High dimensional inference

Part 2 of ebook "The elements of statistical learning: Data mining, inference, and prediction (Second edition)" provides readers with contents including: Chapter 10 - Boosting and additive trees; Chapter 11 - Neural networks; Chapter 12 - Support vector machines and flexible discriminants; Chapter 13 - Prototype methods and nearest-neighbors; Chapter 14 - Unsupervised learning; Chapter 15 - Random forests; Chapter 16 - Ensemble learning; Chapter 17 - Undirected graphical models; Chapter 18 - High-dimensional problems p ≫ N;...

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The random forest (RF) method is a commonly used tool for classification with high dimensional data as well as for ranking candidate predictors based on the so-called random forest variable importance measures (VIMs).

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Traditional anthropometric studies of human face rely on manual measurements of simple features, which are labor intensive and lack of full comprehensive inference. Dense surface registration of three-dimensional (3D) human facial images holds great potential for high throughput quantitative analyses of complex facial traits.

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Principal component analysis (PCA) has been widely used to visualize high-dimensional metabolomic data in a two- or three-dimensional subspace. In metabolomics, some metabolites (e.g., the top 10 metabolites) have been subjectively selected when using factor loading in PCA, and biological inferences are made for these metabolites.

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Different high-dimensional regression methodologies exist for the selection of variables to predict a continuous variable. To improve the variable selection in case clustered observations are present in the training data, an extension towards mixed-effects modeling (MM) is requested, but may not always be straightforward to implement.

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Decoding the temporal control of gene expression patterns is key to the understanding of the complex mechanisms that govern developmental decisions during heart development. High-throughput methods have been employed to systematically study the dynamic and coordinated nature of cardiac differentiation at the global level with multiple dimensions.

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Inferring the topology of gene regulatory networks (GRNs) from microarray gene expression data has many potential applications, such as identifying candidate drug targets and providing valuable insights into the biological processes. It remains a challenge due to the fact that the data is noisy and high dimensional, and there exists a large number of potential interactions.

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Procedures for controlling the false discovery rate (FDR) are widely applied as a solution to the multiple comparisons problem of high-dimensional statistics. Current FDR-controlling procedures require accurately calculated p-values and rely on extrapolation into the unknown and unobserved tails of the null distribution.

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High-throughput technologies have brought tremendous changes to biological domains, and the resulting high-dimensional data has also posed enormous challenges to computational science. A Bayesian network is a probabilistic graphical model represented by a directed acyclic graph, which provides concise semantics to describe the relationship between entities and has an independence assumption that is suitable for sparse omics data.

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Inferring gene regulatory networks (GRNs) from gene expression data remains a challenge in system biology. In past decade, numerous methods have been developed for the inference of GRNs. It remains a challenge due to the fact that the data is noisy and high dimensional, and there exists a large number of potential interactions.

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Probabilistic inference is an attractive approach to uncertain reasoning and empirical learning in artificial intelligence. Computational difficulties arise, however, because probabilistic models with the necessary realism and exibility lead to complex distributions over high-dimensional spaces.

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