Exhaustive Search for Sparse Variable Selection in Linear Regression

Igarashi, Yasuhiko; Takenaka, Hikaru; Nakanishi-Ohno, Yoshinori; Uemura, Makoto; Ikeda, Shiro; Okada, Masato

doi:10.7566/jpsj.87.044802

Cited by 43 publications

(43 citation statements)

References 32 publications

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“…Least angle regression and ordinary least squares (LARS-OLS) [37] is a framework of regression analysis that performs basis search and regression in a stepwise manner. Igarashi et al considered the LARS-OLS as Bayesian inference (called Bayesian LARS-OLS) and proposed a method that achieves the basis search in the Bayesian free energy criterion [21,22]. We extend their method to be able to apply the material's dynamics such as a relaxation process.…”

Section: Evaluation Of Decomposed Modesmentioning

confidence: 99%

“…The isolation of background noise and the extraction of normal modes from measured signals can be recast as a mode selection problem for CP signal estimation. We extend the previously proposed Bayesian LARS-OLS framework [21,22] to be used with SpDMD. Bayesian LARS-OLS is the mode selection framework from the viewpoint of data-driven approach in Bayesian inference.…”

Section: Introductionmentioning

confidence: 99%

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Normal mode analysis of a relaxation process with Bayesian inference

Sakata

Nagano

Igarashi

et al. 2020

Science and Technology of Advanced Materials

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Measurements of relaxation processes are essential in many fields, including nonlinear optics. Relaxation processes provide many insights into atomic/molecular structures and the kinetics and mechanisms of chemical reactions. For the analysis of these processes, the extraction of modes that are specific to the phenomenon of interest (normal modes) is unavoidable. In this study we propose a framework to systematically extract normal modes from the viewpoint of model selection with Bayesian inference. Our approach consists of a well-known method called sparsity-promoting dynamic mode decomposition, which decomposes a mixture of damped oscillations, and the Bayesian model selection framework. We numerically verify the performance of our proposed method by using coherent phonon signals of a bismuth polycrystal and virtual data as typical examples of relaxation processes. Our method succeeds in extracting the normal modes even from experimental data with strong backgrounds. Moreover, the selected set of modes is robust to observation noise, and our method can estimate the level of observation noise. From these observations, our method is applicable to normal mode analysis, especially for data with strong backgrounds. ARTICLE HISTORY

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Section: Evaluation Of Decomposed Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Normal mode analysis of a relaxation process with Bayesian inference

Sakata

Nagano

Igarashi

et al. 2020

Science and Technology of Advanced Materials

Self Cite

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“…Igarashi et al proposed to plot the density of state of CVE and compare various solutions of variable selection on the density of state. 38) They called the method as exhaustive search with density of states (ES-DoS). The state of density for CVE of fatigue strength was plotted in Fig.…”

Section: Linear Regression Modelmentioning

confidence: 99%

Prediction of Fatigue Strength in Steels by Linear Regression and Neural Network

2018

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This paper examines machine learning methods to predict fatigue strength with high accuracy using existing database. The fatigue database was automatically classified by hierarchical clustering method, and a group of carbon steels was selected as a target of machine learning. In linear regression analyses, a model selection was conducted from all possible combinations of explanatory variables based on cross validation technique. The derived linear regression model provided more accurate prediction than existing empirical rules. In neural network models, local and global sensitivity analyses were performed and the results of virtual experiments were consistent with existing knowledge in materials engineering. It demonstrated that the machine learning method provides prediction of fatigue performance with high accuracy and is one of promising method to accelerate material development.

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“…However, there is the risk of a "combination explosion" in an ES method. To overcome this problem, we used a "K-sparse exhaustive search" (ES-K) method [7]. The ES-K method is based on the assumption that the optimal combination of explanatory variables is K-sparse, i.e., that K of the N components are explanatory variables.…”

Section: Realizing Sparse Modeling Es-kmentioning

confidence: 99%

“…This approach exploits the inherent sparseness common to all high-dimensional data and enables us to extract the maximum amount of information from the data efficiently. For the sparse modeling, we have used exhaustive searches with the SVM and a deep neural network (DNN), assuming that the optimal combination of explanatory variables is K-sparse [7]. We denoted these methods as "ES-K-SVM" and "ES-K-DNN", respectively.…”

Section: Introductionmentioning

confidence: 99%

Disruption Prediction by Support Vector Machine and Neural Network with Exhaustive Search

Yokoyama

Sueyoshi

Miyoshi

et al. 2018

Plasma and Fusion Research

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A disruption is an event in which the plasma current suddenly shuts down in a tokamak reactor. Establishing methods to predict, mitigate, and avoid disruptions may be indispensable for realizing a tokamak reactor. In the present study, we have used the large dataset of high-beta experiments at JT-60U to develop a method for predicting the occurrence of disruptions. The method is based on sparse modeling that exploits the inherent sparseness common to all high-dimensional data, and it enables us to extract the maximum amount of information from the data efficiently. To carry out the sparse modeling, we have used exhaustive searches with a support vector machine and a neural network. In this research, we repeated the training and evaluation of the predictor while changing the combination of plasma parameters. As a result of the exhaustive search, we found |B n=1 r | and d|B n=1 r |/dt to be the dominant parameters for disruption predictions. This is not surprising, because MHD instabilities are considered to be the direct triggers of disruption. In addition, we have succeeded in identifying several important parameters that may also be strongly related to disruptions, i.e., β N , β P , q 95 , δ, f GW , and f rad .

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Exhaustive Search for Sparse Variable Selection in Linear Regression

Cited by 43 publications

References 32 publications

Normal mode analysis of a relaxation process with Bayesian inference

Normal mode analysis of a relaxation process with Bayesian inference

Prediction of Fatigue Strength in Steels by Linear Regression and Neural Network

Disruption Prediction by Support Vector Machine and Neural Network with Exhaustive Search

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