Sufficient Dimension Reduction: An Information-Theoretic Viewpoint

Ghosh, Debashis

doi:10.3390/e24020167

Cited by 7 publications

(3 citation statements)

References 39 publications

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“…This gets violated in situations with discrete predictors. Recently, Ghosh ( 2022 ) has developed an interpretation of sufficient dimension reduction methods from an information-theoretic point of view. In this interpretation, the partial least squares algorithm can be viewed as an information-maximization operation under less restrictive distributional assumptions than those required in Theorem 1 of the paper.…”

Section: Methodsmentioning

confidence: 99%

Causal Inference in Radiomics: Framework, Mechanisms, and Algorithms

et al. 2022

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The widespread use of machine learning algorithms in radiomics has led to a proliferation of flexible prognostic models for clinical outcomes. However, a limitation of these techniques is their black-box nature, which prevents the ability for increased mechanistic phenomenological understanding. In this article, we develop an inferential framework for estimating causal effects with radiomics data. A new challenge is that the exposure of interest is latent so that new estimation procedures are needed. We leverage a multivariate version of partial least squares for causal effect estimation. The methodology is illustrated with applications to two radiomics datasets, one in osteosarcoma and one in glioblastoma.

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Section: Methodsmentioning

confidence: 99%

Causal Inference in Radiomics: Framework, Mechanisms, and Algorithms

et al. 2022

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“…Dimension reduction (DR) is an indispensable technique to face the challenge of dramatically increasing data amounts in data analysis [1][2][3][4][5][6]. Non-linear DR is a current research focus, where manifold learning is one of the main research topics [5,6].…”

Section: Introductionmentioning

confidence: 99%

Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field

Zhuang,

Mastorakis

2023

Symmetry

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A self-organized geometric model is proposed for data dimension reduction to improve the robustness of manifold learning. In the model, a novel mechanism for dimension reduction is presented by the autonomous deforming of data manifolds. The autonomous deforming vector field is proposed to guide the deformation of the data manifold. The flattening of the data manifold is achieved as an emergent behavior under the virtual elastic and repulsive interaction between the data points. The manifold’s topological structure is preserved when it evolves to the shape of lower dimension. The soft neighborhood is proposed to overcome the uneven sampling and neighbor point misjudging problems. The simulation experiment results of data sets prove its effectiveness and also indicate that implicit features of data sets can be revealed. In the comparison experiments, the proposed method shows its advantage in robustness.

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“…Dimension reduction methods seek to reduce the number of dimensions [1,2] in the variable space whilst also preserving the most important structure or relationships between the variables, i.e. without significant loss of information (capturing the essential information) [3]. They have also the advantage of handling and visualizing the results of complex and massive amounts of data [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

“Automatic” interpretation of multiple correspondence analysis (MCA) results for nonexpert users, using R programming

Moschidis

Markos

Thanopoulos

2022

ACI

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PurposeThe purpose of this paper is to create an automatic interpretation of the results of the method of multiple correspondence analysis (MCA) for categorical variables, so that the nonexpert user can immediately and safely interpret the results, which concern, as the authors know, the categories of variables that strongly interact and determine the trends of the subject under investigation.Design/methodology/approachThis study is a novel theoretical approach to interpreting the results of the MCA method. The classical interpretation of MCA results is based on three indicators: the projection (F) of the category points of the variables in factorial axes, the point contribution to axis creation (CTR) and the correlation (COR) of a point with an axis. The synthetic use of the aforementioned indicators is arduous, particularly for nonexpert users, and frequently results in misinterpretations. The current study has achieved a synthesis of the aforementioned indicators, so that the interpretation of the results is based on a new indicator, as correspondingly on an index, the well-known method principal component analysis (PCA) for continuous variables is based.FindingsTwo (2) concepts were proposed in the new theoretical approach. The interpretative axis corresponding to the classical factorial axis and the interpretative plane corresponding to the factorial plane that as it will be seen offer clear and safe interpretative results in MCA.Research limitations/implicationsIt is obvious that in the development of the proposed automatic interpretation of the MCA results, the authors do not have in the interpretative axes the actual projections of the points as is the case in the original factorial axes, but this is not of interest to the simple user who is only interested in being able to distinguish the categories of variables that determine the interpretation of the most pronounced trends of the phenomenon being examined.Practical implicationsThe results of this research can have positive implications for the dissemination of MCA as a method and its use as an integrated exploratory data analysis approach.Originality/valueInterpreting the MCA results presents difficulties for the nonexpert user and sometimes lead to misinterpretations. The interpretative difficulty persists in the MCA's other interpretative proposals. The proposed method of interpreting the MCA results clearly and accurately allows for the interpretation of its results and thus contributes to the dissemination of the MCA as an integrated method of categorical data analysis and exploration.

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Sufficient Dimension Reduction: An Information-Theoretic Viewpoint

Cited by 7 publications

References 39 publications

Causal Inference in Radiomics: Framework, Mechanisms, and Algorithms

Causal Inference in Radiomics: Framework, Mechanisms, and Algorithms

Learning by Autonomous Manifold Deformation with an Intrinsic Deforming Field

“Automatic” interpretation of multiple correspondence analysis (MCA) results for nonexpert users, using R programming

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