization, which explicitly promotes a more heavy-tailed spectrum in the weight matrix through regularization. Firstly, we employ the Weighted Alpha and Stable Rank as penalty terms, both of which are differentiable, enabling the direct calculation of their gradients. To circumvent over-regularization, we introduce two variations of the penalty function. Then, adopting a Bayesian statistics perspective and leveraging knowledge from random matrices, we develop two novel heavy-tailed regularization methods, utilizing Powerlaw distribution and Frechet distribution as priors for the global spectrum and maximum eigenvalues, respectively. We empirically show that heavytailed regularization outperforms conventional regularization techniques in terms of generalization performance.
CVSep 11, 2024
AdvLogo: Adversarial Patch Attack against Object Detectors based on Diffusion ModelsBoming Miao, Chunxiao Li, Yao Zhu et al.
With the rapid development of deep learning, object detectors have demonstrated impressive performance; however, vulnerabilities still exist in certain scenarios. Current research exploring the vulnerabilities using adversarial patches often struggles to balance the trade-off between attack effectiveness and visual quality. To address this problem, we propose a novel framework of patch attack from semantic perspective, which we refer to as AdvLogo. Based on the hypothesis that every semantic space contains an adversarial subspace where images can cause detectors to fail in recognizing objects, we leverage the semantic understanding of the diffusion denoising process and drive the process to adversarial subareas by perturbing the latent and unconditional embeddings at the last timestep. To mitigate the distribution shift that exposes a negative impact on image quality, we apply perturbation to the latent in frequency domain with the Fourier Transform. Experimental results demonstrate that AdvLogo achieves strong attack performance while maintaining high visual quality.
CVFeb 26, 2025Code
A Sliding Layer Merging Method for Efficient Depth-Wise Pruning in LLMsXuan Ding, Rui Sun, Yunjian Zhang et al.
Compared to width-wise pruning, depth-wise pruning can significantly accelerate inference in resource-constrained scenarios. However, treating the entire Transformer layer as the minimum pruning unit may degrade model performance by indiscriminately discarding the entire information of the layer. This paper reveals the ``Patch-like'' feature relationship between layers in large language models by analyzing the correlation of the outputs of different layers in the reproducing kernel Hilbert space. Building on this observation, we propose a sliding layer merging method that dynamically selects and fuses consecutive layers from top to bottom according to a pre-defined similarity threshold, thereby simplifying the model structure while maintaining its performance. Extensive experiments on LLMs with various architectures and different parameter scales show that our method outperforms existing pruning techniques in both zero-shot inference performance and retraining recovery quality after pruning. In particular, in the experiment with 35% pruning on the Vicuna-7B model, our method achieved a 1.654% improvement in average performance on zero-shot tasks compared to the existing method. Moreover, we further reveal the potential of combining depth pruning with width pruning to enhance the pruning effect. Our codes are available at https://github.com/920927/SLM-a-sliding-layer-merging-method.
CVOct 20, 2025Code
Benchmarking Out-of-Distribution Detection for Plankton Recognition: A Systematic Evaluation of Advanced Methods in Marine Ecological MonitoringYingzi Han, Jiakai He, Chuanlong Xie et al.
Automated plankton recognition models face significant challenges during real-world deployment due to distribution shifts (Out-of-Distribution, OoD) between training and test data. This stems from plankton's complex morphologies, vast species diversity, and the continuous discovery of novel species, which leads to unpredictable errors during inference. Despite rapid advancements in OoD detection methods in recent years, the field of plankton recognition still lacks a systematic integration of the latest computer vision developments and a unified benchmark for large-scale evaluation. To address this, this paper meticulously designed a series of OoD benchmarks simulating various distribution shift scenarios based on the DYB-PlanktonNet dataset \cite{875n-f104-21}, and systematically evaluated twenty-two OoD detection methods. Extensive experimental results demonstrate that the ViM \cite{wang2022vim} method significantly outperforms other approaches in our constructed benchmarks, particularly excelling in Far-OoD scenarios with substantial improvements in key metrics. This comprehensive evaluation not only provides a reliable reference for algorithm selection in automated plankton recognition but also lays a solid foundation for future research in plankton OoD detection. To our knowledge, this study marks the first large-scale, systematic evaluation and analysis of Out-of-Distribution data detection methods in plankton recognition. Code is available at https://github.com/BlackJack0083/PlanktonOoD.
CVDec 12, 2024Code
An Efficient Framework for Enhancing Discriminative Models via Diffusion TechniquesChunxiao Li, Xiaoxiao Wang, Boming Miao et al.
Image classification serves as the cornerstone of computer vision, traditionally achieved through discriminative models based on deep neural networks. Recent advancements have introduced classification methods derived from generative models, which offer the advantage of zero-shot classification. However, these methods suffer from two main drawbacks: high computational overhead and inferior performance compared to discriminative models. Inspired by the coordinated cognitive processes of rapid-slow pathway interactions in the human brain during visual signal recognition, we propose the Diffusion-Based Discriminative Model Enhancement Framework (DBMEF). This framework seamlessly integrates discriminative and generative models in a training-free manner, leveraging discriminative models for initial predictions and endowing deep neural networks with rethinking capabilities via diffusion models. Consequently, DBMEF can effectively enhance the classification accuracy and generalization capability of discriminative models in a plug-and-play manner. We have conducted extensive experiments across 17 prevalent deep model architectures with different training methods, including both CNN-based models such as ResNet and Transformer-based models like ViT, to demonstrate the effectiveness of the proposed DBMEF. Specifically, the framework yields a 1.51\% performance improvement for ResNet-50 on the ImageNet dataset and 3.02\% on the ImageNet-A dataset. In conclusion, our research introduces a novel paradigm for image classification, demonstrating stable improvements across different datasets and neural networks. The code is available at https://github.com/ChunXiaostudy/DBMEF.
MLJan 28
Empirical Likelihood-Based Fairness Auditing: Distribution-Free Certification and FlaggingJie Tang, Chuanlong Xie, Xianli Zeng et al.
Machine learning models in high-stakes applications, such as recidivism prediction and automated personnel selection, often exhibit systematic performance disparities across sensitive subpopulations, raising critical concerns regarding algorithmic bias. Fairness auditing addresses these risks through two primary functions: certification, which verifies adherence to fairness constraints; and flagging, which isolates specific demographic groups experiencing disparate treatment. However, existing auditing techniques are frequently limited by restrictive distributional assumptions or prohibitive computational overhead. We propose a novel empirical likelihood-based (EL) framework that constructs robust statistical measures for model performance disparities. Unlike traditional methods, our approach is non-parametric; the proposed disparity statistics follow asymptotically chi-square or mixed chi-square distributions, ensuring valid inference without assuming underlying data distributions. This framework uses a constrained optimization profile that admits stable numerical solutions, facilitating both large-scale certification and efficient subpopulation discovery. Empirically, the EL methods outperform bootstrap-based approaches, yielding coverage rates closer to nominal levels while reducing computational latency by several orders of magnitude. We demonstrate the practical utility of this framework on the COMPAS dataset, where it successfully flags intersectional biases, specifically identifying a significantly higher positive prediction rate for African-American males under 25 and a systemic under-prediction for Caucasian females relative to the population mean.
LGJun 25, 2025
DipSVD: Dual-importance Protected SVD for Efficient LLM CompressionXuan Ding, Rui Sun, Yunjian Zhang et al.
The ever-increasing computational demands and deployment costs of large language models (LLMs) have spurred numerous compressing methods. Compared to quantization and unstructured pruning, SVD compression offers superior hardware compatibility and theoretical guarantees. However, existing SVD-based methods focus on the overall discrepancy between the original and compressed matrices while overlooking the protection of critical components within the matrix, which leads to inferior performance in the compressed models. This paper proposes a dual-level importance protection mechanism to enhance SVD-based compression methods: (1) local importance protection: preserving the most critical singular vectors within each weight matrix through channel-weighted data whitening; and (2) global importance protection: enabling less important layers to bear a greater portion of the compression burden through either a heuristic or optimization-based approach, thereby minimizing the impact of compression on critical layers. Extensive experiments demonstrate that DipSVD outperforms existing SVD-based compression approaches across multiple benchmarks, achieving superior model performance especially at high model compression ratios.
MLNov 3, 2024
DSDE: Using Proportion Estimation to Improve Model Selection for Out-of-Distribution DetectionJingyao Geng, Yuan Zhang, Jiaqi Huang et al.
Model library is an effective tool for improving the performance of single-model Out-of-Distribution (OoD) detector, mainly through model selection and detector fusion. However, existing methods in the literature do not provide uncertainty quantification for model selection results. Additionally, the model ensemble process primarily focuses on controlling the True Positive Rate (TPR) while neglecting the False Positive Rate (FPR). In this paper, we emphasize the significance of the proportion of models in the library that identify the test sample as an OoD sample. This proportion holds crucial information and directly influences the error rate of OoD detection.To address this, we propose inverting the commonly-used sequential p-value strategies. We define the rejection region initially and then estimate the error rate. Furthermore, we introduce a novel perspective from change-point detection and propose an approach for proportion estimation with automatic hyperparameter selection. We name the proposed approach as DOS-Storey-based Detector Ensemble (DSDE). Experimental results on CIFAR10 and CIFAR100 demonstrate the effectiveness of our approach in tackling OoD detection challenges. Specifically, the CIFAR10 experiments show that DSDE reduces the FPR from 11.07% to 3.31% compared to the top-performing single-model detector.
LGMar 16, 2024
Enhancing Out-of-Distribution Detection with Multitesting-based Layer-wise Feature FusionJiawei Li, Sitong Li, Shanshan Wang et al.
Deploying machine learning in open environments presents the challenge of encountering diverse test inputs that differ significantly from the training data. These out-of-distribution samples may exhibit shifts in local or global features compared to the training distribution. The machine learning (ML) community has responded with a number of methods aimed at distinguishing anomalous inputs from original training data. However, the majority of previous studies have primarily focused on the output layer or penultimate layer of pre-trained deep neural networks. In this paper, we propose a novel framework, Multitesting-based Layer-wise Out-of-Distribution (OOD) Detection (MLOD), to identify distributional shifts in test samples at different levels of features through rigorous multiple testing procedure. Our approach distinguishes itself from existing methods as it does not require modifying the structure or fine-tuning of the pre-trained classifier. Through extensive experiments, we demonstrate that our proposed framework can seamlessly integrate with any existing distance-based inspection method while efficiently utilizing feature extractors of varying depths. Our scheme effectively enhances the performance of out-of-distribution detection when compared to baseline methods. In particular, MLOD-Fisher achieves superior performance in general. When trained using KNN on CIFAR10, MLOD-Fisher significantly lowers the false positive rate (FPR) from 24.09% to 7.47% on average compared to merely utilizing the features of the last layer.
MLAug 12, 2025
In-Context Learning as Nonparametric Conditional Probability Estimation: Risk Bounds and OptimalityChenrui Liu, Falong Tan, Chuanlong Xie et al.
This paper investigates the expected excess risk of in-context learning (ICL) for multiclass classification. We formalize each task as a sequence of labeled examples followed by a query input; a pretrained model then estimates the query's conditional class probabilities. The expected excess risk is defined as the average truncated Kullback-Leibler (KL) divergence between the predicted and true conditional class distributions over a specified family of tasks. We establish a new oracle inequality for this risk, based on KL divergence, in multiclass classification. This yields tight upper and lower bounds for transformer-based models, showing that the ICL estimator achieves the minimax optimal rate (up to logarithmic factors) for conditional probability estimation. From a technical standpoint, our results introduce a novel method for controlling generalization error via uniform empirical entropy. We further demonstrate that multilayer perceptrons (MLPs) can also perform ICL and attain the same optimal rate (up to logarithmic factors) under suitable assumptions, suggesting that effective ICL need not be exclusive to transformer architectures.
CVJun 15, 2024
Technique Report of CVPR 2024 PBDL ChallengesYing Fu, Yu Li, Shaodi You et al.
The intersection of physics-based vision and deep learning presents an exciting frontier for advancing computer vision technologies. By leveraging the principles of physics to inform and enhance deep learning models, we can develop more robust and accurate vision systems. Physics-based vision aims to invert the processes to recover scene properties such as shape, reflectance, light distribution, and medium properties from images. In recent years, deep learning has shown promising improvements for various vision tasks, and when combined with physics-based vision, these approaches can enhance the robustness and accuracy of vision systems. This technical report summarizes the outcomes of the Physics-Based Vision Meets Deep Learning (PBDL) 2024 challenge, held in CVPR 2024 workshop. The challenge consisted of eight tracks, focusing on Low-Light Enhancement and Detection as well as High Dynamic Range (HDR) Imaging. This report details the objectives, methodologies, and results of each track, highlighting the top-performing solutions and their innovative approaches.
LGNov 9, 2021
MixACM: Mixup-Based Robustness Transfer via Distillation of Activated Channel MapsMuhammad Awais, Fengwei Zhou, Chuanlong Xie et al.
Deep neural networks are susceptible to adversarially crafted, small and imperceptible changes in the natural inputs. The most effective defense mechanism against these examples is adversarial training which constructs adversarial examples during training by iterative maximization of loss. The model is then trained to minimize the loss on these constructed examples. This min-max optimization requires more data, larger capacity models, and additional computing resources. It also degrades the standard generalization performance of a model. Can we achieve robustness more efficiently? In this work, we explore this question from the perspective of knowledge transfer. First, we theoretically show the transferability of robustness from an adversarially trained teacher model to a student model with the help of mixup augmentation. Second, we propose a novel robustness transfer method called Mixup-Based Activated Channel Maps (MixACM) Transfer. MixACM transfers robustness from a robust teacher to a student by matching activated channel maps generated without expensive adversarial perturbations. Finally, extensive experiments on multiple datasets and different learning scenarios show our method can transfer robustness while also improving generalization on natural images.
CVAug 7, 2021
NASOA: Towards Faster Task-oriented Online Fine-tuning with a Zoo of ModelsHang Xu, Ning Kang, Gengwei Zhang et al.
Fine-tuning from pre-trained ImageNet models has been a simple, effective, and popular approach for various computer vision tasks. The common practice of fine-tuning is to adopt a default hyperparameter setting with a fixed pre-trained model, while both of them are not optimized for specific tasks and time constraints. Moreover, in cloud computing or GPU clusters where the tasks arrive sequentially in a stream, faster online fine-tuning is a more desired and realistic strategy for saving money, energy consumption, and CO2 emission. In this paper, we propose a joint Neural Architecture Search and Online Adaption framework named NASOA towards a faster task-oriented fine-tuning upon the request of users. Specifically, NASOA first adopts an offline NAS to identify a group of training-efficient networks to form a pretrained model zoo. We propose a novel joint block and macro-level search space to enable a flexible and efficient search. Then, by estimating fine-tuning performance via an adaptive model by accumulating experience from the past tasks, an online schedule generator is proposed to pick up the most suitable model and generate a personalized training regime with respect to each desired task in a one-shot fashion. The resulting model zoo is more training efficient than SOTA models, e.g. 6x faster than RegNetY-16GF, and 1.7x faster than EfficientNetB3. Experiments on multiple datasets also show that NASOA achieves much better fine-tuning results, i.e. improving around 2.1% accuracy than the best performance in RegNet series under various constraints and tasks; 40x faster compared to the BOHB.
LGJun 8, 2021
Towards a Theoretical Framework of Out-of-Distribution GeneralizationHaotian Ye, Chuanlong Xie, Tianle Cai et al.
Generalization to out-of-distribution (OOD) data is one of the central problems in modern machine learning. Recently, there is a surge of attempts to propose algorithms that mainly build upon the idea of extracting invariant features. Although intuitively reasonable, theoretical understanding of what kind of invariance can guarantee OOD generalization is still limited, and generalization to arbitrary out-of-distribution is clearly impossible. In this work, we take the first step towards rigorous and quantitative definitions of 1) what is OOD; and 2) what does it mean by saying an OOD problem is learnable. We also introduce a new concept of expansion function, which characterizes to what extent the variance is amplified in the test domains over the training domains, and therefore give a quantitative meaning of invariant features. Based on these, we prove OOD generalization error bounds. It turns out that OOD generalization largely depends on the expansion function. As recently pointed out by Gulrajani and Lopez-Paz (2020), any OOD learning algorithm without a model selection module is incomplete. Our theory naturally induces a model selection criterion. Extensive experiments on benchmark OOD datasets demonstrate that our model selection criterion has a significant advantage over baselines.
LGJan 21, 2021
Out-of-Distribution Generalization Analysis via Influence FunctionHaotian Ye, Chuanlong Xie, Yue Liu et al.
The mismatch between training and target data is one major challenge for current machine learning systems. When training data is collected from multiple domains and the target domains include all training domains and other new domains, we are facing an Out-of-Distribution (OOD) generalization problem that aims to find a model with the best OOD accuracy. One of the definitions of OOD accuracy is worst-domain accuracy. In general, the set of target domains is unknown, and the worst over target domains may be unseen when the number of observed domains is limited. In this paper, we show that the worst accuracy over the observed domains may dramatically fail to identify the OOD accuracy. To this end, we introduce Influence Function, a classical tool from robust statistics, into the OOD generalization problem and suggest the variance of influence function to monitor the stability of a model on training domains. We show that the accuracy on test domains and the proposed index together can help us discern whether OOD algorithms are needed and whether a model achieves good OOD generalization.
LGDec 22, 2020
MetaAugment: Sample-Aware Data Augmentation Policy LearningFengwei Zhou, Jiawei Li, Chuanlong Xie et al.
Automated data augmentation has shown superior performance in image recognition. Existing works search for dataset-level augmentation policies without considering individual sample variations, which are likely to be sub-optimal. On the other hand, learning different policies for different samples naively could greatly increase the computing cost. In this paper, we learn a sample-aware data augmentation policy efficiently by formulating it as a sample reweighting problem. Specifically, an augmentation policy network takes a transformation and the corresponding augmented image as inputs, and outputs a weight to adjust the augmented image loss computed by a task network. At training stage, the task network minimizes the weighted losses of augmented training images, while the policy network minimizes the loss of the task network on a validation set via meta-learning. We theoretically prove the convergence of the training procedure and further derive the exact convergence rate. Superior performance is achieved on widely-used benchmarks including CIFAR-10/100, Omniglot, and ImageNet.
MLAug 14, 2020
Provable More Data Hurt in High Dimensional Least Squares EstimatorZeng Li, Chuanlong Xie, Qinwen Wang
This paper investigates the finite-sample prediction risk of the high-dimensional least squares estimator. We derive the central limit theorem for the prediction risk when both the sample size and the number of features tend to infinity. Furthermore, the finite-sample distribution and the confidence interval of the prediction risk are provided. Our theoretical results demonstrate the sample-wise nonmonotonicity of the prediction risk and confirm "more data hurt" phenomenon.
LGJun 13, 2020
Risk Variance PenalizationChuanlong Xie, Haotian Ye, Fei Chen et al.
The key of the out-of-distribution (OOD) generalization is to generalize invariance from training domains to target domains. The variance risk extrapolation (V-REx) is a practical OOD method, which depends on a domain-level regularization but lacks theoretical verifications about its motivation and utility. This article provides theoretical insights into V-REx by studying a variance-based regularizer. We propose Risk Variance Penalization (RVP), which slightly changes the regularization of V-REx but addresses the theory concerns about V-REx. We provide theoretical explanations and a theory-inspired tuning scheme for the regularization parameter of RVP. Our results point out that RVP discovers a robust predictor. Finally, we experimentally show that the proposed regularizer can find an invariant predictor under certain conditions.