Zhiyu Zhang

Zhiyu Zhang, Ashok Cutkosky, Ioannis Ch. Paschalidis · harvard

Motivated by the challenge of nonstationarity in sequential decision making, we study Online Convex Optimization (OCO) under the coupling of two problem structures: the domain is unbounded, and the comparator sequence $u_1,\ldots,u_T$ is arbitrarily time-varying. As no algorithm can guarantee low regret simultaneously against all comparator sequences, handling this setting requires moving from minimax optimality to comparator adaptivity. That is, sensible regret bounds should depend on certain complexity measures of the comparator relative to one's prior knowledge. This paper achieves a new type of these adaptive regret bounds via a sparse coding framework. The complexity of the comparator is measured by its energy and its sparsity on a user-specified dictionary, which offers considerable versatility. Equipped with a wavelet dictionary for example, our framework improves the state-of-the-art bound (Jacobsen & Cutkosky, 2022) by adapting to both ($i$) the magnitude of the comparator average $||\bar u||=||\sum_{t=1}^Tu_t/T||$, rather than the maximum $\max_t||u_t||$; and ($ii$) the comparator variability $\sum_{t=1}^T||u_t-\bar u||$, rather than the uncentered sum $\sum_{t=1}^T||u_t||$. Furthermore, our analysis is simpler due to decoupling function approximation from regret minimization.

Zhiyu Zhang, Heng Yang, Ashok Cutkosky et al. · harvard

We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and ($ii$) the comparator norm adaptivity also known as "parameter freeness" in the literature. In particular, - our algorithm does not employ the impractical doubling trick, and does not require an a priori estimate of the time-uniform Lipschitz constant; - the associated regret bound has the optimal $O(\sqrt{V_T})$ dependence on the gradient variance $V_T$, without the typical logarithmic multiplicative factor; - the leading constant in the regret bound is "almost" optimal. Central to these results is a continuous time approach to online learning. We first show that the aimed simultaneous adaptivity can be achieved fairly easily in a continuous time analogue of the problem, where the environment is modeled by an arbitrary continuous semimartingale. Then, our key innovation is a new discretization argument that preserves such adaptivity in the discrete time adversarial setting. This refines a non-gradient-adaptive discretization argument from (Harvey et al., 2023), both algorithmically and analytically, which could be of independent interest.

Zhiyu Zhang, Ashok Cutkosky, Ioannis Ch. Paschalidis · harvard

Practical online learning tasks are often naturally defined on unconstrained domains, where optimal algorithms for general convex losses are characterized by the notion of comparator adaptivity. In this paper, we design such algorithms in the presence of switching cost - the latter penalizes the typical optimism in adaptive algorithms, leading to a delicate design trade-off. Based on a novel dual space scaling strategy discovered by a continuous-time analysis, we propose a simple algorithm that improves the existing comparator adaptive regret bound [ZCP22a] to the optimal rate. The obtained benefits are further extended to the expert setting, and the practicality of the proposed algorithm is demonstrated through a sequential investment task.

Shibo Yin, Zhiyu Zhang, Peirong Ning et al.

In streaming media services, video transcoding is a common practice to alleviate bandwidth demands. Unfortunately, traditional methods employing a uniform rate factor (RF) across all videos often result in significant inefficiencies. Content-adaptive encoding (CAE) techniques address this by dynamically adjusting encoding parameters based on video content characteristics. However, existing CAE methods are often tightly coupled with specific encoding strategies, leading to inflexibility. In this paper, we propose a model that predicts both RF-quality and RF-bitrate curves, which can be utilized to derive a comprehensive bitrate-quality curve. This approach facilitates flexible adjustments to the encoding strategy without necessitating model retraining. The model leverages codec features, content features, and anchor features to predict the bitrate-quality curve accurately. Additionally, we introduce an anchor suspension method to enhance prediction accuracy. Experiments confirm that the actual quality metric (VMAF) of the compressed video stays within 1 of the target, achieving an accuracy of 99.14%. By incorporating our quality improvement strategy with the rate-quality curve prediction model, we conducted online A/B tests, obtaining both +0.107% improvements in video views and video completions and +0.064% app duration time. Our model has been deployed on the Xiaohongshu App.

SII-OpenMOSS Team, Donghua Yu, Mingshu Chen et al.

Audio is indispensable for real-world video, yet generation models have largely overlooked audio components. Current approaches to producing audio-visual content often rely on cascaded pipelines, which increase cost, accumulate errors, and degrade overall quality. While systems such as Veo 3 and Sora 2 emphasize the value of simultaneous generation, joint multimodal modeling introduces unique challenges in architecture, data, and training. Moreover, the closed-source nature of existing systems limits progress in the field. In this work, we introduce MOVA (MOSS Video and Audio), an open-source model capable of generating high-quality, synchronized audio-visual content, including realistic lip-synced speech, environment-aware sound effects, and content-aligned music. MOVA employs a Mixture-of-Experts (MoE) architecture, with a total of 32B parameters, of which 18B are active during inference. It supports IT2VA (Image-Text to Video-Audio) generation task. By releasing the model weights and code, we aim to advance research and foster a vibrant community of creators. The released codebase features comprehensive support for efficient inference, LoRA fine-tuning, and prompt enhancement.

Zhiyu Zhang, Aaditya Ramdas

Adversarial online linear optimization (OLO) is essentially about making performance tradeoffs with respect to the unknown difficulty of the adversary. In the setting of one-dimensional fixed-time OLO on a bounded domain, it has been observed since Cover (1966) that achievable tradeoffs are governed by probabilistic inequalities, and these descriptive results can be converted into algorithms via dynamic programming, which, however, is not computationally efficient. We address this limitation by showing that Stein's method, a classical framework underlying the proofs of probabilistic limit theorems, can be operationalized as computationally efficient OLO algorithms. The associated regret and total loss upper bounds are "additively sharp", meaning that they surpass the conventional big-O optimality and match normal-approximation-based lower bounds by additive lower order terms. Our construction is inspired by the remarkably clean proof of a Wasserstein martingale central limit theorem (CLT) due to Röllin (2018). Several concrete benefits can be obtained from this general technique. First, with the same computational complexity, the proposed algorithm improves upon the total loss upper bounds of online gradient descent (OGD) and multiplicative weight update (MWU). Second, our algorithm can realize a continuum of optimal two-point tradeoffs between the total loss and the maximum regret over comparators, improving upon prior works in parameter-free online learning. Third, by allowing the adversary to randomize on an unbounded support, we achieve sharp in-expectation performance guarantees for OLO with noisy feedback.

Wei Chen, Yuting Wu, Shuhan Wu et al.

Reasoning future unknowable facts on temporal knowledge graphs (TKGs) is a challenging task, holding significant academic and practical values for various fields. Existing studies exploring explainable reasoning concentrate on modeling comprehensible temporal paths relevant to the query. Yet, these path-based methods primarily focus on local temporal paths appearing in recent times, failing to capture the complex temporal paths in TKG and resulting in the loss of longer historical relations related to the query. Motivated by the Dual Process Theory in cognitive science, we propose a \textbf{Cogn}itive \textbf{T}emporal \textbf{K}nowledge \textbf{E}xtrapolation framework (CognTKE), which introduces a novel temporal cognitive relation directed graph (TCR-Digraph) and performs interpretable global shallow reasoning and local deep reasoning over the TCR-Digraph. Specifically, the proposed TCR-Digraph is constituted by retrieving significant local and global historical temporal relation paths associated with the query. In addition, CognTKE presents the global shallow reasoner and the local deep reasoner to perform global one-hop temporal relation reasoning (System 1) and local complex multi-hop path reasoning (System 2) over the TCR-Digraph, respectively. The experimental results on four benchmark datasets demonstrate that CognTKE achieves significant improvement in accuracy compared to the state-of-the-art baselines and delivers excellent zero-shot reasoning ability. \textit{The code is available at https://github.com/WeiChen3690/CognTKE}.

Zhiyu Zhang, Da Liu, Shengqiang Liu et al.

Contrastive learning has become one of the most impressive approaches for multi-modal representation learning. However, previous multi-modal works mainly focused on cross-modal understanding, ignoring in-modal contrastive learning, which limits the representation of each modality. In this paper, we propose a novel contrastive learning strategy, called $Turbo$, to promote multi-modal understanding by joint in-modal and cross-modal contrastive learning. Specifically, multi-modal data pairs are sent through the forward pass twice with different hidden dropout masks to get two different representations for each modality. With these representations, we obtain multiple in-modal and cross-modal contrastive objectives for training. Finally, we combine the self-supervised Turbo with the supervised multi-modal classification and demonstrate its effectiveness on two audio-text classification tasks, where the state-of-the-art performance is achieved on a speech emotion recognition benchmark dataset.

Enhao Huang, Zhiyu Zhang, Tianxiang Xu et al.

Complex-valued signals encode both amplitude and phase, yet most deep models treat attention as real-valued correlation, overlooking interference effects. We introduce the Holographic Transformer, a physics-inspired architecture that incorporates wave interference principles into self-attention. Holographic attention modulates interactions by relative phase and coherently superimposes values, ensuring consistency between amplitude and phase. A dual-headed decoder simultaneously reconstructs the input and predicts task outputs, preventing phase collapse when losses prioritize magnitude over phase. We demonstrate that holographic attention implements a discrete interference operator and maintains phase consistency under linear mixing. Experiments on PolSAR image classification and wireless channel prediction show strong performance, achieving high classification accuracy and F1 scores, low regression error, and increased robustness to phase perturbations. These results highlight that enforcing physical consistency in attention leads to generalizable improvements in complex-valued learning and provides a unified, physics-based framework for coherent signal modeling. The code is available at https://github.com/EonHao/Holographic-Transformers.

Enhao Huang, Pengyu Sun, Zixin Lin et al.

Large Language Models (LLMs) have achieved impressive performance in diverse natural language processing tasks, but specialized domains such as Web3 present new challenges and require more tailored evaluation. Despite the significant user base and capital flows in Web3, encompassing smart contracts, decentralized finance (DeFi), non-fungible tokens (NFTs), decentralized autonomous organizations (DAOs), on-chain governance, and novel token-economics, no comprehensive benchmark has systematically assessed LLM performance in this domain. To address this gap, we introduce the DMind Benchmark, a holistic Web3-oriented evaluation suite covering nine critical subfields: fundamental blockchain concepts, blockchain infrastructure, smart contract, DeFi mechanisms, DAOs, NFTs, token economics, meme concept, and security vulnerabilities. Beyond multiple-choice questions, DMind Benchmark features domain-specific tasks such as contract debugging and on-chain numeric reasoning, mirroring real-world scenarios. We evaluated 26 models, including ChatGPT, Claude, DeepSeek, Gemini, Grok, and Qwen, uncovering notable performance gaps in specialized areas like token economics and security-critical contract analysis. While some models excel in blockchain infrastructure tasks, advanced subfields remain challenging. Our benchmark dataset and evaluation pipeline are open-sourced on https://huggingface.co/datasets/DMindAI/DMind_Benchmark, reaching number one in Hugging Face's trending dataset charts within a week of release.

Bin Ren, Hang Guo, Lei Sun et al.

This paper presents a comprehensive review of the NTIRE 2025 Challenge on Single-Image Efficient Super-Resolution (ESR). The challenge aimed to advance the development of deep models that optimize key computational metrics, i.e., runtime, parameters, and FLOPs, while achieving a PSNR of at least 26.90 dB on the $\operatorname{DIV2K\_LSDIR\_valid}$ dataset and 26.99 dB on the $\operatorname{DIV2K\_LSDIR\_test}$ dataset. A robust participation saw \textbf{244} registered entrants, with \textbf{43} teams submitting valid entries. This report meticulously analyzes these methods and results, emphasizing groundbreaking advancements in state-of-the-art single-image ESR techniques. The analysis highlights innovative approaches and establishes benchmarks for future research in the field.

Zhiyu Zhang, Chenkaixiang Lu, Wenchong Tian et al.

Physics-based models are computationally time-consuming and infeasible for real-time scenarios of urban drainage networks, and a surrogate model is needed to accelerate the online predictive modelling. Fully-connected neural networks (NNs) are potential surrogate models, but may suffer from low interpretability and efficiency in fitting complex targets. Owing to the state-of-the-art modelling power of graph neural networks (GNNs) and their match with urban drainage networks in the graph structure, this work proposes a GNN-based surrogate of the flow routing model for the hydraulic prediction problem of drainage networks, which regards recent hydraulic states as initial conditions, and future runoff and control policy as boundary conditions. To incorporate hydraulic constraints and physical relationships into drainage modelling, physics-guided mechanisms are designed on top of the surrogate model to restrict the prediction variables with flow balance and flooding occurrence constraints. According to case results in a stormwater network, the GNN-based model is more cost-effective with better hydraulic prediction accuracy than the NN-based model after equal training epochs, and the designed mechanisms further limit prediction errors with interpretable domain knowledge. As the model structure adheres to the flow routing mechanisms and hydraulic constraints in urban drainage networks, it provides an interpretable and effective solution for data-driven surrogate modelling. Simultaneously, the surrogate model accelerates the predictive modelling of urban drainage networks for real-time use compared with the physics-based model.

Kwangjun Ahn, Zhiyu Zhang, Yunbum Kook et al. · harvard

Despite the success of the Adam optimizer in practice, the theoretical understanding of its algorithmic components still remains limited. In particular, most existing analyses of Adam show the convergence rate that can be simply achieved by non-adative algorithms like SGD. In this work, we provide a different perspective based on online learning that underscores the importance of Adam's algorithmic components. Inspired by Cutkosky et al. (2023), we consider the framework called online learning of updates/increments, where we choose the updates/increments of an optimizer based on an online learner. With this framework, the design of a good optimizer is reduced to the design of a good online learner. Our main observation is that Adam corresponds to a principled online learning framework called Follow-the-Regularized-Leader (FTRL). Building on this observation, we study the benefits of its algorithmic components from the online learning perspective.

Zhiyu Zhang, David Bombara, Heng Yang · harvard

We study online learning in adversarial nonstationary environments. Since the future can be very different from the past, a critical challenge is to gracefully forget the history while new data comes in. To formalize this intuition, we revisit the discounted regret in online convex optimization, and propose an adaptive (i.e., instance optimal), FTRL-based algorithm that improves the widespread non-adaptive baseline -- gradient descent with a constant learning rate. From a practical perspective, this refines the classical idea of regularization in lifelong learning: we show that designing good regularizers can be guided by the principled theory of adaptive online optimization. Complementing this result, we also consider the (Gibbs and Candès, 2021)-style online conformal prediction problem, where the goal is to sequentially predict the uncertainty sets of a black-box machine learning model. We show that the FTRL nature of our algorithm can simplify the conventional gradient-descent-based analysis, leading to instance-dependent performance guarantees.

Zhiyu Zhang, Guo Lu, Huanxiong Liang et al.

Volumetric videos, benefiting from immersive 3D realism and interactivity, hold vast potential for various applications, while the tremendous data volume poses significant challenges for compression. Recently, NeRF has demonstrated remarkable potential in volumetric video compression thanks to its simple representation and powerful 3D modeling capabilities, where a notable work is ReRF. However, ReRF separates the modeling from compression process, resulting in suboptimal compression efficiency. In contrast, in this paper, we propose a volumetric video compression method based on dynamic NeRF in a more compact manner. Specifically, we decompose the NeRF representation into the coefficient fields and the basis fields, incrementally updating the basis fields in the temporal domain to achieve dynamic modeling. Additionally, we perform end-to-end joint optimization on the modeling and compression process to further improve the compression efficiency. Extensive experiments demonstrate that our method achieves higher compression efficiency compared to ReRF on various datasets.

Zhiyu Zhang, Guo Lu, Huanxiong Liang et al.

The neural radiance fields (NeRF) have advanced the development of 3D volumetric video technology, but the large data volumes they involve pose significant challenges for storage and transmission. To address these problems, the existing solutions typically compress these NeRF representations after the training stage, leading to a separation between representation training and compression. In this paper, we try to directly learn a compact NeRF representation for volumetric video in the training stage based on the proposed rate-aware compression framework. Specifically, for volumetric video, we use a simple yet effective modeling strategy to reduce temporal redundancy for the NeRF representation. Then, during the training phase, an implicit entropy model is utilized to estimate the bitrate of the NeRF representation. This entropy model is then encoded into the bitstream to assist in the decoding of the NeRF representation. This approach enables precise bitrate estimation, thereby leading to a compact NeRF representation. Furthermore, we propose an adaptive quantization strategy and learn the optimal quantization step for the NeRF representations. Finally, the NeRF representation can be optimized by using the rate-distortion trade-off. Our proposed compression framework can be used for different representations and experimental results demonstrate that our approach significantly reduces the storage size with marginal distortion and achieves state-of-the-art rate-distortion performance for volumetric video on the HumanRF and ReRF datasets. Compared to the previous state-of-the-art method TeTriRF, we achieved an approximately -80% BD-rate on the HumanRF dataset and -60% BD-rate on the ReRF dataset.

Zhou Lu, Y. Jennifer Sun, Zhiyu Zhang

We study the problem of controlling population dynamics, a class of linear dynamical systems evolving on the probability simplex, from the perspective of online non-stochastic control. While Golowich et.al. 2024 analyzed the fully observable setting, we focus on the more realistic, partially observable case, where only a low-dimensional representation of the state is accessible. In classical non-stochastic control, inputs are set as linear combinations of past disturbances. However, under partial observations, disturbances cannot be directly computed. To address this, Simchowitz et.al. 2020 proposed to construct oblivious signals, which are counterfactual observations with zero control, as a substitute. This raises several challenges in our setting: (1) how to construct oblivious signals under simplex constraints, where zero control is infeasible; (2) how to design a sufficiently expressive convex controller parameterization tailored to these signals; and (3) how to enforce the simplex constraint on control when projections may break the convexity of cost functions. Our main contribution is a new controller that achieves the optimal $\tilde{O}(\sqrt{T})$ regret with respect to a natural class of mixing linear dynamic controllers. To tackle these challenges, we construct signals based on hypothetical observations under a constant control adapted to the simplex domain, and introduce a new controller parameterization that approximates general control policies linear in non-oblivious observations. Furthermore, we employ a novel convex extension surrogate loss, inspired by Lattimore 2024, to bypass the projection-induced convexity issue.

Zhou Lu, Y. Jennifer Sun, Zhiyu Zhang

Focusing on the expert problem in online learning, this paper studies the interpolation of several performance metrics via $φ$-regret minimization, which measures the total loss of an algorithm by its regret with respect to an arbitrary action modification rule $φ$. With $d$ experts and $T\gg d$ rounds in total, we present a single algorithm achieving the instance-adaptive $φ$-regret bound \begin{equation*} \tilde O\left(\min\left\{\sqrt{d-d^{\mathrm{unif}}_φ+1},\sqrt{d-d^{\mathrm{self}}_φ}\right\}\cdot\sqrt{T}\right), \end{equation*} where $d^{\mathrm{unif}}_φ$ is the maximum amount of experts modified identically by $φ$, and $d^{\mathrm{self}}_φ$ is the amount of experts that $φ$ trivially modifies to themselves. By recovering the optimal $O(\sqrt{T\log d})$ external regret bound when $d^{\mathrm{unif}}_φ=d$, the standard $\tilde O(\sqrt{T})$ internal regret bound when $d^{\mathrm{self}}_φ=d-1$ and the optimal $\tilde O(\sqrt{dT})$ swap regret bound in the worst case, we improve upon existing algorithms in the intermediate regimes. In addition, the computational complexity of our algorithm matches that of the standard swap-regret minimization algorithm due to (Blum and Mansour, 2007). Technically, building on the well-known reduction from $φ$-regret minimization to external regret minimization on stochastic matrices, our main idea is to further convert the latter to online linear regression using Haar-wavelet-inspired matrix features. Then, by associating the complexity of each $φ$ instance with its sparsity under the feature representation, we apply techniques from comparator-adaptive online learning to exploit the sparsity in this regression subroutine.

Weiyuan Gong, Tongyang Li, Xinzhao Wang et al.

The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well known that MMWU achieves the minimax-optimal regret bound of $O(\sqrt{T\log d})$, where $T$ is the time horizon. In this paper, we present an improved algorithm achieving the instance-optimal regret bound of $O(\sqrt{T\cdot S(X||d^{-1}I_d)})$, where $X$ is the comparator in the regret, $I_d$ is the identity matrix, and $S(\cdot||\cdot)$ denotes the quantum relative entropy. Furthermore, our algorithm has the same computational complexity as MMWU, indicating that the improvement in the regret bound is ``free''. Technically, we first develop a general potential-based framework for matrix LEA, with MMWU being its special case induced by the standard exponential potential. Then, the crux of our analysis is a new ``one-sided'' Jensen's trace inequality built on a Laplace transform technique, which allows the application of general potential functions beyond exponential to matrix LEA. Our algorithm is finally induced by an optimal potential function from the vector LEA problem, based on the imaginary error function. Complementing the above, we provide a memory lower bound for matrix LEA, and explore the applications of our algorithm in quantum learning theory. We show that it outperforms the state of the art for learning quantum states corrupted by depolarization noise, random quantum states, and Gibbs states. In addition, applying our algorithm to linearized convex losses enables predicting nonlinear quantum properties, such as purity, quantum virtual cooling, and Rényi-$2$ correlation.

Kevin Kasa, Zhiyu Zhang, Heng Yang et al.

Recently there has been a surge of interest to deploy confidence set predictions rather than point predictions in machine learning. Unfortunately, the effectiveness of such prediction sets is frequently impaired by distribution shifts in practice, and the challenge is often compounded by the lack of ground truth labels at test time. Focusing on a standard set-valued prediction framework called conformal prediction (CP), this paper studies how to improve its practical performance using only unlabeled data from the shifted test domain. This is achieved by two new methods called ECP and EACP, whose main idea is to adjust the score function in CP according to its base model's own uncertainty evaluation. Through extensive experiments on a number of large-scale datasets and neural network architectures, we show that our methods provide consistent improvement over existing baselines and nearly match the performance of fully supervised methods.

Zhiyu Zhang, Ashok Cutkosky, Ioannis Paschalidis

Unconstrained Online Linear Optimization (OLO) is a practical problem setting to study the training of machine learning models. Existing works proposed a number of potential-based algorithms, but in general the design of these potential functions relies heavily on guessing. To streamline this workflow, we present a framework that generates new potential functions by solving a Partial Differential Equation (PDE). Specifically, when losses are 1-Lipschitz, our framework produces a novel algorithm with anytime regret bound $C\sqrt{T}+||u||\sqrt{2T}[\sqrt{\log(1+||u||/C)}+2]$, where $C$ is a user-specified constant and $u$ is any comparator unknown and unbounded a priori. Such a bound attains an optimal loss-regret trade-off without the impractical doubling trick. Moreover, a matching lower bound shows that the leading order term, including the constant multiplier $\sqrt{2}$, is tight. To our knowledge, the proposed algorithm is the first to achieve such optimalities.

Zhiyu Zhang, Ashok Cutkosky, Ioannis Ch. Paschalidis

We consider the problem of tracking an adversarial state sequence in a linear dynamical system subject to adversarial disturbances and loss functions, generalizing earlier settings in the literature. To this end, we develop three techniques, each of independent interest. First, we propose a comparator-adaptive algorithm for online linear optimization with movement cost. Without tuning, it nearly matches the performance of the optimally tuned gradient descent in hindsight. Next, considering a related problem called online learning with memory, we construct a novel strongly adaptive algorithm that uses our first contribution as a building block. Finally, we present the first reduction from adversarial tracking control to strongly adaptive online learning with memory. Summarizing these individual techniques, we obtain an adversarial tracking controller with a strong performance guarantee even when the reference trajectory has a large range of movement.

Zhiyu Zhang, Ioannis Paschalidis

Due to recent empirical successes, the options framework for hierarchical reinforcement learning is gaining increasing popularity. Rather than learning from rewards which suffers from the curse of dimensionality, we consider learning an options-type hierarchical policy from expert demonstrations. Such a problem is referred to as hierarchical imitation learning. Converting this problem to parameter inference in a latent variable model, we theoretically characterize the EM approach proposed by Daniel et al. (2016). The population level algorithm is analyzed as an intermediate step, which is nontrivial due to the samples being correlated. If the expert policy can be parameterized by a variant of the options framework, then under regularity conditions, we prove that the proposed algorithm converges with high probability to a norm ball around the true parameter. To our knowledge, this is the first performance guarantee for an hierarchical imitation learning algorithm that only observes primitive state-action pairs.

Wentao Ma, Dongqiao Zheng, Yuanhao Li et al.

This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum correntropy criterion (NMCC) is derived from a correntropy based cost function, which is rather robust with respect to impulsive noises. To deal with the noisy input, we introduce a bias-compensated vector (BCV) to the NMCC algorithm, and then an unbiasedness criterion and some reasonable assumptions are used to compute the BCV. Taking advantage of the BCV, the bias caused by the input noise can be effectively suppressed. System identification simulation results demonstrate that the proposed BCNMCC algorithm can outperform other related algorithms with noisy input especially in an impulsive output noise environment.