A method for high-dimensional smoothing

Xu, Yaxian; Jasra, Ajay

doi:10.1016/j.jkss.2018.08.004

Cited by 3 publications

(3 citation statements)

References 21 publications

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Section: Optimization By Smc Samplingmentioning

confidence: 99%

“…In short, particle filtering at the current parameter values can help with computing the expected values of those derivatives needed in the optimization step. For the EM approach, readers can find general discussions in Kantas et al (2009Kantas et al ( , 2015, and Xu and Jasra (2019), and stable variance estimation in Duan and Fulop (2011). Now working with Equation ( 12), directly computing the MLE when facing higher-dimensional latent stochastic processes actually becomes practical.…”

Section: Smc 2 Optimizationmentioning

confidence: 99%

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Sequential Monte Carlo optimization and statistical inference

Duan

2022

WIREs Computational Stats

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Sequential Monte Carlo (SMC) is a powerful technique originally developed for particle filtering and Bayesian inference. As a generic optimizer for statistical and nonstatistical objectives, its role is far less known. Density-tempered SMC is a highly efficient sampling technique ideally suited for challenging global optimization problems and is implementable with a somewhat arbitrary initialization sampler instead of relying on a prior distribution. SMC optimization is anchored at the fact that all optimization tasks (continuous, discontinuous, combinatorial, or noisy objective function) can be turned into sampling under a density or probability function short of a norming constant. The point with the highest functional value is the SMC estimate for the maximum. Through examples, we systematically present various density-tempered SMC algorithms and their superior performance vs. other techniques like Markov Chain Monte Carlo. Data cloning and k-fold duplication are two easily implementable accuracy accelerators, and their complementarity is discussed. The Extreme Value Theorem on the maximum order statistic can also help assess the quality of the SMC optimum. Our coverage includes the algorithmic essence of the density-tempered SMC with various enhancements and solutions for (1) a bi-modal nonstatistical function without and with constraints, (2) a multidimensional step function, (3) offline and online optimizations, (4) combinatorial variable selection, and (5) noninvertibility of the Hessian. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods Algorithms and Computational Methods > Stochastic Optimization Algorithms and Computational Methods > Integer Programming K E Y W O R D S combinatorial optimization, data cloning, density tempering, extreme value 1 | INTRODUCTION Sequential Monte Carlo (SMC) is, as the name suggests, a family of Monte Carlo sampling techniques that sequentially adapt to the target density/probability function by moving/concentrating the simulated sample to the most desirable

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Section: Optimization By Smc Samplingmentioning

confidence: 99%

Section: Smc 2 Optimizationmentioning

confidence: 99%

Sequential Monte Carlo optimization and statistical inference

Duan

2022

WIREs Computational Stats

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“…Noise reduction applies to both socalled, label noise (class noise) where the problem relates to incorrect classification of markings for input values, and attribute noise resulting from incorrect or incomplete values (García-Gil et al, 2019). Noise smoothing is based on an attempt to capture patterns by modifying individual points to reduce unevenness (Xu & Jasra, 2019;Ylioinas et al, 2016). At the data cleaning stage, less spectacular and statistically advanced operations are carried out to improve the process.…”

Section: The Process Of Discovering Knowledge From Datamentioning

confidence: 99%

Managing Data in Digital Marketing

Szymkowiak¹

2019

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In Chapter 3, a discussion was undertaken about the merits of distinguishing data science as an area of science and the perception of data science due to the progress of computational possibilities. The historical outline of data science was discussed, along with a reference to the data-driven approach. An additional problem raised in this chapter relates to determining the role of the scientist in the process of knowledge discovery. Moreover, in the context of the development of the tooling and methodological apparatus based on analytical autonomous operation. Various areas of data science were characterized, and traditional and modern methods were compared in the process of knowledge discovery, also showing the relationship between individual elements based on the knowledge pyramid. In addition, areas of marketing where data mining

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A Novel RPCA Method Using Log-Weighted Nuclear and L_(2,1) Norms Combined with Contrast-Limited Adaptive Histogram Equalization (CLAHE) for High Dimensional Natural and Medical Image Data

LIKASSA,

Chen,

Sun

2024

ijsmr

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Estimating the true underlying images from distorted high-dimensional data is crucial for applications in high-profile fields such as crime detection in security, clinical settings and medical diagnosis in healthcare, and radar imaging in signal processing. Existing statistical methods often struggle with robustness and image reconstruction quality when processing high-dimensional image data. While Robust Principal Component Analysis (RPCA) is widely used for image recovery, its reliance on uniform weights with singular value decomposition (SVD) weakens performance, especially in noisy environments. The L1 norm also fails to capture image details and recovery under high noise levels, a critical limitation for applications like medical diagnoses, where detail is essential. These challenges emphasize the need for improved methods to handle noise and enhance image quality in sensitive fields. Therefore, this paper proposes a novel RPCA method that integrates CLAHE with Log weighted nuclear norm (LWNN) and the L2,1 norm for high-dimensional natural and medical imaging. To reduce the computational load, our novel method is formulated into a new optimization problem and solved using the Alternating Direction Method of Multipliers (ADMM). This method leverages LWNN for enhanced low-rank approximation to drastically prune out the anomalies in images and the norm for improved sparse component recovery. Our approach has superior performance in image reconstruction compared to other state-of-the-art methods (SOTAs), showing significant advancements with real-world datasets. An interesting finding of this research is that combining the LWNN with the L2,1 norm is highly effective at removing noise from images. Furthermore, when the CLAHE technique is combined with LWNN and the L2,1 norm, it significantly enhances the extraction of previously unseen features, making blood vessels in medical images much clearer and more distinguishable. This combination proves to be a powerful approach for medical image analysis, revealing details that are otherwise difficult to detect. This method will be used for crime detection in security intelligence, and clinical settings and medical diagnosis in human retinal eyes.

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A method for high-dimensional smoothing

Cited by 3 publications

References 21 publications

Sequential Monte Carlo optimization and statistical inference

Sequential Monte Carlo optimization and statistical inference

Managing Data in Digital Marketing

A Novel RPCA Method Using Log-Weighted Nuclear and L_(2,1) Norms Combined with Contrast-Limited Adaptive Histogram Equalization (CLAHE) for High Dimensional Natural and Medical Image Data

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