Robust kernel adaptive filters based on mean p-power error for noisy chaotic time series prediction

Ma, Wentao; Duan, Jiandong; Man, Weishi; Zhao, Haiquan; Chen, Badong

doi:10.1016/j.engappai.2016.11.010

Cited by 65 publications

(35 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Alternative loss functions, designed in a similar way to that of the correntropic loss, can be also found in [23,24]. Among the previous methods, approaches that employ KRLS-type of iterations can be found in [12,20,21]. The learning task: With the positive integer ∈ ℤ >0 denoting discrete time, and with the input-output data pair ( , ) becoming available to the user at time , the goal is to devise an online non-parametric algorithm to learn the unknown non-linear and multi-output system via a reproducing kernel Hilbert space ℋ, where the ×1 vector may carry also noise and outliers.…”

Section: Introductionmentioning

confidence: 99%

“…Rather than adapting the classical RLS iterations [6] into KAF, as in [7,12,20,21], the proposed Algorithm 1 stems from the stochastic-approximation framework [26]. Similarly to [12], a sample average ℓ -norm error loss is used also here to define the objective function in the optimization problem of the learning task. Nevertheless, apart from the outlier contaminated data and in contrast to [12,20,21], the present framework allows also the use of faithful data, devoid of noise and outliers, as side information.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Outlier-Robust Kernel Hierarchical-Optimization RLS on a Budget With Affine Constraints

Slavakis¹,

Yukawa²

2021

Preprint

View full text Add to dashboard Cite

<div>This paper introduces a non-parametric learning framework to combat outliers in online, multi-output, and nonlinear regression tasks. A hierarchical-optimization problem underpins the learning task: Search in a reproducing kernel Hilbert space (RKHS) for a function that minimizes a sample average $\ell_p$-norm ($1 \leq p \leq 2$) error loss on data contaminated by noise and outliers, subject to side information that takes the form of affine constraints defined as the set of minimizers of a quadratic loss on a finite number of faithful data devoid of noise and outliers. To surmount the computational obstacles inflicted by the choice of loss and the potentially infinite dimensional RKHS, approximations of the $\ell_p$-norm loss, as well as a novel twist of the criterion of approximate linear dependency are devised to keep the computational-complexity footprint of the proposed algorithm bounded over time. Numerical tests on datasets showcase the robust behavior of the advocated framework against different types of outliers, under a low computational load, while satisfying at the same time the affine constraints, in contrast to the state-of-the-art methods which are constraint agnostic.</div><div><br></div><div>-------</div><div><br></div><div>© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<br></div>

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Outlier-Robust Kernel Hierarchical-Optimization RLS on a Budget With Affine Constraints

Slavakis¹,

Yukawa²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The MPE criterion based on the pth absolute moment of the error can deal with non-Gaussian data with a proper p-value, efficiently. In general, MPE is robust to large outliers when p < 2 [15], generating robust adaptive filters [15], e.g., the kernel least mean p-power (KLMP) algorithm [18] and the kernel recursive least mean p-power (KRLP) algorithm [18]. ITL can incorporate the complete distribution of errors into the learning process, resulting in the improvement of filtering precision and robustness to outliers.…”

Section: Introductionmentioning

confidence: 99%

Kernel Risk-Sensitive Mean p-Power Error Algorithms for Robust Learning

Zhang

Wang

Zhang

et al. 2019

Entropy

View full text Add to dashboard Cite

As a nonlinear similarity measure defined in the reproducing kernel Hilbert space (RKHS), the correntropic loss (C-Loss) has been widely applied in robust learning and signal processing. However, the highly non-convex nature of C-Loss results in performance degradation. To address this issue, a convex kernel risk-sensitive loss (KRL) is proposed to measure the similarity in RKHS, which is the risk-sensitive loss defined as the expectation of an exponential function of the squared estimation error. In this paper, a novel nonlinear similarity measure, namely kernel risk-sensitive mean p-power error (KRP), is proposed by combining the mean p-power error into the KRL, which is a generalization of the KRL measure. The KRP with p = 2 reduces to the KRL, and can outperform the KRL when an appropriate p is configured in robust learning. Some properties of KRP are presented for discussion. To improve the robustness of the kernel recursive least squares algorithm (KRLS) and reduce its network size, two robust recursive kernel adaptive filters, namely recursive minimum kernel risk-sensitive mean p-power error algorithm (RMKRP) and its quantized RMKRP (QRMKRP), are proposed in the RKHS under the minimum kernel risk-sensitive mean p-power error (MKRP) criterion, respectively. Monte Carlo simulations are conducted to confirm the superiorities of the proposed RMKRP and its quantized version.

show abstract

“…As a commonly used OLA, the kernel adaptive filter (KAF) [2] is proposed to solve complicated nonlinear issues. However, the network size of KAF is linearly growing, thus leading to high computational overhead.…”

mentioning

confidence: 99%

“…where θ k denotes the weight in the RFFS. In the following, Bayesian inference based on the assumption of Gaussian distribution for the weight and noise is used to estimate θ k in the network with the fixed dimension D shown in (2). First, a Gaussian diffusion process associated with a Gaussian distribution noise N (q; 0, δ 2 D I) is used to model the system parameters, i.e.,…”

mentioning

confidence: 99%