Yunlong Feng

Binyuan Hui, Jian Yang, Zeyu Cui et al.

In this report, we introduce the Qwen2.5-Coder series, a significant upgrade from its predecessor, CodeQwen1.5. This series includes six models: Qwen2.5-Coder-(0.5B/1.5B/3B/7B/14B/32B). As a code-specific model, Qwen2.5-Coder is built upon the Qwen2.5 architecture and continues pretrained on a vast corpus of over 5.5 trillion tokens. Through meticulous data cleaning, scalable synthetic data generation, and balanced data mixing, Qwen2.5-Coder demonstrates impressive code generation capabilities while retaining general and math skills. These models have been evaluated on a wide range of code-related tasks, achieving state-of-the-art (SOTA) performance across more than 10 benchmarks, including code generation, completion, reasoning, and repair, consistently outperforming larger models of the same model size. We believe that the release of the Qwen2.5-Coder series will advance research in code intelligence and, with its permissive licensing, support wider adoption by developers in real-world applications.

Bohan Li, Xiao Xu, Xinghao Wang et al.

Existing image augmentation methods consist of two categories: perturbation-based methods and generative methods. Perturbation-based methods apply pre-defined perturbations to augment an original image, but only locally vary the image, thus lacking image diversity. In contrast, generative methods bring more image diversity in the augmented images but may not preserve semantic consistency, thus incorrectly changing the essential semantics of the original image. To balance image diversity and semantic consistency in augmented images, we propose SGID, a Semantic-guided Generative Image augmentation method with Diffusion models for image classification. Specifically, SGID employs diffusion models to generate augmented images with good image diversity. More importantly, SGID takes image labels and captions as guidance to maintain semantic consistency between the augmented and original images. Experimental results show that SGID outperforms the best augmentation baseline by 1.72% on ResNet-50 (from scratch), 0.33% on ViT (ImageNet-21k), and 0.14% on CLIP-ViT (LAION-2B). Moreover, SGID can be combined with other image augmentation baselines and further improves the overall performance. We demonstrate the semantic consistency and image diversity of SGID through quantitative human and automated evaluations, as well as qualitative case studies.

Bohan Li, Longxu Dou, Yutai Hou et al.

Prompt-based learning has shown considerable promise in reformulating various downstream tasks as cloze problems by combining original input with a predetermined template. This approach demonstrates its effectiveness, especially in few-shot learning scenarios, where the model is trained on a scarce amount of data. Despite its successes, the limited templates and text in few-shot prompt-based learning scenarios leave significant room for performance improvement. Moreover, existing methods sometimes resort to model ensembles, which, while effective, could potentially hamper model efficiency due to increased computational demands. To address these issues, we introduce MixPro, an augmentation method designed to augment both the vanilla input text and the templates. We implement this through the token-level, the sentence-level, and the template-level Mixup strategies. The experimental results on five few-shot datasets show that MixPro outperforms other augmentation baselines, improving model performance by an average of 5.08% compared to before augmentation.

Yunlong Feng, Bohan Li, Libo Qin et al.

Cross-domain text classification aims to adapt models to a target domain that lacks labeled data. It leverages or reuses rich labeled data from the different but related source domain(s) and unlabeled data from the target domain. To this end, previous work focuses on either extracting domain-invariant features or task-agnostic features, ignoring domain-aware features that may be present in the target domain and could be useful for the downstream task. In this paper, we propose a two-stage framework for cross-domain text classification. In the first stage, we finetune the model with mask language modeling (MLM) and labeled data from the source domain. In the second stage, we further fine-tune the model with self-supervised distillation (SSD) and unlabeled data from the target domain. We evaluate its performance on a public cross-domain text classification benchmark and the experiment results show that our method achieves new state-of-the-art results for both single-source domain adaptations (94.17% $\uparrow$1.03%) and multi-source domain adaptations (95.09% $\uparrow$1.34%).

Mouxiang Chen, Lei Zhang, Yunlong Feng et al.

We propose SWE-Universe, a scalable and efficient framework for automatically constructing real-world software engineering (SWE) verifiable environments from GitHub pull requests (PRs). To overcome the prevalent challenges of automatic building, such as low production yield, weak verifiers, and prohibitive cost, our framework utilizes a building agent powered by an efficient custom-trained model. This agent employs iterative self-verification and in-loop hacking detection to ensure the reliable generation of high-fidelity, verifiable tasks. Using this method, we scale the number of real-world multilingual SWE environments to a million scale (807,693). We demonstrate the profound value of our environments through large-scale agentic mid-training and reinforcement learning. Finally, we applied this technique to Qwen3-Max-Thinking and achieved a score of 75.3% on SWE-Bench Verified. Our work provides both a critical resource and a robust methodology to advance the next generation of coding agents.

Shanghaoran Quan, Jiaxi Yang, Bowen Yu et al.

With the increasing code reasoning capabilities of existing large language models (LLMs) and breakthroughs in reasoning models like OpenAI o1 and o3, there is a growing need to develop more challenging and comprehensive benchmarks that effectively test their sophisticated competition-level coding abilities. Existing benchmarks, like LiveCodeBench and USACO, fall short due to the unavailability of private test cases, lack of support for special judges, and misaligned execution environments. To bridge this gap, we introduce CodeElo, a standardized competition-level code generation benchmark that effectively addresses all these challenges for the first time. CodeElo benchmark is mainly based on the official CodeForces platform and tries to align with the platform as much as possible. We compile the recent six months of contest problems on CodeForces with detailed information such as contest divisions, problem difficulty ratings, and problem algorithm tags. We introduce a unique judging method in which problems are submitted directly to the platform and develop a reliable Elo rating calculation system that aligns with the platform and is comparable with human participants but has lower variance. By testing on our CodeElo, we provide the Elo ratings of 30 existing popular open-source and 3 proprietary LLMs for the first time. The results show that o1-mini and QwQ-32B-Preview stand out significantly, achieving Elo ratings of 1578 and 1261, respectively, while other models struggle even with the easiest problems, placing in the lowest 25 percent among all human participants. Detailed analysis experiments are also conducted to provide insights into performance across algorithms and comparisons between using C++ and Python, which can suggest directions for future studies.

Yang Xu, Yunlong Feng, Honglin Mu et al.

Through reading the documentation in the context, tool-using language models can dynamically extend their capability using external tools. The cost is that we have to input lengthy documentation every time the model needs to use the tool, occupying the input window as well as slowing down the decoding process. Given the progress in general-purpose compression, soft context compression is a suitable approach to alleviate the problem. However, when compressing tool documentation, existing methods suffer from the weaknesses of key information loss (specifically, tool/parameter name errors) and difficulty in adjusting the length of compressed sequences based on documentation lengths. To address these problems, we propose two strategies for compressing tool documentation into concise and precise summary sequences for tool-using language models. 1) Selective compression strategy mitigates key information loss by deliberately retaining key information as raw text tokens. 2) Block compression strategy involves dividing tool documentation into short chunks and then employing a fixed-length compression model to achieve variable-length compression. This strategy facilitates the flexible adjustment of the compression ratio. Results on API-Bank and APIBench show that our approach reaches a performance comparable to the upper-bound baseline under up to 16x compression ratio.

Jianbo Dai, Jianqiao Lu, Yunlong Feng et al.

Recent advancements in large language models (LLMs) have greatly improved code generation, specifically at the function level. For instance, GPT-4o has achieved a 91.0\% pass rate on HumanEval. However, this draws into question the adequacy of existing benchmarks in thoroughly assessing function-level code generation capabilities. Our study analyzed two common benchmarks, HumanEval and MBPP, and found that these might not thoroughly evaluate LLMs' code generation capacities due to limitations in quality, difficulty, and granularity. To resolve this, we introduce the Mostly Hard Python Problems (MHPP) dataset, consisting of 210 unique human-curated problems. By focusing on the combination of natural language and code reasoning, MHPP gauges LLMs' abilities to comprehend specifications and restrictions, engage in multi-step reasoning, and apply coding knowledge effectively. Initial evaluations of 26 LLMs using MHPP showed many high-performing models on HumanEval failed to achieve similar success on MHPP. Moreover, MHPP highlighted various previously undiscovered limitations within various LLMs, leading us to believe that it could pave the way for a better understanding of LLMs' capabilities and limitations. MHPP, evaluation pipeline, and leaderboard can be found in https://github.com/SparksofAGI/MHPP.

Bohan Li, Jiannan Guan, Longxu Dou et al.

The Myers-Briggs Type Indicator (MBTI) is one of the most influential personality theories reflecting individual differences in thinking, feeling, and behaving. MBTI personality detection has garnered considerable research interest and has evolved significantly over the years. However, this task tends to be overly optimistic, as it currently does not align well with the natural distribution of population personality traits. Specifically, (1) the self-reported labels in existing datasets result in incorrect labeling issues, and (2) the hard labels fail to capture the full range of population personality distributions. In this paper, we optimize the task by constructing MBTIBench, the first manually annotated high-quality MBTI personality detection dataset with soft labels, under the guidance of psychologists. As for the first challenge, MBTIBench effectively solves the incorrect labeling issues, which account for 29.58% of the data. As for the second challenge, we estimate soft labels by deriving the polarity tendency of samples. The obtained soft labels confirm that there are more people with non-extreme personality traits. Experimental results not only highlight the polarized predictions and biases in LLMs as key directions for future research, but also confirm that soft labels can provide more benefits to other psychological tasks than hard labels. The code and data are available at https://github.com/Personality-NLP/MbtiBench.

Hang Su, Yunlong Feng, Daniel Gehrig et al.

Structure and continuous motion estimation from point correspondences is a fundamental problem in computer vision that has been powered by well-known algorithms such as the familiar 5-point or 8-point algorithm. However, despite their acclaim, these algorithms are limited to processing point correspondences originating from a pair of views each one representing an instantaneous capture of the scene. Yet, in the case of rolling shutter cameras, or more recently, event cameras, this synchronization breaks down. In this work, we present a unified approach for structure and linear motion estimation from 2D point correspondences with arbitrary timestamps, from an arbitrary set of views. By formulating the problem in terms of first-order dynamics and leveraging a constant velocity motion model, we derive a novel, linear point incidence relation allowing for the efficient recovery of both linear velocity and 3D points with predictable degeneracies and solution multiplicities. Owing to its general formulation, it can handle correspondences from a wide range of sensing modalities such as global shutter, rolling shutter, and event cameras, and can even combine correspondences from different collocated sensors. We validate the effectiveness of our solver on both simulated and real-world data, where we show consistent improvement across all modalities when compared to recent approaches. We believe our work opens the door to efficient structure and motion estimation from asynchronous data. Code can be found at https://github.com/suhang99/AsyncTrack-Motion-Solver.

Yunlong Feng, Dechuan Teng, Yang Xu et al.

Decompilation transforms compiled code back into a high-level programming language for analysis when source code is unavailable. Previous work has primarily focused on enhancing decompilation performance by increasing the scale of model parameters or training data for pre-training. Based on the characteristics of the decompilation task, we propose two methods: (1) Without fine-tuning, the Self-Constructed Context Decompilation (sc$^2$dec) method recompiles the LLM's decompilation results to construct pairs for in-context learning, helping the model improve decompilation performance. (2) Fine-grained Alignment Enhancement (FAE), which meticulously aligns assembly code with source code at the statement level by leveraging debugging information, is employed during the fine-tuning phase to achieve further improvements in decompilation. By integrating these two methods, we achieved a Re-Executability performance improvement of approximately 3.90% on the Decompile-Eval benchmark, establishing a new state-of-the-art performance of 52.41%. The code, data, and models are available at https://github.com/AlongWY/sccdec.

Libo Qin, Qiguang Chen, Xiao Xu et al.

Spoken Language Understanding (SLU) is one of the core components of a task-oriented dialogue system, which aims to extract the semantic meaning of user queries (e.g., intents and slots). In this work, we introduce OpenSLU, an open-source toolkit to provide a unified, modularized, and extensible toolkit for spoken language understanding. Specifically, OpenSLU unifies 10 SLU models for both single-intent and multi-intent scenarios, which support both non-pretrained and pretrained models simultaneously. Additionally, OpenSLU is highly modularized and extensible by decomposing the model architecture, inference, and learning process into reusable modules, which allows researchers to quickly set up SLU experiments with highly flexible configurations. OpenSLU is implemented based on PyTorch, and released at \url{https://github.com/LightChen233/OpenSLU}.

Wanxiang Che, Yunlong Feng, Libo Qin et al.

We introduce \texttt{N-LTP}, an open-source neural language technology platform supporting six fundamental Chinese NLP tasks: {lexical analysis} (Chinese word segmentation, part-of-speech tagging, and named entity recognition), {syntactic parsing} (dependency parsing), and {semantic parsing} (semantic dependency parsing and semantic role labeling). Unlike the existing state-of-the-art toolkits, such as \texttt{Stanza}, that adopt an independent model for each task, \texttt{N-LTP} adopts the multi-task framework by using a shared pre-trained model, which has the advantage of capturing the shared knowledge across relevant Chinese tasks. In addition, a knowledge distillation method \cite{DBLP:journals/corr/abs-1907-04829} where the single-task model teaches the multi-task model is further introduced to encourage the multi-task model to surpass its single-task teacher. Finally, we provide a collection of easy-to-use APIs and a visualization tool to make users to use and view the processing results more easily and directly. To the best of our knowledge, this is the first toolkit to support six Chinese NLP fundamental tasks. Source code, documentation, and pre-trained models are available at \url{https://github.com/HIT-SCIR/ltp}.

Yunlong Feng, Yang Xu, Libo Qin et al.

Large-scale high-quality training data is important for improving the performance of models. After trained with data that has rationales (reasoning steps), models gain reasoning capability. However, the dataset with high-quality rationales is relatively scarce due to the high annotation cost. To address this issue, we propose \textit{Self-motivated Learning} framework. The framework motivates the model itself to automatically generate rationales on existing datasets. Based on the inherent rank from correctness across multiple rationales, the model learns to generate better rationales, leading to higher reasoning capability. Specifically, we train a reward model with the rank to evaluate the quality of rationales, and improve the performance of reasoning through reinforcement learning. Experiment results of Llama2 7B on multiple reasoning datasets show that our method significantly improves the reasoning ability of models, even outperforming text-davinci-002 in some datasets.

Honglin Mu, Yang Xu, Yunlong Feng et al.

With the rise of Large Language Models (LLMs), AI assistants' ability to utilize tools, especially through API calls, has advanced notably. This progress has necessitated more accurate evaluation methods. Many existing studies adopt static evaluation, where they assess AI assistants' API call based on pre-defined dialogue histories. However, such evaluation method can be misleading, as an AI assistant might fail in generating API calls from preceding human interaction in real cases. Instead of the resource-intensive method of direct human-machine interactions, we propose Automated Dynamic Evaluation (AutoDE) to assess an assistant's API call capability without human involvement. In our framework, we endeavor to closely mirror genuine human conversation patterns in human-machine interactions, using a LLM-based user agent, equipped with a user script to ensure human alignment. Experimental results highlight that AutoDE uncovers errors overlooked by static evaluations, aligning more closely with human assessment. Testing four AI assistants using our crafted benchmark, our method further mirrored human evaluation compared to conventional static evaluations.

Honglin Mu, Han He, Yuxin Zhou et al.

Large language model (LLM) safety is a critical issue, with numerous studies employing red team testing to enhance model security. Among these, jailbreak methods explore potential vulnerabilities by crafting malicious prompts that induce model outputs contrary to safety alignments. Existing black-box jailbreak methods often rely on model feedback, repeatedly submitting queries with detectable malicious instructions during the attack search process. Although these approaches are effective, the attacks may be intercepted by content moderators during the search process. We propose an improved transfer attack method that guides malicious prompt construction by locally training a mirror model of the target black-box model through benign data distillation. This method offers enhanced stealth, as it does not involve submitting identifiable malicious instructions to the target model during the search phase. Our approach achieved a maximum attack success rate of 92%, or a balanced value of 80% with an average of 1.5 detectable jailbreak queries per sample against GPT-3.5 Turbo on a subset of AdvBench. These results underscore the need for more robust defense mechanisms.

Yunlong Feng, Yang Xu, Xiao Xu et al.

While code large language models have demonstrated remarkable progress in code generation, the generated code often exhibits poor runtime efficiency, limiting its practical application in performance-sensitive scenarios. To address this limitation, we propose an efficiency-oriented reinforcement learning framework guided by a novel performance reward. Based on this framework, we take a deeper dive into the code efficiency problem, identifying then proposing methods to overcome key bottlenecks: (1) Dynamic exploration overcomes the static data constraints of offline fine-tuning, enabling the discovery of more efficient code implementations. (2) The error-insensitive reinforcement learning method and high-contrast efficiency signals are crucial for mitigating systematic errors and achieving effective optimization. (3) Online exploration is most effective when starting from a high-correctness baseline, as this allows for efficiency improvements without sacrificing accuracy. With these discoveries, we finally propose a two-stage tuning method, which achieves high and balanced performance across correctness and efficiency. The results of experiments show the effectiveness of the method, which improves code correctness by 10.18\% and runtime efficiency by 7.75\% on a 7B model, achieving performance comparable to much larger model.

Yunlong Feng, Qiang Wu

We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_σ$. Using Huber regression as a close-up example within Tikhonov-regularized risk minimization in reproducing kernel Hilbert spaces (RKHS), we address two central challenges: (i) the breakdown of standard concentration tools under weak moment assumptions, and (ii) the analytical difficulties introduced by unbounded hypothesis spaces. Our first message is conceptual: conventional generalization-error bounds for robust losses do not faithfully capture out-of-sample performance. We argue that learnability should instead be quantified through prediction error, namely the $L_2$-distance to the truth $f^\star$, which is $σ$-independent and directly reflects the target of robust estimation. To make this workable under unboundedness, we introduce a \emph{probabilistic effective hypothesis space} that confines the estimator with high probability and enables a meaningful bias--variance decomposition under weak $(1+ε)$-moment conditions. Technically, we establish new comparison theorems linking the excess robust risk to the $L_2$ prediction error up to a residual of order $\mathcal{O}(σ^{-2ε})$, clarifying the robustness--bias trade-off induced by the scale parameter $σ$. Building on this, we derive explicit finite-sample error bounds and convergence rates for Huber regression in RKHS that hold without uniform boundedness and under heavy-tailed noise. Our study delivers principled tuning rules, extends beyond Huber to other robust losses, and highlights prediction error, not excess generalization risk, as the fundamental lens for analyzing robust learning.

Renxi Wang, Honglin Mu, Liqun Ma et al.

Evaluating large language models' (LLMs) long-context understanding capabilities remains challenging. We present SCALAR (Scientific Citation-based Live Assessment of Long-context Academic Reasoning), a novel benchmark that leverages academic papers and their citation networks. SCALAR features automatic generation of high-quality ground truth labels without human annotation, controllable difficulty levels, and a dynamic updating mechanism that prevents data contamination. Using ICLR 2025 papers, we evaluate 8 state-of-the-art LLMs, revealing key insights about their capabilities and limitations in processing long scientific documents across different context lengths and reasoning types. Our benchmark provides a reliable and sustainable way to track progress in long-context understanding as LLM capabilities evolve.

Haochen Tan, Zhijiang Guo, Zhan Shi et al.

Large Language Models (LLMs) have succeeded remarkably in understanding long-form contents. However, exploring their capability for generating long-form contents, such as reports and articles, has been relatively unexplored and inadequately assessed by existing benchmarks. The prevalent evaluation methods, which predominantly rely on crowdsourcing, are recognized for their labor-intensive nature and lack of efficiency, whereas automated metrics, such as the ROUGE score, demonstrate discordance with human judgment criteria. In this paper, we propose ProxyQA, an innovative framework dedicated to assessing long-text generation. ProxyQA comprises in-depth human-curated meta-questions spanning various domains, each accompanied by specific proxy-questions with pre-annotated answers. LLMs are tasked to generate extensive content in response to these meta-questions, by engaging an evaluator and incorporating the generated texts as contextual background, ProxyQA assesses the generated content's quality through the evaluator's accuracy in addressing the proxy-questions. We examine multiple LLMs, emphasizing ProxyQA's demanding nature as a high-quality assessment tool. Human evaluation demonstrates that the proxy-question method is notably self-consistent and aligns closely with human evaluative standards. The dataset and leaderboard is available at \url{https://proxy-qa.com}.

Yunlong Feng, Qiang Wu

We develop in this paper a framework of empirical gain maximization (EGM) to address the robust regression problem where heavy-tailed noise or outliers may present in the response variable. The idea of EGM is to approximate the density function of the noise distribution instead of approximating the truth function directly as usual. Unlike the classical maximum likelihood estimation that encourages equal importance of all observations and could be problematic in the presence of abnormal observations, EGM schemes can be interpreted from a minimum distance estimation viewpoint and allow the ignorance of those observations. Furthermore, it is shown that several well-known robust nonconvex regression paradigms, such as Tukey regression and truncated least square regression, can be reformulated into this new framework. We then develop a learning theory for EGM, by means of which a unified analysis can be conducted for these well-established but not fully-understood regression approaches. Resulting from the new framework, a novel interpretation of existing bounded nonconvex loss functions can be concluded. Within this new framework, the two seemingly irrelevant terminologies, the well-known Tukey's biweight loss for robust regression and the triweight kernel for nonparametric smoothing, are closely related. More precisely, it is shown that the Tukey's biweight loss can be derived from the triweight kernel. Similarly, other frequently employed bounded nonconvex loss functions in machine learning such as the truncated square loss, the Geman-McClure loss, and the exponential squared loss can also be reformulated from certain smoothing kernels in statistics. In addition, the new framework enables us to devise new bounded nonconvex loss functions for robust learning.

Yunlong Feng, Qiang Wu

As one of the triumphs and milestones of robust statistics, Huber regression plays an important role in robust inference and estimation. It has also been finding a great variety of applications in machine learning. In a parametric setup, it has been extensively studied. However, in the statistical learning context where a function is typically learned in a nonparametric way, there is still a lack of theoretical understanding of how Huber regression estimators learn the conditional mean function and why it works in the absence of light-tailed noise assumptions. To address these fundamental questions, we conduct an assessment of Huber regression from a statistical learning viewpoint. First, we show that the usual risk consistency property of Huber regression estimators, which is usually pursued in machine learning, cannot guarantee their learnability in mean regression. Second, we argue that Huber regression should be implemented in an adaptive way to perform mean regression, implying that one needs to tune the scale parameter in accordance with the sample size and the moment condition of the noise. Third, with an adaptive choice of the scale parameter, we demonstrate that Huber regression estimators can be asymptotic mean regression calibrated under $(1+ε)$-moment conditions ($ε>0$). Last but not least, under the same moment conditions, we establish almost sure convergence rates for Huber regression estimators. Note that the $(1+ε)$-moment conditions accommodate the special case where the response variable possesses infinite variance and so the established convergence rates justify the robustness feature of Huber regression estimators. In the above senses, the present study provides a systematic statistical learning assessment of Huber regression estimators and justifies their merits in terms of robustness from a theoretical viewpoint.

Yunlong Feng

Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively explored and studied. Its application to regression problems leads to the robustness enhanced regression paradigm -- namely, correntropy based regression. Having drawn a great variety of successful real-world applications, its theoretical properties have also been investigated recently in a series of studies from a statistical learning viewpoint. The resulting big picture is that correntropy based regression regresses towards the conditional mode function or the conditional mean function robustly under certain conditions. Continuing this trend and going further, in the present study, we report some new insights into this problem. First, we show that under the additive noise regression model, such a regression paradigm can be deduced from minimum distance estimation, implying that the resulting estimator is essentially a minimum distance estimator and thus possesses robustness properties. Second, we show that the regression paradigm, in fact, provides a unified approach to regression problems in that it approaches the conditional mean, the conditional mode, as well as the conditional median functions under certain conditions. Third, we present some new results when it is utilized to learn the conditional mean function by developing its error bounds and exponential convergence rates under conditional $(1+ε)$-moment assumptions. The saturation effect on the established convergence rates, which was observed under $(1+ε)$-moment assumptions, still occurs, indicating the inherent bias of the regression estimator. These novel insights deepen our understanding of correntropy based regression, help cement the theoretic correntropy framework, and also enable us to investigate learning schemes induced by general bounded nonconvex loss functions.

Yunlong Feng, Yiming Ying

In recent years, correntropy and its applications in machine learning have been drawing continuous attention owing to its merits in dealing with non-Gaussian noise and outliers. However, theoretical understanding of correntropy, especially in the statistical learning context, is still limited. In this study, within the statistical learning framework, we investigate correntropy based regression in the presence of non-Gaussian noise or outliers. Motivated by the practical way of generating non-Gaussian noise or outliers, we introduce mixture of symmetric stable noise, which include Gaussian noise, Cauchy noise, and their mixture as special cases, to model non-Gaussian noise or outliers. We demonstrate that under the mixture of symmetric stable noise assumption, correntropy based regression can learn the conditional mean function or the conditional median function well without resorting to the finite-variance or even the finite first-order moment condition on the noise. In particular, for the above two cases, we establish asymptotic optimal learning rates for correntropy based regression estimators that are asymptotically of type $\mathcal{O}(n^{-1})$. These results justify the effectiveness of the correntropy based regression estimators in dealing with outliers as well as non-Gaussian noise. We believe that the present study completes our understanding towards correntropy based regression from a statistical learning viewpoint, and may also shed some light on robust statistical learning for regression.

Yunlong Feng, Jun Fan, Johan A. K. Suykens

This paper studies the nonparametric modal regression problem systematically from a statistical learning view. Originally motivated by pursuing a theoretical understanding of the maximum correntropy criterion based regression (MCCR), our study reveals that MCCR with a tending-to-zero scale parameter is essentially modal regression. We show that nonparametric modal regression problem can be approached via the classical empirical risk minimization. Some efforts are then made to develop a framework for analyzing and implementing modal regression. For instance, the modal regression function is described, the modal regression risk is defined explicitly and its \textit{Bayes} rule is characterized; for the sake of computational tractability, the surrogate modal regression risk, which is termed as the generalization risk in our study, is introduced. On the theoretical side, the excess modal regression risk, the excess generalization risk, the function estimation error, and the relations among the above three quantities are studied rigorously. It turns out that under mild conditions, function estimation consistency and convergence may be pursued in modal regression as in vanilla regression protocols, such as mean regression, median regression, and quantile regression. However, it outperforms these regression models in terms of robustness as shown in our study from a re-descending M-estimation view. This coincides with and in return explains the merits of MCCR on robustness. On the practical side, the implementation issues of modal regression including the computational algorithm and the tuning parameters selection are discussed. Numerical assessments on modal regression are also conducted to verify our findings empirically.

Hanyuan Hang, Ingo Steinwart, Yunlong Feng et al.

We study the density estimation problem with observations generated by certain dynamical systems that admit a unique underlying invariant Lebesgue density. Observations drawn from dynamical systems are not independent and moreover, usual mixing concepts may not be appropriate for measuring the dependence among these observations. By employing the $\mathcal{C}$-mixing concept to measure the dependence, we conduct statistical analysis on the consistency and convergence of the kernel density estimator. Our main results are as follows: First, we show that with properly chosen bandwidth, the kernel density estimator is universally consistent under $L_1$-norm; Second, we establish convergence rates for the estimator with respect to several classes of dynamical systems under $L_1$-norm. In the analysis, the density function $f$ is only assumed to be Hölder continuous which is a weak assumption in the literature of nonparametric density estimation and also more realistic in the dynamical system context. Last but not least, we prove that the same convergence rates of the estimator under $L_\infty$-norm and $L_1$-norm can be achieved when the density function is Hölder continuous, compactly supported and bounded. The bandwidth selection problem of the kernel density estimator for dynamical system is also discussed in our study via numerical simulations.

Hanyuan Hang, Yunlong Feng, Ingo Steinwart et al.

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a unified treatment on analyzing the learning schemes with various mixing processes can be conducted and a sharp oracle inequality for generic regularized empirical risk minimization schemes can be established. The obtained oracle inequality is then applied to derive convergence rates for several learning schemes such as empirical risk minimization (ERM), least squares support vector machines (LS-SVMs) using given generic kernels, and SVMs using Gaussian kernels for both least squares and quantile regression. It turns out that for i.i.d.~processes, our learning rates for ERM recover the optimal rates. On the other hand, for non-i.i.d.~processes including geometrically $α$-mixing Markov processes, geometrically $α$-mixing processes with restricted decay, $φ$-mixing processes, and (time-reversed) geometrically $\mathcal{C}$-mixing processes, our learning rates for SVMs with Gaussian kernels match, up to some arbitrarily small extra term in the exponent, the optimal rates. For the remaining cases, our rates are at least close to the optimal rates. As a by-product, the assumed generalized Bernstein-type inequality also provides an interpretation of the so-called "effective number of observations" for various mixing processes.