Risk of Selection of Irrelevant Features from High-Dimensional Data with Small Sample Size

In this work we demonstrate the effect of small sample size on the risk that feature selection algorithms will select irrelevant features when dealing with high-dimensional data. We develop a simple analytical model to quantify this risk; we verify this model by the means of simulation. These results (i) explain the inherent instability of feature selection from high-dimensional, small sample size data and (ii) can be used to estimate the minimum required sample size which leads to good stability of features. Such results are useful when dealing with data from high-throughput studies.