Introduction to gglasso
Install the package
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 -0.115058449Cross-Validation
## 1
## (Intercept) 8.226716e+00
## V1 -9.635740e-03
## V2 -5.084061e-02
## V3 3.291428e-02
## V4 8.459574e-03
## V5 -8.452885e-02
## V6 2.706252e-04
## V7 9.201146e-04
## V8 6.286221e-04
## V9 4.431794e-05
## V10 -1.692116e-03
## V11 1.691817e-02
## V12 -1.733717e-02
## V13 5.052269e-05
## V14 1.467610e-03
## V15 -3.487459e-02
## V16 6.840565e-03
## V17 4.161445e-02
## V18 -2.115620e-02
## V19 -5.998927e-03
## V20 -7.223187e-02
## V21 5.674403e-02
## V22 7.860444e-02
## V23 -4.982707e-02
## V24 -1.515584e-02
## V25 -1.908265e-01
## V26 1.015941e-01
## V27 3.579452e-02
## V28 -2.235126e-02
## V29 5.299329e-03
## V30 -1.783018e-01
## V31 0.000000e+00
## V32 0.000000e+00
## V33 0.000000e+00
## V34 0.000000e+00
## V35 0.000000e+00
## V36 3.454886e-02
## V37 -2.116777e-02
## V38 8.384875e-03
## V39 1.167973e-02
## V40 -6.184521e-02
## V41 0.000000e+00
## V42 0.000000e+00
## V43 0.000000e+00
## V44 0.000000e+00
## V45 0.000000e+00
## V46 -4.970931e-02
## V47 3.588603e-02
## V48 6.571630e-02
## V49 1.073318e-02
## V50 1.256063e-02
## V51 -1.310646e-02
## V52 -6.181994e-04
## V53 8.971670e-02
## V54 1.462995e-01
## V55 4.174255e-02
## V56 0.000000e+00
## V57 0.000000e+00
## V58 0.000000e+00
## V59 0.000000e+00
## V60 0.000000e+00
## V61 -4.671701e-02
## V62 2.198836e-02
## V63 1.783872e-03
## V64 7.292415e-02
## V65 1.600456e-01
## V66 -1.927752e-02
## V67 2.996560e-03
## V68 2.244526e-02
## V69 2.550181e-02
## V70 2.543310e-03
## V71 -9.518966e-03
## V72 -4.846444e-03
## V73 3.046000e-02
## V74 -2.054210e-03
## V75 1.499520e-02
## V76 -1.614234e-02
## V77 1.387057e-02
## V78 4.126647e-02
## V79 -6.838469e-04
## V80 1.649933e-02
## V81 5.027452e-03
## V82 -1.109285e-02
## V83 5.654746e-03
## V84 5.367879e-03
## V85 -1.945426e-02
## V86 1.094152e-02
## V87 -5.227341e-02
## V88 1.192871e-02
## V89 3.113514e-02
## V90 -7.470814e-02
## V91 1.268292e-03
## V92 -2.220488e-04
## V93 -4.511828e-04
## V94 9.765719e-04
## V95 -1.962050e-03
## V96 0.000000e+00
## V97 0.000000e+00
## V98 0.000000e+00
## V99 0.000000e+00
## V100 0.000000e+00Weight Least squares regression
We can also perform weighted least-squares regression by specifying
loss='wls', and providing a n × 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)
## 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