Calculate information criteria.

This function uses the degrees of freedom to calculate various information criteria. This function uses the "unknown variance" version of the likelihood. Only implemented for Gaussian regression. The constant is ignored (as in stats::extractAIC()).

Usage

estimate_risk(object, x, type = c("AIC", "BIC", "GCV"), approx_df = FALSE)

Arguments

object: fitted object from a call to sparsegl().
x: Matrix. The matrix of predictors used to estimate the sparsegl object. May be missing if approx_df = TRUE.
type: one or more of AIC, BIC, or GCV.
approx_df: the df component of a sparsegl object is an approximation (albeit a fairly accurate one) to the actual degrees-of-freedom. However, the exact value requires inverting a portion of X'X. So this computation may take some time (the default computes the exact df).

Value

a data.frame with as many rows as object$lambda. It contains columns lambda, df, and the requested risk types.

References

Vaiter S, Deledalle C, Peyré G, Fadili J, Dossal C. (2012). The Degrees of Freedom of the Group Lasso for a General Design. https://arxiv.org/pdf/1212.6478.pdf.

Examples

n <- 100
p <- 20
X <- matrix(rnorm(n * p), nrow = n)
eps <- rnorm(n)
beta_star <- c(rep(5, 5), c(5, -5, 2, 0, 0), rep(-5, 5), rep(0, (p - 15)))
y <- X %*% beta_star + eps
groups <- rep(1:(p / 5), each = 5)
fit1 <- sparsegl(X, y, group = groups)
estimate_risk(fit1, type = "AIC", approx_df = TRUE)
#>           lambda        df        AIC
#> s0  5.921308e-01  0.000000 5.62511380
#> s1  5.395275e-01  5.311419 5.72305786
#> s2  4.915974e-01  6.977741 5.67767125
#> s3  4.479252e-01  7.649619 5.62023813
#> s4  4.081328e-01 14.674902 5.64244754
#> s5  3.718754e-01 15.875112 5.52197579
#> s6  3.388390e-01 16.460216 5.39453962
#> s7  3.087375e-01 16.812670 5.26841723
#> s8  2.813101e-01 22.458141 5.20837399
#> s9  2.563193e-01 23.216783 5.04414653
#> s10 2.335486e-01 23.634093 4.87296726
#> s11 2.128008e-01 23.905164 4.69879650
#> s12 1.938961e-01 24.097675 4.52304107
#> s13 1.766709e-01 24.242154 4.34637371
#> s14 1.609760e-01 24.354717 4.16918975
#> s15 1.466753e-01 24.444809 3.99176406
#> s16 1.336451e-01 24.518397 3.81431716
#> s17 1.217724e-01 24.579466 3.63704779
#> s18 1.109545e-01 24.630794 3.46015131
#> s19 1.010976e-01 24.674385 3.28383160
#> s20 9.211637e-02 24.711726 3.10830980
#> s21 8.393300e-02 24.743949 2.93383129
#> s22 7.647663e-02 24.771927 2.76067182
#> s23 6.968265e-02 24.796349 2.58914288
#> s24 6.349224e-02 24.817767 2.41959642
#> s25 5.785176e-02 24.836626 2.25242871
#> s26 5.271237e-02 24.853291 2.08808274
#> s27 4.802955e-02 26.851382 1.96668124
#> s28 4.376274e-02 26.866232 1.80947420
#> s29 3.987498e-02 26.879453 1.65667494
#> s30 3.633259e-02 26.891250 1.50888978
#> s31 3.310491e-02 26.901798 1.36674130
#> s32 3.016396e-02 26.911246 1.23094486
#> s33 2.748427e-02 26.919724 1.10190415
#> s34 2.504265e-02 26.927341 0.98025729
#> s35 2.281793e-02 26.934194 0.86646922
#> s36 2.079085e-02 26.940367 0.76089872
#> s37 1.894384e-02 26.945934 0.66377750
#> s38 1.726093e-02 26.950958 0.57519562
#> s39 1.572751e-02 26.955497 0.49509586
#> s40 1.433032e-02 26.959601 0.42339832
#> s41 1.305726e-02 26.963314 0.35952238
#> s42 1.189729e-02 26.966675 0.30315924
#> s43 1.084036e-02 26.969720 0.25379056
#> s44 9.877336e-03 26.972480 0.21084082
#> s45 8.999861e-03 26.974982 0.17370599
#> s46 8.200338e-03 26.977252 0.14177739
#> s47 7.471843e-03 26.979313 0.11446127
#> s48 6.808065e-03 26.981183 0.09128276
#> s49 6.203255e-03 26.982881 0.07152875
#> s50 5.652175e-03 26.984425 0.05482024
#> s51 5.150051e-03 26.985827 0.04073024
#> s52 4.692535e-03 34.018902 0.16566601
#> s53 4.275663e-03 34.834162 0.16791184
#> s54 3.895825e-03 35.196135 0.16322204
#> s55 3.549731e-03 35.400385 0.15725964
#> s56 3.234382e-03 35.531086 0.15143058
#> s57 2.947049e-03 35.621573 0.14615812
#> s58 2.685241e-03 35.687686 0.14154877
#> s59 2.446692e-03 35.737915 0.13759186
#> s60 2.229334e-03 35.777221 0.13423252
#> s61 2.031286e-03 35.808521 0.13143672
#> s62 1.850832e-03 35.834226 0.12906154
#> s63 1.686410e-03 35.855516 0.12707643
#> s64 1.536594e-03 35.873363 0.12542459
#> s65 1.400087e-03 35.888478 0.12405420
#> s66 1.275707e-03 35.901393 0.12292026
#> s67 1.162377e-03 33.933588 0.08240652
#> s68 1.059114e-03 33.940875 0.08159125
#> s69 9.650256e-04 33.947227 0.08091957
#> s70 8.792954e-04 35.937855 0.12006794
#> s71 8.011812e-04 35.944284 0.11965737
#> s72 7.300065e-04 35.949927 0.11934121
#> s73 6.651547e-04 35.954983 0.11905780
#> s74 6.060642e-04 35.959483 0.11882344
#> s75 5.522231e-04 35.963492 0.11863281
#> s76 5.031651e-04 35.967068 0.11847895
#> s77 4.584653e-04 35.970265 0.11835551
#> s78 4.177365e-04 35.973128 0.11825707
#> s79 3.806260e-04 35.975696 0.11817907
#> s80 3.468122e-04 35.977966 0.11814228
#> s81 3.160024e-04 35.980072 0.11807347
#> s82 2.879296e-04 35.981920 0.11805185
#> s83 2.623507e-04 35.983602 0.11802603
#> s84 2.390442e-04 35.985125 0.11800391
#> s85 2.178082e-04 35.986503 0.11798665
#> s86 1.984587e-04 35.987749 0.11797385
#> s87 1.808282e-04 35.988877 0.11796484
#> s88 1.647639e-04 35.989897 0.11795893
#> s89 1.501267e-04 35.990822 0.11795549
#> s90 1.367899e-04 35.991659 0.11795400
#> s91 1.246378e-04 35.992419 0.11795403
#> s92 1.135654e-04 35.993107 0.11795520
#> s93 1.034765e-04 35.993732 0.11795722
#> s94 9.428396e-05 35.994299 0.11795987
#> s95 8.590803e-05 35.994814 0.11796294
#> s96 7.827620e-05 35.995282 0.11796630
#> s97 7.132236e-05 35.995707 0.11796982
#> s98 6.498628e-05 35.996093 0.11797341
#> s99 5.921308e-05 35.996445 0.11797699

Usage

Arguments

Value

References

See also

Examples