Least squares regression
library(gglasso)
# load bardet data set
data(bardet)
group1 <- rep(1:20, each = 5)
fit_ls <- gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "ls")
plot(fit_ls)
## s89 s90 s91 s92 s93
## (Intercept) 8.099354325 8.098922472 8.098531366 8.098175719 8.097849146
## V1 -0.119580203 -0.120877799 -0.122079683 -0.123223779 -0.124310183
## V2 -0.113742329 -0.114834411 -0.115853997 -0.116837630 -0.117782854
## V3 -0.002584792 -0.003487571 -0.004328519 -0.005134215 -0.005904892
## V4 -0.084771705 -0.088304073 -0.091674509 -0.094978960 -0.098212775
## s94 s95 s96 s97 s98
## (Intercept) 8.097574095 8.097295166 8.097058895 8.096833259 8.096637676
## V1 -0.125274109 -0.126284595 -0.127173301 -0.128011016 -0.128738414
## V2 -0.118630121 -0.119526679 -0.120326451 -0.121086672 -0.121754134
## V3 -0.006593702 -0.007323107 -0.007970047 -0.008583011 -0.009116809
## V4 -0.101161988 -0.104349829 -0.107241330 -0.110045942 -0.112543755
## s99
## (Intercept) 8.096455264
## V1 -0.129453437
## V2 -0.122415680
## V3 -0.009645386
## V4 -0.115058449
Cross-Validation
cvfit_ls <- cv.gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "ls")
plot(cvfit_ls)
coef(cvfit_ls, s = "lambda.min")
## 1
## (Intercept) 8.197773e+00
## V1 -2.672925e-02
## V2 -6.183860e-02
## V3 3.687290e-02
## V4 8.694734e-03
## V5 -8.829105e-02
## V6 -8.456807e-05
## V7 6.822711e-04
## V8 6.317361e-04
## V9 6.848111e-05
## V10 -1.123480e-03
## V11 2.820666e-02
## V12 -3.695297e-02
## V13 -4.326627e-03
## V14 6.422049e-03
## V15 -5.692340e-02
## V16 -2.198106e-04
## V17 4.512853e-02
## V18 -2.560941e-02
## V19 -5.128320e-03
## V20 -6.528665e-02
## V21 4.313356e-02
## V22 8.934235e-02
## V23 -4.545772e-02
## V24 -2.241544e-02
## V25 -1.662608e-01
## V26 1.207781e-01
## V27 2.789045e-02
## V28 -3.449442e-02
## V29 1.260556e-02
## V30 -1.873208e-01
## V31 -1.844027e-02
## V32 8.501327e-03
## V33 3.583815e-03
## V34 1.191608e-02
## V35 1.866050e-02
## V36 3.895912e-02
## V37 -1.437030e-02
## V38 6.427634e-03
## V39 1.168648e-02
## V40 -5.657613e-02
## V41 -2.330551e-03
## V42 -3.064803e-03
## V43 1.191571e-03
## V44 7.216732e-03
## V45 3.345442e-03
## V46 -9.474428e-02
## V47 7.760270e-02
## V48 9.471451e-02
## V49 1.466030e-02
## V50 2.249739e-02
## V51 -1.008583e-02
## V52 1.112999e-02
## V53 9.524593e-02
## V54 1.597186e-01
## V55 3.856741e-02
## V56 5.048018e-05
## V57 -1.063163e-05
## V58 -1.613658e-04
## V59 2.666697e-04
## V60 8.414123e-05
## V61 -5.692919e-02
## V62 3.423488e-02
## V63 1.331030e-03
## V64 8.528575e-02
## V65 2.249628e-01
## V66 -3.302048e-02
## V67 1.017548e-02
## V68 2.540641e-02
## V69 4.124517e-02
## V70 3.031728e-03
## V71 -8.444857e-03
## V72 -1.748408e-03
## V73 2.958499e-02
## V74 -4.612260e-03
## V75 8.148859e-03
## V76 -1.818270e-02
## V77 2.363876e-02
## V78 5.281023e-02
## V79 -8.057897e-03
## V80 1.797602e-02
## V81 5.307318e-03
## V82 -1.623854e-02
## V83 8.314143e-03
## V84 8.236939e-03
## V85 -2.402224e-02
## V86 5.402119e-03
## V87 -6.397635e-02
## V88 9.012578e-04
## V89 4.500677e-02
## V90 -7.815789e-02
## V91 1.665534e-02
## V92 -5.759135e-03
## V93 -6.432123e-03
## V94 1.552064e-02
## V95 -2.118880e-02
## V96 -2.735230e-03
## V97 2.547208e-03
## V98 -5.347579e-04
## V99 5.831298e-04
## V100 4.605191e-03
Weight Least squares regression
We can also perform weighted least-squares regression by specifying
loss='wls', and providing a \(n
\times n\) weight matrix in the weights argument,
where \(n\) is the number of
observations. Note that cross-validation is NOT
IMPLEMENTED for loss='wls'.
# generate weight matrix
times <- seq_along(bardet$y)
rho <- 0.5
sigma <- 1
H <- abs(outer(times, times, "-"))
V <- sigma * rho^H
p <- nrow(V)
V[cbind(1:p, 1:p)] <- V[cbind(1:p, 1:p)] * sigma
# reduce eps to speed up convergence for vignette build
fit_wls <- gglasso(x = bardet$x, y = bardet$y, group = group1, loss = "wls",
weight = V, eps = 1e-4)
plot(fit_wls)
coef(fit_wls)[1:5,90:100]
## s89 s90 s91 s92 s93
## (Intercept) 8.09429262 8.09340481 8.09254573 8.09170743 8.09089247
## V1 -0.13922372 -0.14077803 -0.14222609 -0.14359110 -0.14487482
## V2 -0.15966042 -0.16117772 -0.16261019 -0.16397683 -0.16527730
## V3 0.03917529 0.03880296 0.03847035 0.03816594 0.03788642
## V4 -0.16548208 -0.17057112 -0.17546237 -0.18021267 -0.18481370
## s94 s95 s96 s97 s98
## (Intercept) 8.09011527 8.08935394 8.08862146 8.08793054 8.08727098
## V1 -0.14606257 -0.14719352 -0.14824987 -0.14921624 -0.15011520
## V2 -0.16649386 -0.16766459 -0.16877053 -0.16979410 -0.17075592
## V3 0.03763241 0.03739356 0.03717453 0.03697953 0.03680099
## V4 -0.18919074 -0.19347289 -0.19758499 -0.20145156 -0.20513769
## s99
## (Intercept) 8.08664325
## V1 -0.15094837
## V2 -0.17165664
## V3 0.03663899
## V4 -0.20863833