Model-based SIR for dimension reduction
This is an incremental improvement for statisticians and data scientists working on dimension reduction, addressing a specific failure case in SIR without additional assumptions.
The authors tackled the limitation of sliced inverse regression (SIR) in handling symmetric relationships by proposing a model-based SIR (MSIR) method using Gaussian finite mixtures, which performed comparably or better than existing methods, especially with larger sample sizes, as shown in numerical studies and real data examples.
A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the presence of regression symmetric relationships, without the need to impose further assumptions. Extensive numerical studies are presented to compare the new method with some of most popular dimension reduction methods, such as SIR, sliced average variance estimation, principal Hessian direction, and directional regression. MSIR appears sufficiently flexible to accommodate various regression functions, and its performance is comparable with or better, particularly as sample size grows, than other available methods. Lastly, MSIR is illustrated with two real data examples about ozone concentration regression, and hand-written digit classification.