Projection pursuit for discrete data

Diaconis, Persi; Salzman, Julia

doi:10.1214/193940307000000482

Cited by 7 publications

(7 citation statements)

References 52 publications

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“…Although much effort in the literature on

PP

has been put into theoretical aspects and computational approaches for low‐dimensional data, various open problems and challenging issues remain in high dimensions. These include (a) conjectures in Bickel et al , (2018) and cases not yet covered for asymptotic studies, especially, observed data of correlated and/or non‐Gaussian variables

X_{1}, \dots, X_{p}

, with applications to financial time series satisfying stylized facts (De Luca & Loperfido, 2004; De Luca et al , 2006); (b) handling practical data of discrete variables in discrete exploratory

PP

(Klinke, 1995), and analysis of discrete data arising from syllable patterns (Diaconis & Salzman, 2008), symbolic data or data with special structure in numerous disciplines; (c) nonlinear projections (Blanchard et al , 2006; Guo et al , 2020). There is more to be explored along the lines, driven by the need of new adaptations and methodological results, as well as real applications.…”

Section: Discussionmentioning

confidence: 99%

A Computational Perspective on Projection Pursuit in High Dimensions: Feasible or Infeasible Feature Extraction

Zhang

Wang

2022

Int Statistical Rev

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Summary Finding a suitable representation of multivariate data is fundamental in many scientific disciplines. Projection pursuit ( PP) aims to extract interesting ‘non‐Gaussian’ features from multivariate data, and tends to be computationally intensive even when applied to data of low dimension. In high‐dimensional settings, a recent work (Bickel et al., 2018) on PP addresses asymptotic characterization and conjectures of the feasible projections as the dimension grows with sample size. To gain practical utility of and learn theoretical insights into PP in an integral way, data analytic tools needed to evaluate the behaviour of PP in high dimensions become increasingly desirable but are less explored in the literature. This paper focuses on developing computationally fast and effective approaches central to finite sample studies for (i) visualizing the feasibility of PP in extracting features from high‐dimensional data, as compared with alternative methods like PCA and ICA, and (ii) assessing the plausibility of PP in cases where asymptotic studies are lacking or unavailable, with the goal of better understanding the practicality, limitation and challenge of PP in the analysis of large data sets.

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“…Although much effort in the literature on

PP

X_{1}, \dots, X_{p}

, with applications to financial time series satisfying stylized facts (De Luca & Loperfido, 2004; De Luca et al , 2006); (b) handling practical data of discrete variables in discrete exploratory

PP

Section: Discussionmentioning

confidence: 99%

A Computational Perspective on Projection Pursuit in High Dimensions: Feasible or Infeasible Feature Extraction

Zhang

Wang

2022

Int Statistical Rev

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“…Several possibilities for choosing this distance function exist, such as the footrule distance, the Spearman distance, and the Kendall distance. 31 In this article, we choose to use the footrule distance, defined as

, the equivalent of an

measure between rankings. The choice of this distance is motivated by its greater computational efficiency compared to its competitors, such as the Kendall distance, which is more computationally intensive.…”

Section: Lower‐dimensional Bayesian Mallows Modelmentioning

confidence: 99%

Rank‐based Bayesian variable selection for genome‐wide transcriptomic analyses

Emilie

Fleischer

Vitelli

2022

Statistics in Medicine

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Variable selection is crucial in high‐dimensional omics‐based analyses, since it is biologically reasonable to assume only a subset of non‐noisy features contributes to the data structures. However, the task is particularly hard in an unsupervised setting, and a priori ad hoc variable selection is still a very frequent approach, despite the evident drawbacks and lack of reproducibility. We propose a Bayesian variable selection approach for rank‐based unsupervised transcriptomic analysis. Making use of data rankings instead of the actual continuous measurements increases the robustness of conclusions when compared to classical statistical methods, and embedding variable selection into the inferential tasks allows complete reproducibility. Specifically, we develop a novel extension of the Bayesian Mallows model for variable selection that allows for a full probabilistic analysis, leading to coherent quantification of uncertainties. Simulation studies demonstrate the versatility and robustness of the proposed method in a variety of scenarios, as well as its superiority with respect to several competitors when varying the data dimension or data generating process. We use the novel approach to analyze genome‐wide RNAseq gene expression data from ovarian cancer patients: several genes that affect cancer development are correctly detected in a completely unsupervised fashion, showing the usefulness of the method in the context of signature discovery for cancer genomics. Moreover, the possibility to also perform uncertainty quantification plays a key role in the subsequent biological investigation.

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“…In statistics the most commonplace use of Correspondence Analysis is in ordination or seriation, that is , the search for a hidden gradient in contingency tables. As an example we take data analyzed by Cox and Brandwood [4] and Diaconis [6], who wanted to seriate Plato's works using the proportion of sentence endings in a given book with a given stress pattern. The seven books studied here are Republic, Laws, Critias, Philebus, Sophist, Timoeus.…”

Section: Correspondence Analysismentioning

confidence: 99%

“…As an example we take data analyzed by Cox and Brandwood [4] and Diaconis [6], who wanted to seriate Plato's works using the proportion of sentence endings in a given book with a given stress pattern. The seven books studied here are Republic, Laws, Critias, Philebus, Sophist, Timoeus.…”

Section: Correspondence Analysismentioning

confidence: 99%

Multivariate data analysis: The French way

Holmes

2008

Institute of Mathematical Statistics Collections

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This paper presents exploratory techniques for multivariate data, many of them well known to French statisticians and ecologists, but few well understood in North American culture. We present the general framework of duality diagrams which encompasses discriminant analysis, correspondence analysis and principal components, and we show how this framework can be generalized to the regression of graphs on covariates.Comment: Published in at http://dx.doi.org/10.1214/193940307000000455 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

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Projection pursuit for discrete data

Cited by 7 publications

References 52 publications

A Computational Perspective on Projection Pursuit in High Dimensions: Feasible or Infeasible Feature Extraction

A Computational Perspective on Projection Pursuit in High Dimensions: Feasible or Infeasible Feature Extraction

Rank‐based Bayesian variable selection for genome‐wide transcriptomic analyses

Multivariate data analysis: The French way

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