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) 8.3148748322
## V1 0.0000000000
## V2 0.0000000000
## V3 0.0000000000
## V4 0.0000000000
## V5 0.0000000000
## V6 0.0000000000
## V7 0.0000000000
## V8 0.0000000000
## V9 0.0000000000
## V10 0.0000000000
## V11 0.0066204570
## V12 0.0061635778
## V13 -0.0022150081
## V14 -0.0021557725
## V15 -0.0162654586
## V16 0.0143604578
## V17 0.0174086662
## V18 -0.0103166902
## V19 -0.0030749981
## V20 -0.0370748121
## V21 0.1042391472
## V22 0.0831533457
## V23 -0.0730339677
## V24 -0.0134293267
## V25 -0.2166621808
## V26 0.0132488930
## V27 0.0184136028
## V28 -0.0011901735
## V29 -0.0008708406
## V30 -0.0345949679
## V31 0.0000000000
## V32 0.0000000000
## V33 0.0000000000
## V34 0.0000000000
## V35 0.0000000000
## V36 0.0000000000
## V37 0.0000000000
## V38 0.0000000000
## V39 0.0000000000
## V40 0.0000000000
## V41 0.0000000000
## V42 0.0000000000
## V43 0.0000000000
## V44 0.0000000000
## V45 0.0000000000
## V46 0.0000000000
## V47 0.0000000000
## V48 0.0000000000
## V49 0.0000000000
## V50 0.0000000000
## V51 -0.0102795843
## V52 -0.0251770227
## V53 0.0475609169
## V54 0.0618869468
## V55 0.0219921423
## V56 0.0000000000
## V57 0.0000000000
## V58 0.0000000000
## V59 0.0000000000
## V60 0.0000000000
## V61 0.0000000000
## V62 0.0000000000
## V63 0.0000000000
## V64 0.0000000000
## V65 0.0000000000
## V66 0.0000000000
## V67 0.0000000000
## V68 0.0000000000
## V69 0.0000000000
## V70 0.0000000000
## V71 0.0000000000
## V72 0.0000000000
## V73 0.0000000000
## V74 0.0000000000
## V75 0.0000000000
## V76 0.0000000000
## V77 0.0000000000
## V78 0.0000000000
## V79 0.0000000000
## V80 0.0000000000
## V81 0.0000000000
## V82 0.0000000000
## V83 0.0000000000
## V84 0.0000000000
## V85 0.0000000000
## V86 0.0000000000
## V87 0.0000000000
## V88 0.0000000000
## V89 0.0000000000
## V90 0.0000000000
## V91 0.0000000000
## V92 0.0000000000
## V93 0.0000000000
## V94 0.0000000000
## V95 0.0000000000
## V96 0.0000000000
## V97 0.0000000000
## V98 0.0000000000
## V99 0.0000000000
## V100 0.0000000000
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