scholarly journals A generalized information criterion for high-dimensional PCA rank selection

2022 ◽  
Author(s):  
Hung Hung ◽  
Su-Yun Huang ◽  
Ching-Kang Ing
Keyword(s):  
Information Criterion ◽  
High Dimensional ◽  
Generalized Information Criterion ◽  
Generalized Information

A Generalized Information Criterion for Generalized Minor Component Extraction

2017 ◽  
Vol 65 (4) ◽  
pp. 947-959 ◽  
Author(s):  
Gao Yingbin ◽  
Kong Xiangyu ◽  
Hu Changhua ◽  
Li Hongzeng ◽  
Hou Li'an
Keyword(s):  
Minor Component ◽  
Information Criterion ◽  
Generalized Information Criterion ◽  
Generalized Information ◽  
Component Extraction

GENERALIZED INFORMATION CRITERION FOR LINEAR AND NONLINEAR PROCESSES

2002 ◽  
Vol 12 (02) ◽  
pp. 389-395 ◽  
Author(s):  
IKUO MATSUBA
Keyword(s):  
Present Method ◽  
Stochastic Systems ◽  
Information Criterion ◽  
Parametric Models ◽  
Type Method ◽  
Correlation Integral ◽  
Generalized Information Criterion ◽  
Generalized Information ◽  
Deterministic Processes ◽  
Delay Coordinates

A generalized information criterion is proposed to determine an embedding dimension and a delay time for delay coordinates of the reconstructed dynamics both for linear stochastic and nonlinear deterministic processes. While the standard maximum likelihood type method requires statistical parametric models such as autoregressive models, the generalized information criterion is constructed from the quantity in accordance with the second-order Renyi entropy in terms of the correlation integral for the finite number of data which is directly obtained from a time delay vector. It is found numerically that the present method works well when applied to chaotic and stochastic systems.

A derivation of the information criteria for selecting autoregressive models

1986 ◽  
Vol 18 (02) ◽  
pp. 360-387 ◽  
Author(s):  
R. J. Bhansali
Keyword(s):  
Loss Function ◽  
Risk Function ◽  
Information Criterion ◽  
Information Criteria ◽  
Predictive Density ◽  
Generalized Information Criterion ◽  
Generalized Information ◽  
Independent Process ◽  
Leibler Information ◽  
Asymptotically Unbiased Estimator

The Akaike information criterion, AIC, for autoregressive model selection is derived by adopting −2Ttimes the expected predictive density of a future observation of an independent process as a loss function, whereTis the length of the observed time series. The conditions under which AIC provides an asymptotically unbiased estimator of the corresponding risk function are derived. When the unbiasedness property fails, the use of AIC is justified heuristically. However, a method for estimating the risk function, which is applicable for all fitted orders, is given. A derivation of the generalized information criterion, AICα, is also given; the loss function used being obtained by a modification of the Kullback-Leibler information measure. Results paralleling those for AIC are also obtained for the AICαcriterion.

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