Stability selection.
stabsel.RdPerforms stability selection based on gradient boosting.
stabsel(formula, data, family = "gaussian",
q, maxit, B = 100, thr = .9, fraction = 0.5, seed = NULL, ...)
## Plot selection frequencies.
# S3 method for stabsel
plot(x, show = NULL,
pal = function(n) gray.colors(n, start = 0.9, end = 0.3), ...)Arguments
- formula
A formula or extended formula.
- data
A
data.frame.- family
A
bamlss.familyobject.- q
An integer specifying how many terms to select in each boosting run.
- maxit
An integer specifying the maximum number of boosting iterations. See
opt_boost. Either chooseqormaxitas hyper-parameter for regularization.- B
An integer. The boosting is run B times.
- thr
Cut-off threshold of relative frequencies (between 0 and 1) for selection.
- fraction
Numeric between 0 and 1. The fraction of data to be used in each boosting run.
- seed
A seed to be set before the stability selection.
- x
A object of class stabsel.
- show
Number of terms to be shown.
- pal
Color palette for different model terms.
- ...
Not used yet in
stabsel.
Value
A object of class stabsel.
Details
stabsel performs stability selection based on gradient
boosting (opt_boost): The boosting algorithm is run
B times on a randomly drawn fraction of the data.
Each boosting run is stopped either when q terms have been selected,
or when maxit iterations have been performed, i.e. either q
or maxit can be used to tune the regularization of the boosting.
After the boosting the relative selection frequencies are evaluated.
Terms with a relative selection frequency larger then thr
are suggested for a final regression model.
If neither q nor maxit has been specified, q
will be set to the square root of the number of columns in data.
Gradient boosting does not depend on random numbers. Thus, the individual boosting runs differ only in the subset of data which is used.
Examples
if (FALSE) ## Simulate some data.
set.seed(111)
d <- GAMart()
n <- nrow(d)
## Add some noise variables.
for(i in 4:9)
d[[paste0("x",i)]] <- rnorm(n)
f <- paste0("~ ", paste("s(x", 1:9, ")", collapse = "+", sep = ""))
f <- paste(f, "+ te(lon,lat)")
f <- as.formula(f)
f <- list(update(f, num ~ .), f)
## Run stability selection.
sel <- stabsel(f, data = d, q = 6, B = 10)
#> Stability selection boosting run 1 / 10
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#>
#> elapsed time: 0.32sec
#> Stability selection boosting run 2 / 10
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#>
#> elapsed time: 0.26sec
#> Stability selection boosting run 3 / 10
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#>
#> elapsed time: 0.31sec
#> Stability selection boosting run 4 / 10
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#>
#> elapsed time: 0.24sec
#> Stability selection boosting run 6 / 10
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#> elapsed time: 0.29sec
#> Stability selection boosting run 8 / 10
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#> logLik 40.3144 eps 0.0046 iteration 78 qsel 5
#> logLik 41.0630 eps 0.0170 iteration 79 qsel 6
#>
#> elapsed time: 0.24sec
#> Stability selection boosting run 9 / 10
#> logLik -125.595 eps 0.3992 iteration 2 qsel 1
#> logLik -119.793 eps 0.7282 iteration 3 qsel 1
#> logLik -114.758 eps 0.7832 iteration 4 qsel 2
#> logLik -110.010 eps 0.2769 iteration 5 qsel 2
#> logLik -105.887 eps 58.563 iteration 6 qsel 2
#> logLik -102.002 eps 0.2570 iteration 7 qsel 2
#> logLik -98.6247 eps 0.3091 iteration 8 qsel 2
#> logLik -95.4447 eps 0.1572 iteration 9 qsel 2
#> logLik -92.1143 eps 0.3855 iteration 10 qsel 3
#> logLik -89.3596 eps 0.3979 iteration 11 qsel 3
#> logLik -86.8114 eps 0.1706 iteration 12 qsel 3
#> logLik -84.1389 eps 0.2030 iteration 13 qsel 3
#> logLik -81.8385 eps 0.0134 iteration 14 qsel 3
#> logLik -79.4766 eps 0.7750 iteration 15 qsel 3
#> logLik -77.3290 eps 0.2032 iteration 16 qsel 3
#> logLik -74.9568 eps 0.0133 iteration 17 qsel 3
#> logLik -72.5803 eps 1.7943 iteration 18 qsel 3
#> logLik -70.3728 eps 0.0125 iteration 19 qsel 3
#> logLik -68.2445 eps 0.5178 iteration 20 qsel 3
#> logLik -66.2108 eps 0.0116 iteration 21 qsel 3
#> logLik -64.2180 eps 0.3582 iteration 22 qsel 3
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#> logLik -60.0350 eps 0.0115 iteration 24 qsel 3
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#> logLik -56.2346 eps 0.0107 iteration 26 qsel 3
#> logLik -54.4794 eps 0.2160 iteration 27 qsel 3
#> logLik -52.6043 eps 0.0985 iteration 28 qsel 3
#> logLik -50.7122 eps 0.0104 iteration 29 qsel 3
#> logLik -49.0066 eps 0.1487 iteration 30 qsel 3
#> logLik -47.2940 eps 0.0097 iteration 31 qsel 3
#> logLik -45.7529 eps 0.2509 iteration 32 qsel 3
#> logLik -44.2126 eps 0.0090 iteration 33 qsel 3
#> logLik -42.6945 eps 0.3272 iteration 34 qsel 3
#> logLik -40.9640 eps 0.0835 iteration 35 qsel 3
#> logLik -39.4357 eps 0.0088 iteration 36 qsel 3
#> logLik -38.0901 eps 0.0734 iteration 37 qsel 3
#> logLik -36.7271 eps 0.0081 iteration 38 qsel 3
#> logLik -35.3847 eps 0.0983 iteration 39 qsel 3
#> logLik -33.8520 eps 0.0768 iteration 40 qsel 3
#> logLik -32.5180 eps 0.0079 iteration 41 qsel 3
#> logLik -31.3473 eps 0.0695 iteration 42 qsel 3
#> logLik -30.1666 eps 0.0073 iteration 43 qsel 3
#> logLik -28.9848 eps 0.0913 iteration 44 qsel 3
#> logLik -25.5366 eps 0.1061 iteration 45 qsel 4
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#> logLik -22.8151 eps 0.0078 iteration 47 qsel 4
#> logLik -21.6635 eps 0.0070 iteration 48 qsel 4
#> logLik -20.5967 eps 0.1281 iteration 49 qsel 4
#> logLik -19.5809 eps 0.0064 iteration 50 qsel 4
#> logLik -18.5395 eps 0.0663 iteration 51 qsel 4
#> logLik -15.1929 eps 0.1720 iteration 52 qsel 4
#> logLik -13.9992 eps 0.1061 iteration 53 qsel 4
#> logLik -12.7992 eps 0.0069 iteration 54 qsel 4
#> logLik -11.8120 eps 0.0061 iteration 55 qsel 4
#> logLik -10.8490 eps 0.0572 iteration 56 qsel 4
#> logLik -9.9614 eps 0.0791 iteration 57 qsel 4
#> logLik -6.9215 eps 0.1145 iteration 58 qsel 4
#> logLik -5.7996 eps 0.0065 iteration 59 qsel 4
#> logLik -4.8771 eps 0.0058 iteration 60 qsel 4
#> logLik -4.0268 eps 0.0393 iteration 61 qsel 4
#> logLik -2.9155 eps 0.0603 iteration 62 qsel 4
#> logLik -0.2107 eps 0.0663 iteration 63 qsel 4
#> logLik 0.8313 eps 0.0061 iteration 64 qsel 4
#> logLik 1.6875 eps 0.0054 iteration 65 qsel 4
#> logLik 2.4743 eps 0.0467 iteration 66 qsel 4
#> logLik 3.2194 eps 0.0050 iteration 67 qsel 4
#> logLik 3.9771 eps 0.0257 iteration 68 qsel 4
#> logLik 4.9925 eps 0.0368 iteration 69 qsel 4
#> logLik 7.4315 eps 0.1914 iteration 70 qsel 4
#> logLik 8.2689 eps 0.0052 iteration 71 qsel 4
#> logLik 8.9560 eps 0.0047 iteration 72 qsel 4
#> logLik 9.6473 eps 0.0265 iteration 73 qsel 4
#> logLik 10.3006 eps 0.0275 iteration 74 qsel 4
#> logLik 11.2103 eps 0.0515 iteration 75 qsel 4
#> logLik 11.8844 eps 0.0046 iteration 76 qsel 4
#> logLik 12.5144 eps 0.0249 iteration 77 qsel 5
#> logLik 14.6735 eps 0.0543 iteration 78 qsel 5
#> logLik 15.3635 eps 0.0046 iteration 79 qsel 5
#> logLik 15.9566 eps 0.0243 iteration 80 qsel 5
#> logLik 16.5502 eps 0.0042 iteration 81 qsel 5
#> logLik 17.1236 eps 0.0181 iteration 82 qsel 5
#> logLik 17.9470 eps 0.0515 iteration 83 qsel 5
#> logLik 18.5053 eps 0.0221 iteration 84 qsel 6
#>
#> elapsed time: 0.26sec
#> Stability selection boosting run 10 / 10
#> logLik -124.376 eps 0.2020 iteration 2 qsel 1
#> logLik -118.987 eps 0.5100 iteration 3 qsel 2
#> logLik -113.866 eps 0.6241 iteration 4 qsel 2
#> logLik -109.470 eps 0.6343 iteration 5 qsel 2
#> logLik -105.293 eps 0.7178 iteration 6 qsel 2
#> logLik -101.705 eps 0.6067 iteration 7 qsel 2
#> logLik -98.2963 eps 0.8038 iteration 8 qsel 2
#> logLik -94.7609 eps 0.3064 iteration 9 qsel 3
#> logLik -91.8834 eps 0.2975 iteration 10 qsel 3
#> logLik -89.1459 eps 2.7590 iteration 11 qsel 3
#> logLik -86.3403 eps 0.2020 iteration 12 qsel 3
#> logLik -84.0302 eps 0.2105 iteration 13 qsel 3
#> logLik -81.8280 eps 0.2773 iteration 14 qsel 3
#> logLik -79.5039 eps 0.0134 iteration 15 qsel 3
#> logLik -77.1583 eps 0.1994 iteration 16 qsel 3
#> logLik -74.9976 eps 0.0125 iteration 17 qsel 3
#> logLik -72.9517 eps 0.2246 iteration 18 qsel 3
#> logLik -70.9681 eps 0.0117 iteration 19 qsel 3
#> logLik -68.9214 eps 0.2521 iteration 20 qsel 3
#> logLik -66.8672 eps 0.1343 iteration 21 qsel 3
#> logLik -64.8421 eps 0.0115 iteration 22 qsel 3
#> logLik -63.0387 eps 0.1115 iteration 23 qsel 3
#> logLik -61.1993 eps 0.0107 iteration 24 qsel 3
#> logLik -59.3917 eps 1.0918 iteration 25 qsel 3
#> logLik -57.5930 eps 0.1030 iteration 26 qsel 3
#> logLik -55.7527 eps 0.0105 iteration 27 qsel 3
#> logLik -54.1679 eps 0.0611 iteration 28 qsel 3
#> logLik -52.5117 eps 0.0097 iteration 29 qsel 3
#> logLik -50.9194 eps 0.2067 iteration 30 qsel 3
#> logLik -49.3459 eps 0.0956 iteration 31 qsel 3
#> logLik -47.7168 eps 0.0094 iteration 32 qsel 3
#> logLik -46.3297 eps 0.0508 iteration 33 qsel 3
#> logLik -44.8754 eps 0.0087 iteration 34 qsel 3
#> logLik -43.4776 eps 0.0830 iteration 35 qsel 3
#> logLik -39.4144 eps 0.1214 iteration 36 qsel 4
#> logLik -37.7792 eps 0.0091 iteration 37 qsel 4
#> logLik -36.3660 eps 0.1503 iteration 38 qsel 4
#> logLik -34.9042 eps 0.0084 iteration 39 qsel 4
#> logLik -33.6987 eps 0.0693 iteration 40 qsel 4
#> logLik -32.4044 eps 0.0077 iteration 41 qsel 4
#> logLik -31.1368 eps 0.0492 iteration 42 qsel 4
#> logLik -27.2140 eps 0.0991 iteration 43 qsel 4
#> logLik -25.7622 eps 0.0081 iteration 44 qsel 4
#> logLik -24.4921 eps 0.0538 iteration 45 qsel 4
#> logLik -23.2016 eps 0.0075 iteration 46 qsel 4
#> logLik -22.1183 eps 0.0368 iteration 47 qsel 4
#> logLik -20.9814 eps 0.0069 iteration 48 qsel 4
#> logLik -19.8790 eps 0.0321 iteration 49 qsel 4
#> logLik -16.2228 eps 0.1847 iteration 50 qsel 4
#> logLik -14.9614 eps 0.0072 iteration 51 qsel 4
#> logLik -13.8200 eps 0.0425 iteration 52 qsel 4
#> logLik -12.7042 eps 0.0066 iteration 53 qsel 4
#> logLik -11.7390 eps 0.0416 iteration 54 qsel 4
#> logLik -10.7607 eps 0.0061 iteration 55 qsel 4
#> logLik -9.8037 eps 0.0352 iteration 56 qsel 4
#> logLik -6.4734 eps 0.4235 iteration 57 qsel 4
#> logLik -5.4018 eps 0.0063 iteration 58 qsel 4
#> logLik -4.3775 eps 0.0460 iteration 59 qsel 4
#> logLik -3.3362 eps 0.0586 iteration 60 qsel 5
#> logLik -2.3253 eps 0.0060 iteration 61 qsel 5
#> logLik -1.4666 eps 0.0740 iteration 62 qsel 5
#> logLik -0.5850 eps 0.0056 iteration 63 qsel 5
#> logLik 0.3035 eps 0.0438 iteration 64 qsel 6
#>
#> elapsed time: 0.22sec
#>
plot(sel)
## Estimate selected model.
nf <- formula(sel)
b <- bamlss(nf, data = d)
#> AICc -123.239 logPost 69.3283 logLik 93.6099 edf 30.006 eps 0.5816 iteration 1
#> AICc -263.907 logPost 149.7018 logLik 164.6302 edf 30.610 eps 0.2569 iteration 2
#> AICc -287.393 logPost 162.0310 logLik 180.4552 edf 34.172 eps 0.1674 iteration 3
#> AICc -290.935 logPost 147.4173 logLik 183.1285 edf 34.952 eps 0.1033 iteration 4
#> AICc -293.177 logPost -89.8766 logLik 183.5869 edf 34.380 eps 0.0116 iteration 5
#> AICc -293.821 logPost -2574.92 logLik 183.6353 edf 34.143 eps 0.0040 iteration 6
#> AICc -293.824 logPost -2574.92 logLik 183.6394 edf 34.145 eps 0.0007 iteration 7
#> AICc -293.824 logPost -2574.92 logLik 183.6400 edf 34.145 eps 0.0000 iteration 8
#> AICc -293.824 logPost -2574.92 logLik 183.6400 edf 34.145 eps 0.0000 iteration 8
#> elapsed time: 0.29sec
#> Starting the sampler...
#>
#> | | 0% 5.36sec
#> |* | 5% 4.98sec 0.26sec
#> |** | 10% 4.84sec 0.54sec
#> |*** | 15% 4.58sec 0.81sec
#> |**** | 20% 4.31sec 1.08sec
#> |***** | 25% 4.11sec 1.37sec
#> |****** | 30% 3.88sec 1.66sec
#> |******* | 35% 3.65sec 1.97sec
#> |******** | 40% 3.38sec 2.25sec
#> |********* | 45% 3.12sec 2.55sec
#> |********** | 50% 2.85sec 2.85sec
#> |*********** | 55% 2.56sec 3.12sec
#> |************ | 60% 2.28sec 3.43sec
#> |************* | 65% 2.00sec 3.72sec
#> |************** | 70% 1.71sec 4.00sec
#> |*************** | 75% 1.43sec 4.30sec
#> |**************** | 80% 1.15sec 4.61sec
#> |***************** | 85% 0.86sec 4.90sec
#> |****************** | 90% 0.58sec 5.19sec
#> |******************* | 95% 0.29sec 5.48sec
#> |********************| 100% 0.00sec 5.77sec
plot(b)
