BioMed Research International / 2019 / Article / Tab 3

Review Article

Incorporating Pathway Information into Feature Selection towards Better Performed Gene Signatures

Table 3

Penalty terms used in the bilevel selection methods.

Methods Mathematical notation Characteristics

General form  
See equation (2) for what , and represent
Outer bridge penalty + inner ridge penalty
It cannot identify the important genes within the selected gene sets and thus is actually incapable of bilevel selection and also heavily shrinks large coefficients (leading to estimate biases for large coefficients)
Group bridge [59]Outer bridge penalty+ inner LASSO penaltyIt can provide sparse solutions at both pathway and gene levels, but it is associated with big empirical difficulties since the bridge penalty is not everywhere differentiable.
Group MCP [31]Outer MCP penalty+ inner MCP penaltyAllow coefficients to grow large and groups to remain sparse.
Group exponential LASSO [18]Outer exponential penalty + inner LASSO penaltyA decay parameter controls the degree to which gene selection is coupled together within gene sets and has several advantages over the other composite penalty term such as group bridge.
Sparse group LASSO [60]  
taking the additive format
Convex and thus highly likely to get the global minimum, but extra care is needed since the group coordinate descent algorithms cannot be applied.

Note: the general formatting for group LASSO, group bridge, and group MCP was given by Breheny & Huang [31]. It is too general to guarantee all combinations of outer and inner penalties produce sensible models. Thus the second general form was proposed by Huang et al. [59] to address this issue specifically.

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