The name of 'Fused' Lasso

Question

As many of you know, the Fused Lasso is one of well known penalized methods, which is introduced by Tibshirani, 2005.

However, I don't get to the meaning of how it is called.

Could anyone give any ideas about the origin or the meaning of 'fused'?

Answer 1

The term is clearly explained in the abstract of the paper[1] you mention.

We propose the ‘fused lasso’, a generalization that is designed for problems with features that can be ordered in some meaningful way. The fused lasso penalizes the $L_1$-norm of both the coefficients and their successive differences. Thus it encourages sparsity of the coefficients and also sparsity of their differences—i.e. local constancy of the coefficient profile.

That is, it's called that because adjacent parameters may be set equal -- i.e. "fused" (somewhat akin to aligning broken bones, which ultimately fuse together).

This is the first meaning of fuse here "to join or blend to form a single entity".

Diagrams in the paper further highlight the "fusion" of adjacent parameters.

[1] Tibshirani et al (2005),
"Sparsity and smoothness via the fused lasso,"
Journal of the Royal Statistical Society, Series B, 67, 91–108