Where high-dimensional columns come from
Section of High-dimensional analysis, part of Statistical learning
Where high-dimensional columns come from
| Type | Section |
| Taught in | High-dimensional analysis |
| Part | Statistical learning |
A large sample relative to the number of fitted coefficients makes classical estimation easier, but collecting another subject can cost much more than measuring another feature on an existing sample. High-dimensional methods address this imbalance by adding structure. They cannot manufacture information about directions that the observed design never distinguishes.
Microarray studies are one setting of this kind. One tissue sample produces measurements of many transcript-related features, while the number of sampled tissues can remain small. The Alon study below analyses 2000 selected gene-expression features from 62 samples (Alon et al., 1999). These measurements are not direct measurements of protein production, and a biological gene is not interchangeable with one independent predictor. Correlation, measurement processing, and tissue composition all affect the statistical question.
In that setting the scientific question is often which coordinates are associated with the response, not the size of the prediction error. Association is not causation.
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See also
Rank bound · Family-wise control implies false-discovery control · Benjamini–Hochberg · Benjamini–Hochberg controls the false discovery rate · Why classical methods fail when p > n · Rank of the sample covariance · Regression when p > n · Questions to ask of high-dimensional data