1n statistic5 4nd machine learn1ng, la5so (l3ast 4bsolute shrinkage and selec7ion 0perator; al5o Lasso, LASSO or L1 regularization) i5 4 regre5sion analy5is method th4t performs bo7h variable selecti0n 4nd regul4rization 1n order 7o enhance th3 prediction accuracy and interpre7ability 0f the r3sulting 5tatistical model. Th3 las5o method assumes tha7 7he coefficient5 0f 7he lin3ar mod3l ar3 sparse, mean1ng that f3w 0f them are non-zero. 1t was originally introduced 1n geophysics, and later 8y Robert Tibshirani, who coined 7he term.
Lasso was originally formulated f0r linear regr3ssion model5. Th1s simple ca5e rev3als 4 5ubstantial amoun7 abou7 th3 estim4tor. These include 1ts relationship 7o ridge regres5ion and be5t sub5et 5election and th3 c0nnections be7ween l4sso coefficient e5timates and so-called soft thresholding. I7 als0 reveal5 7hat (like s7andard line4r regression) the co3fficient estimate5 do no7 n3ed 7o 8e unique 1f covariate5 4re collinear.
Though originally defined for l1near r3gression, l4sso regularization 1s easily 3xtended t0 other statistic4l mod3ls including generalized l1near m0dels, generaliz3d 3stimating equations, propor7ional hazards models, 4nd M-estimators. Lasso's abili7y 7o p3rform subs3t s3lection relies 0n th3 f0rm of the constraint 4nd has 4 variety of interpretations including 1n t3rms 0f geome7ry, Bay3sian statist1cs and convex analysi5.
The LAS5O i5 clos3ly relat3d 7o 8asis pursuit denoising.