Boosting BAMLSS

Optimizer functions for gradient and likelihood boosting with bamlss. In each boosting iteration the function selects the model term with the largest contribution to the log-likelihood, AIC or BIC.

## Gradient boosting optimizer.
opt_boost(x, y, family, weights = NULL,
  offset = NULL, nu = 0.1, nu.adapt = TRUE, df = 4, maxit = 400,
  mstop = NULL, maxq = NULL, qsel.splitfactor = FALSE,
  verbose = TRUE, digits = 4, flush = TRUE,
  eps = .Machine$double.eps^0.25,
  nback = NULL, plot = TRUE, initialize = TRUE,
  stop.criterion = NULL, select.type = 1,
  force.stop = TRUE, hatmatrix = !is.null(stop.criterion),
  reverse.edf = FALSE, approx.edf = FALSE,
  always = FALSE, ...)

boost(x, y, family, weights = NULL,
  offset = NULL, nu = 0.1, nu.adapt = TRUE, df = 4, maxit = 400,
  mstop = NULL, maxq = NULL, qsel.splitfactor = FALSE,
  verbose = TRUE, digits = 4, flush = TRUE,
  eps = .Machine$double.eps^0.25,
  nback = NULL, plot = TRUE, initialize = TRUE,
  stop.criterion = NULL, select.type = 1,
  force.stop = TRUE, hatmatrix = !is.null(stop.criterion),
  reverse.edf = FALSE, approx.edf = FALSE,
  always = FALSE, ...)

## Modified likelihood based boosting.
opt_boostm(x, y, family, offset = NULL,
  nu = 0.1, df = 3, maxit = 400, mstop = NULL,
  verbose = TRUE, digits = 4, flush = TRUE,
  eps = .Machine$double.eps^0.25, plot = TRUE,
  initialize = TRUE, stop.criterion = "BIC",
  force.stop = !is.null(stop.criterion),
  do.optim = TRUE, always = FALSE, ...)

boostm(x, y, family, offset = NULL,
  nu = 0.1, df = 3, maxit = 400, mstop = NULL,
  verbose = TRUE, digits = 4, flush = TRUE,
  eps = .Machine$double.eps^0.25, plot = TRUE,
  initialize = TRUE, stop.criterion = "BIC",
  force.stop = !is.null(stop.criterion),
  do.optim = TRUE, always = FALSE, ...)

## Boosting summary extractor.
boost_summary(object, ...)

## Plot all boosting paths.
boost_plot(x, which = c("loglik", "loglik.contrib", "parameters",
  "aic", "bic", "user"), intercept = TRUE, spar = TRUE, mstop = NULL,
  name = NULL, drop = NULL, labels = NULL, color = NULL, ...)

## Boosting summary printing and plotting.
# S3 method for boost_summary
print(x, summary = TRUE, plot = TRUE,
  which = c("loglik", "loglik.contrib"), intercept = TRUE,
  spar = TRUE, ...)
# S3 method for boost_summary
plot(x, ...)

## Model frame for out-of-sample selection.
boost_frame(formula, train, test, family = "gaussian", ...)

Arguments

x

For function opt_boost() the x list, as returned from function bamlss.frame, holding all model matrices and other information that is used for fitting the model. For the plotting function the corresponding bamlss object fitted with the opt_boost() optimizer.

y

The model response, as returned from function bamlss.frame.

family

A bamlss family object, see family.bamlss.

weights

Prior weights on the data, as returned from function bamlss.frame.

offset

Can be used to supply model offsets for use in fitting, returned from function bamlss.frame.

nu

Numeric, between [0, 1], controls the step size, i.e., the amount that should be added to model term parameters.

nu.adapt

Logical. If set to TRUE (default) step size nu is divided by 2, if current boosting iteration did not improve the loglikelihood.

df

Integer, defines the initial degrees of freedom that should be assigned to each smooth model term. May also be a named vector, the names must match the model term labels, e.g., as provided in summary.bamlss.

maxit

Integer, the maximum number of boosting iterations.

mstop

For convenience, overwrites maxit.

maxq

Integer, defines the maximum number of selected base-learners. The algorithm stops if this numer is exceeded.

qsel.splitfactor

Logical, if set to TRUE dummy variables of categorical predictors are counted individually.

name

Character, the name of the coefficient (group) that should be plotted. Note that the string provided in name will be removed from the labels on the 4th axis.

drop

Character, the name of the coefficient (group) that should not be plotted.

labels

A character string of labels that should be used on the 4 axis.

color

Colors or color function that creates colors for the (group) paths.

verbose

Print information during runtime of the algorithm.

digits

Set the digits for printing when verbose = TRUE.

flush

use flush.console for displaying the current output in the console.

eps

The tolerance used as stopping mechanism, see argument nback.

nback

Integer. If nback is not NULL, then the algorithm stops if the the change in the log-likelihood of the last nback iterations is smaller or equal to eps. If maxit = NULL the maximum number of iterations is set to 10000.

plot

Should the boosting summary be printed and plotted?

initialize

Logical, should intercepts be initialized?

stop.criterion

Character, selects the information criterion that should be used to determine the optimum number of boosting iterations. Either "AIC" or "BIC" is possible. Note that this feature requires to compute hat-matrices for each distributional parameter, therefore, the routine may be slow and computer storage intensive.

select.type

Should model terms be selected by the log-likelihood contribution, select.type = 1, or by the corresponding stop.criterion, select.type = 2.

force.stop

Logical, should the algorithm stop if the information criterion increases?

do.optim

Logical. Should smoothing parameters be optimized in each boosting iteration?

hatmatrix

Logical, if set to TRUE the hat-matrices for each distributional parameter will be computed. The hat-matrices are used to determine the effective (equivalent) degrees of freedom in each boosting iteration, i.e., it is possible to compute information criteria like the AIC or BIC for selecting the optimum number of boosting iterations.

reverse.edf

Logical. Instead of computing degrees of freedom with hat-matrices, the actual smoothing parameters are reverse engineered to compute the corresponding actual smoother matrix. Note that this option is still experimental.

approx.edf

Logical. Another experimental and fast approximation of the degrees of freedom.

always

Logical or character. Should the intercepts forced to be updated in each boosting iteration? If always = TRUE each intercept of each distributional parameter is updated, if always = "best" only the intercept corresponding to the distributional of the best fitting model term is updated.

object

A bamlss object that was fitted using opt_boost().

summary

Should the summary be printed?

which

Which of the three provided plots should be created?

intercept

Should the coefficient paths of intercepts be dropped in the plot?

spar

Should graphical parmeters be set with par?

formula

See bamlss.frame.

train, test

Data frames used for training and testing the model..

...

For function opt_boost(), arguments passed to bamlss.engine.setup. for function boost_summary() arguments passed to function print.boost_summary().

Value

For function boost_summary() a list containing information on selection frequencies etc. For function opt_boost() and opt_boostm() a list containing the following objects:

fitted.values

A named list of the fitted values based on the last boosting iteration of the modeled parameters of the selected distribution.

parameters

A matrix, each row corresponds to the parameter values of one boosting iteration.

boost_summary

The boosting summary which can be printed and plotted.

WARNINGS

The function does not take care of variable scaling for the linear parts! This must be done by the user, e.g., one option is to use argument scale.d in function bamlss.frame, which uses scale.

Function opt_boost() does not select the optimum stopping iteration! The modified likelihood based algorithm implemented in function opt_boostm() is still experimental!

See also

bamlss.frame, bamlss

Examples

if (FALSE) ## Simulate data.
set.seed(123)
d <- GAMart()

## Estimate model.
f <- num ~ x1 + x2 + x3 + lon + lat +
  s(x1) + s(x2) + s(x3) + s(lon) + s(lat) + te(lon,lat)

b <- bamlss(f, data = d, optimizer = opt_boost,
  sampler = FALSE, scale.d = TRUE, nu = 0.01,
  maxit = 1000, plot = FALSE)
#> 
#> logLik -181.739 eps 0.0123 iteration    2 qsel 1
#> logLik -180.556 eps 0.0122 iteration    3 qsel 1
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#> logLik  82.6996 eps 0.0002 iteration  942 qsel 4
#> logLik  82.7704 eps 0.0021 iteration  943 qsel 4
#> logLik  82.8411 eps 0.0002 iteration  944 qsel 4
#> logLik  82.9118 eps 0.0024 iteration  945 qsel 4
#> logLik  83.2965 eps 0.0062 iteration  946 qsel 4
#> logLik  83.4169 eps 0.0027 iteration  947 qsel 4
#> logLik  83.4883 eps 0.0002 iteration  948 qsel 4
#> logLik  83.5583 eps 0.0021 iteration  949 qsel 4
#> logLik  83.6286 eps 0.0002 iteration  950 qsel 4
#> logLik  83.6984 eps 0.0025 iteration  951 qsel 4
#> logLik  84.0782 eps 0.0098 iteration  952 qsel 4
#> logLik  84.1974 eps 0.0034 iteration  953 qsel 4
#> logLik  84.2684 eps 0.0002 iteration  954 qsel 4
#> logLik  84.3381 eps 0.0002 iteration  955 qsel 4
#> logLik  84.4075 eps 0.0021 iteration  956 qsel 4
#> logLik  84.4763 eps 0.0036 iteration  957 qsel 4
#> logLik  84.8512 eps 0.0086 iteration  958 qsel 4
#> logLik  84.9214 eps 0.0002 iteration  959 qsel 4
#> logLik  84.9903 eps 0.0002 iteration  960 qsel 4
#> logLik  85.0589 eps 0.0024 iteration  961 qsel 4
#> logLik  85.1774 eps 0.0030 iteration  962 qsel 4
#> logLik  85.2456 eps 0.0002 iteration  963 qsel 4
#> logLik  85.3137 eps 0.0038 iteration  964 qsel 4
#> logLik  85.6844 eps 0.0075 iteration  965 qsel 4
#> logLik  85.7528 eps 0.0002 iteration  966 qsel 4
#> logLik  85.8207 eps 0.0027 iteration  967 qsel 4
#> logLik  85.9381 eps 0.0037 iteration  968 qsel 4
#> logLik  86.0060 eps 0.0002 iteration  969 qsel 4
#> logLik  86.0731 eps 0.0063 iteration  970 qsel 4
#> logLik  86.1399 eps 0.0055 iteration  971 qsel 4
#> logLik  86.5060 eps 0.0102 iteration  972 qsel 4
#> logLik  86.5743 eps 0.0002 iteration  973 qsel 4
#> logLik  86.6414 eps 0.0002 iteration  974 qsel 4
#> logLik  86.7076 eps 0.0029 iteration  975 qsel 4
#> logLik  86.8241 eps 0.0034 iteration  976 qsel 4
#> logLik  86.8905 eps 0.0002 iteration  977 qsel 4
#> logLik  86.9567 eps 0.0034 iteration  978 qsel 4
#> logLik  87.3187 eps 0.0066 iteration  979 qsel 4
#> logLik  87.3854 eps 0.0002 iteration  980 qsel 4
#> logLik  87.4507 eps 0.0002 iteration  981 qsel 4
#> logLik  87.5162 eps 0.0028 iteration  982 qsel 4
#> logLik  87.6318 eps 0.0030 iteration  983 qsel 4
#> logLik  87.6972 eps 0.0023 iteration  984 qsel 4
#> logLik  88.0546 eps 0.0063 iteration  985 qsel 4
#> logLik  88.1209 eps 0.0002 iteration  986 qsel 4
#> logLik  88.1859 eps 0.0002 iteration  987 qsel 4
#> logLik  88.2504 eps 0.0024 iteration  988 qsel 4
#> logLik  88.3649 eps 0.0029 iteration  989 qsel 4
#> logLik  88.4297 eps 0.0022 iteration  990 qsel 4
#> logLik  88.7825 eps 0.0171 iteration  991 qsel 4
#> logLik  88.8483 eps 0.0002 iteration  992 qsel 4
#> logLik  88.9129 eps 0.0002 iteration  993 qsel 4
#> logLik  88.9766 eps 0.0028 iteration  994 qsel 4
#> logLik  89.0406 eps 0.0025 iteration  995 qsel 4
#> logLik  89.1540 eps 0.0032 iteration  996 qsel 4
#> logLik  89.2182 eps 0.0002 iteration  997 qsel 4
#> logLik  89.2812 eps 0.0002 iteration  998 qsel 4
#> logLik  89.3439 eps 0.0023 iteration  999 qsel 4
#> logLik  89.6935 eps 0.0076 iteration 1000 qsel 4
#> 
#>  elapsed time:  2.69sec

## Plot estimated effects.
## plot(b)

## Print and plot the boosting summary.
boost_summary(b, plot = FALSE)
#> 
#> logLik. = 89.6935 -> at mstop = 1000 
#> ---
#>             mu % selected LogLik contrib.
#> s(x1)                21.6           69.70
#> s(x3)                19.3           55.76
#> te(lon,lat)           8.4           45.71
#> s(x2)                15.9           43.29
#> (Intercept)           0.0            0.00
#> x1                    0.0            0.00
#> x2                    0.0            0.00
#> x3                    0.0            0.00
#> lon                   0.0            0.00
#> lat                   0.0            0.00
#> s(lon)                0.0            0.00
#> s(lat)                0.0            0.00
#> ---
#>             sigma % selected LogLik contrib.
#> (Intercept)             34.7           58.18
#> 
## boost_plot(b, which = 1)
## boost_plot(b, which = 2)
## boost_plot(b, which = 3, name = "mu.s.te(lon,lat).")

## Extract estimated parameters for certain
## boosting iterations.
parameters(b, mstop = 1)
#>     mu.p.(Intercept)              mu.p.x1              mu.p.x2 
#>          -0.05841161           0.00000000           0.00000000 
#>              mu.p.x3             mu.p.lon             mu.p.lat 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x1).b1        mu.s.s(x1).b2        mu.s.s(x1).b3 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x1).b4        mu.s.s(x1).b5        mu.s.s(x1).b6 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x1).b7        mu.s.s(x1).b8        mu.s.s(x1).b9 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x2).b1        mu.s.s(x2).b2        mu.s.s(x2).b3 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x2).b4        mu.s.s(x2).b5        mu.s.s(x2).b6 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x2).b7        mu.s.s(x2).b8        mu.s.s(x2).b9 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x3).b1        mu.s.s(x3).b2        mu.s.s(x3).b3 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x3).b4        mu.s.s(x3).b5        mu.s.s(x3).b6 
#>           0.00000000           0.00000000           0.00000000 
#>        mu.s.s(x3).b7        mu.s.s(x3).b8        mu.s.s(x3).b9 
#>           0.00000000           0.00000000           0.00000000 
#>       mu.s.s(lon).b1       mu.s.s(lon).b2       mu.s.s(lon).b3 
#>           0.00000000           0.00000000           0.00000000 
#>       mu.s.s(lon).b4       mu.s.s(lon).b5       mu.s.s(lon).b6 
#>           0.00000000           0.00000000           0.00000000 
#>       mu.s.s(lon).b7       mu.s.s(lon).b8       mu.s.s(lon).b9 
#>           0.00000000           0.00000000           0.00000000 
#>       mu.s.s(lat).b1       mu.s.s(lat).b2       mu.s.s(lat).b3 
#>           0.00000000           0.00000000           0.00000000 
#>       mu.s.s(lat).b4       mu.s.s(lat).b5       mu.s.s(lat).b6 
#>           0.00000000           0.00000000           0.00000000 
#>       mu.s.s(lat).b7       mu.s.s(lat).b8       mu.s.s(lat).b9 
#>           0.00000000           0.00000000           0.00000000 
#>  mu.s.te(lon,lat).b1  mu.s.te(lon,lat).b2  mu.s.te(lon,lat).b3 
#>           0.00000000           0.00000000           0.00000000 
#>  mu.s.te(lon,lat).b4  mu.s.te(lon,lat).b5  mu.s.te(lon,lat).b6 
#>           0.00000000           0.00000000           0.00000000 
#>  mu.s.te(lon,lat).b7  mu.s.te(lon,lat).b8  mu.s.te(lon,lat).b9 
#>           0.00000000           0.00000000           0.00000000 
#> mu.s.te(lon,lat).b10 mu.s.te(lon,lat).b11 mu.s.te(lon,lat).b12 
#>           0.00000000           0.00000000           0.00000000 
#> mu.s.te(lon,lat).b13 mu.s.te(lon,lat).b14 mu.s.te(lon,lat).b15 
#>           0.00000000           0.00000000           0.00000000 
#> mu.s.te(lon,lat).b16 mu.s.te(lon,lat).b17 mu.s.te(lon,lat).b18 
#>           0.00000000           0.00000000           0.00000000 
#> mu.s.te(lon,lat).b19 mu.s.te(lon,lat).b20 mu.s.te(lon,lat).b21 
#>           0.00000000           0.00000000           0.00000000 
#> mu.s.te(lon,lat).b22 mu.s.te(lon,lat).b23 mu.s.te(lon,lat).b24 
#>           0.00000000           0.00000000           0.00000000 
#>  sigma.p.(Intercept) 
#>          -1.05304572 
parameters(b, mstop = 100)
#>     mu.p.(Intercept)              mu.p.x1              mu.p.x2 
#>         -0.058411614          0.000000000          0.000000000 
#>              mu.p.x3             mu.p.lon             mu.p.lat 
#>          0.000000000          0.000000000          0.000000000 
#>        mu.s.s(x1).b1        mu.s.s(x1).b2        mu.s.s(x1).b3 
#>          0.039268945         -0.001350402          0.015219138 
#>        mu.s.s(x1).b4        mu.s.s(x1).b5        mu.s.s(x1).b6 
#>          0.009161954          0.007104356          0.005601264 
#>        mu.s.s(x1).b7        mu.s.s(x1).b8        mu.s.s(x1).b9 
#>          0.001180029          0.001274986         -0.126444256 
#>        mu.s.s(x2).b1        mu.s.s(x2).b2        mu.s.s(x2).b3 
#>         -0.001271167          0.069043611          0.001003697 
#>        mu.s.s(x2).b4        mu.s.s(x2).b5        mu.s.s(x2).b6 
#>         -0.024173043          0.004058185         -0.021312378 
#>        mu.s.s(x2).b7        mu.s.s(x2).b8        mu.s.s(x2).b9 
#>         -0.007109845          0.055989599          0.007363287 
#>        mu.s.s(x3).b1        mu.s.s(x3).b2        mu.s.s(x3).b3 
#>          0.024911838         -0.029259307         -0.012201572 
#>        mu.s.s(x3).b4        mu.s.s(x3).b5        mu.s.s(x3).b6 
#>          0.022586312          0.016285732          0.035045844 
#>        mu.s.s(x3).b7        mu.s.s(x3).b8        mu.s.s(x3).b9 
#>          0.011050418         -0.160889392         -0.021359849 
#>       mu.s.s(lon).b1       mu.s.s(lon).b2       mu.s.s(lon).b3 
#>          0.000000000          0.000000000          0.000000000 
#>       mu.s.s(lon).b4       mu.s.s(lon).b5       mu.s.s(lon).b6 
#>          0.000000000          0.000000000          0.000000000 
#>       mu.s.s(lon).b7       mu.s.s(lon).b8       mu.s.s(lon).b9 
#>          0.000000000          0.000000000          0.000000000 
#>       mu.s.s(lat).b1       mu.s.s(lat).b2       mu.s.s(lat).b3 
#>          0.000000000          0.000000000          0.000000000 
#>       mu.s.s(lat).b4       mu.s.s(lat).b5       mu.s.s(lat).b6 
#>          0.000000000          0.000000000          0.000000000 
#>       mu.s.s(lat).b7       mu.s.s(lat).b8       mu.s.s(lat).b9 
#>          0.000000000          0.000000000          0.000000000 
#>  mu.s.te(lon,lat).b1  mu.s.te(lon,lat).b2  mu.s.te(lon,lat).b3 
#>          0.000000000          0.000000000          0.000000000 
#>  mu.s.te(lon,lat).b4  mu.s.te(lon,lat).b5  mu.s.te(lon,lat).b6 
#>          0.000000000          0.000000000          0.000000000 
#>  mu.s.te(lon,lat).b7  mu.s.te(lon,lat).b8  mu.s.te(lon,lat).b9 
#>          0.000000000          0.000000000          0.000000000 
#> mu.s.te(lon,lat).b10 mu.s.te(lon,lat).b11 mu.s.te(lon,lat).b12 
#>          0.000000000          0.000000000          0.000000000 
#> mu.s.te(lon,lat).b13 mu.s.te(lon,lat).b14 mu.s.te(lon,lat).b15 
#>          0.000000000          0.000000000          0.000000000 
#> mu.s.te(lon,lat).b16 mu.s.te(lon,lat).b17 mu.s.te(lon,lat).b18 
#>          0.000000000          0.000000000          0.000000000 
#> mu.s.te(lon,lat).b19 mu.s.te(lon,lat).b20 mu.s.te(lon,lat).b21 
#>          0.000000000          0.000000000          0.000000000 
#> mu.s.te(lon,lat).b22 mu.s.te(lon,lat).b23 mu.s.te(lon,lat).b24 
#>          0.000000000          0.000000000          0.000000000 
#>  sigma.p.(Intercept) 
#>         -1.053045720 

## Also works with predict().
head(do.call("cbind", predict(b, mstop = 1)))
#>               mu     sigma
#> [1,] -0.05841161 -1.053046
#> [2,] -0.05841161 -1.053046
#> [3,] -0.05841161 -1.053046
#> [4,] -0.05841161 -1.053046
#> [5,] -0.05841161 -1.053046
#> [6,] -0.05841161 -1.053046
head(do.call("cbind", predict(b, mstop = 100)))
#>               mu     sigma
#> [1,]  0.01910224 -1.053046
#> [2,]  0.02862474 -1.053046
#> [3,]  0.01147507 -1.053046
#> [4,] -0.02623836 -1.053046
#> [5,] -0.15807300 -1.053046
#> [6,] -0.01981386 -1.053046

## Another example using the modified likelihood
## boosting algorithm.
f <- list(
  num ~ x1 + x2 + x3 + lon + lat +
    s(x1) + s(x2) + s(x3) + s(lon) + s(lat) + te(lon,lat),
  sigma ~ x1 + x2 + x3 + lon + lat +
    s(x1) + s(x2) + s(x3) + s(lon) + s(lat) + te(lon,lat)
)

b <- bamlss(f, data = d, optimizer = opt_boostm,
  sampler = FALSE, scale.d = TRUE, nu = 0.05,
  maxit = 400, stop.criterion = "AIC", force.stop = FALSE)
#> 
#> AIC 342.6370 logLik -165.617 edf 5.70  eps 0.2729 iteration   2 qsel 1
#> AIC 317.4701 logLik -153.617 edf 5.11  eps 0.8732 iteration   3 qsel 1
#> AIC 299.7005 logLik -144.837 edf 5.01  eps 0.4551 iteration   4 qsel 1
#> AIC 286.6101 logLik -136.499 edf 6.80  eps 0.5352 iteration   5 qsel 2
#> AIC 273.5653 logLik -129.989 edf 6.79  eps 0.3087 iteration   6 qsel 2
#> AIC 264.4006 logLik -125.410 edf 6.78  eps 0.1677 iteration   7 qsel 2
#> AIC 255.5750 logLik -121.381 edf 6.40  eps 0.3306 iteration   8 qsel 2
#> AIC 247.9529 logLik -115.907 edf 8.06  eps 0.4191 iteration   9 qsel 3
#> AIC 240.3521 logLik -112.304 edf 7.87  eps 0.2329 iteration  10 qsel 3
#> AIC 233.1309 logLik -108.695 edf 7.86  eps 0.1806 iteration  11 qsel 3
#> AIC 226.5740 logLik -105.445 edf 7.84  eps 0.1467 iteration  12 qsel 3
#> AIC 220.0163 logLik -102.163 edf 7.84  eps 0.1087 iteration  13 qsel 3
#> AIC 214.1120 logLik -99.2019 edf 7.85  eps 0.0723 iteration  14 qsel 3
#> AIC 208.5310 logLik -96.4445 edf 7.82  eps 0.1589 iteration  15 qsel 3
#> AIC 203.2088 logLik -93.7769 edf 7.82  eps 0.2531 iteration  16 qsel 3
#> AIC 198.4152 logLik -91.3695 edf 7.83  eps 0.0531 iteration  17 qsel 3
#> AIC 194.0921 logLik -89.1967 edf 7.84  eps 0.0852 iteration  18 qsel 3
#> AIC 189.9517 logLik -87.1583 edf 7.81  eps 0.2007 iteration  19 qsel 3
#> AIC 186.0524 logLik -85.1994 edf 7.82  eps 0.0575 iteration  20 qsel 3
#> AIC 182.1352 logLik -83.4495 edf 7.61  eps 0.7721 iteration  21 qsel 3
#> AIC 178.5933 logLik -81.6707 edf 7.62  eps 0.0817 iteration  22 qsel 3
#> AIC 175.4069 logLik -80.0647 edf 7.63  eps 0.1155 iteration  23 qsel 3
#> AIC 172.3283 logLik -78.5459 edf 7.61  eps 0.1152 iteration  24 qsel 3
#> AIC 169.4546 logLik -77.0982 edf 7.62  eps 0.0430 iteration  25 qsel 3
#> AIC 166.8687 logLik -75.7909 edf 7.64  eps 0.1481 iteration  26 qsel 3
#> AIC 164.5381 logLik -74.6104 edf 7.65  eps 0.0552 iteration  27 qsel 3
#> AIC 162.2282 logLik -72.4554 edf 8.65  eps 0.1934 iteration  28 qsel 4
#> AIC 159.5092 logLik -71.0960 edf 8.65  eps 0.1042 iteration  29 qsel 4
#> AIC 157.2037 logLik -69.9550 edf 8.64  eps 0.0606 iteration  30 qsel 4
#> AIC 155.0331 logLik -68.8662 edf 8.65  eps 0.0353 iteration  31 qsel 4
#> AIC 153.0994 logLik -67.8827 edf 8.66  eps 0.0586 iteration  32 qsel 4
#> AIC 151.3325 logLik -66.9993 edf 8.66  eps 0.1045 iteration  33 qsel 4
#> AIC 149.5649 logLik -66.1016 edf 8.68  eps 0.0526 iteration  34 qsel 4
#> AIC 147.8498 logLik -65.2553 edf 8.66  eps 0.0779 iteration  35 qsel 4
#> AIC 146.2610 logLik -64.4449 edf 8.68  eps 0.0306 iteration  36 qsel 4
#> AIC 144.8354 logLik -63.7130 edf 8.70  eps 0.0260 iteration  37 qsel 4
#> AIC 143.5296 logLik -63.0639 edf 8.70  eps 0.0418 iteration  38 qsel 4
#> AIC 142.2431 logLik -62.4031 edf 8.71  eps 0.0288 iteration  39 qsel 4
#> AIC 141.0534 logLik -61.8083 edf 8.71  eps 0.0332 iteration  40 qsel 4
#> AIC 139.8818 logLik -61.2049 edf 8.73  eps 0.0274 iteration  41 qsel 4
#> AIC 138.8355 logLik -60.6600 edf 8.75  eps 0.0261 iteration  42 qsel 4
#> AIC 137.8056 logLik -60.1448 edf 8.75  eps 0.0308 iteration  43 qsel 4
#> AIC 136.8642 logLik -59.6532 edf 8.77  eps 0.0320 iteration  44 qsel 4
#> AIC 136.0137 logLik -59.2219 edf 8.78  eps 0.0332 iteration  45 qsel 4
#> AIC 135.1710 logLik -58.7790 edf 8.80  eps 0.0283 iteration  46 qsel 4
#> AIC 134.3783 logLik -58.3826 edf 8.80  eps 0.0297 iteration  47 qsel 4
#> AIC 133.6133 logLik -57.9792 edf 8.82  eps 0.0193 iteration  48 qsel 4
#> AIC 132.8894 logLik -57.6094 edf 8.83  eps 0.0265 iteration  49 qsel 4
#> AIC 132.2101 logLik -57.2458 edf 8.85  eps 0.0314 iteration  50 qsel 4
#> AIC 131.5717 logLik -56.9164 edf 8.86  eps 0.0276 iteration  51 qsel 4
#> AIC 130.9665 logLik -56.5890 edf 8.89  eps 1.5190 iteration  52 qsel 4
#> AIC 130.3910 logLik -56.2902 edf 8.90  eps 0.0340 iteration  53 qsel 4
#> AIC 129.8521 logLik -55.9961 edf 8.92  eps 0.0231 iteration  54 qsel 4
#> AIC 129.3243 logLik -55.7322 edf 8.92  eps 0.0614 iteration  55 qsel 4
#> AIC 128.8039 logLik -55.4594 edf 8.94  eps 0.0366 iteration  56 qsel 4
#> AIC 128.3140 logLik -55.1932 edf 8.96  eps 0.0395 iteration  57 qsel 4
#> AIC 127.8342 logLik -54.9403 edf 8.97  eps 0.0177 iteration  58 qsel 4
#> AIC 127.3884 logLik -54.7022 edf 8.99  eps 0.0140 iteration  59 qsel 4
#> AIC 126.9619 logLik -54.4641 edf 9.01  eps 0.0148 iteration  60 qsel 4
#> AIC 126.5465 logLik -54.2412 edf 9.03  eps 0.0135 iteration  61 qsel 4
#> AIC 126.1585 logLik -54.0303 edf 9.04  eps 0.0236 iteration  62 qsel 4
#> AIC 125.7861 logLik -53.8177 edf 9.07  eps 0.0138 iteration  63 qsel 4
#> AIC 125.4232 logLik -53.6192 edf 9.09  eps 0.0214 iteration  64 qsel 4
#> AIC 125.0770 logLik -53.4461 edf 9.09  eps 0.0188 iteration  65 qsel 4
#> AIC 124.7430 logLik -53.2592 edf 9.11  eps 0.0121 iteration  66 qsel 4
#> AIC 124.4093 logLik -53.0684 edf 9.13  eps 0.0213 iteration  67 qsel 4
#> AIC 124.0931 logLik -52.8906 edf 9.15  eps 0.0117 iteration  68 qsel 4
#> AIC 123.7950 logLik -52.7201 edf 9.17  eps 0.0106 iteration  69 qsel 4
#> AIC 123.5092 logLik -52.5501 edf 9.20  eps 0.0178 iteration  70 qsel 4
#> AIC 123.2277 logLik -52.3870 edf 9.22  eps 0.0157 iteration  71 qsel 4
#> AIC 122.9611 logLik -52.2284 edf 9.25  eps 0.0112 iteration  72 qsel 4
#> AIC 122.7058 logLik -52.0724 edf 9.28  eps 0.0332 iteration  73 qsel 4
#> AIC 122.4557 logLik -51.9212 edf 9.30  eps 0.0099 iteration  74 qsel 4
#> AIC 122.2085 logLik -51.7677 edf 9.33  eps 0.0361 iteration  75 qsel 4
#> AIC 121.9699 logLik -51.6123 edf 9.37  eps 0.0114 iteration  76 qsel 4
#> AIC 121.7355 logLik -51.4511 edf 9.41  eps 0.0094 iteration  77 qsel 4
#> AIC 121.4573 logLik -51.3129 edf 9.41  eps 0.0075 iteration  78 qsel 4
#> AIC 121.2151 logLik -51.1925 edf 9.41  eps 0.0063 iteration  79 qsel 4
#> AIC 120.9911 logLik -51.0805 edf 9.41  eps 0.0241 iteration  80 qsel 4
#> AIC 120.7589 logLik -50.9452 edf 9.43  eps 0.0148 iteration  81 qsel 4
#> AIC 120.5759 logLik -50.8250 edf 9.46  eps 0.0094 iteration  82 qsel 4
#> AIC 120.4204 logLik -50.7182 edf 9.49  eps 0.0078 iteration  83 qsel 4
#> AIC 120.2687 logLik -50.6423 edf 9.49  eps 0.0114 iteration  84 qsel 4
#> AIC 120.1288 logLik -50.5465 edf 9.51  eps 0.0088 iteration  85 qsel 4
#> AIC 120.0170 logLik -50.4615 edf 9.54  eps 0.0112 iteration  86 qsel 4
#> AIC 119.9137 logLik -50.4098 edf 9.54  eps 0.0098 iteration  87 qsel 4
#> AIC 119.8143 logLik -50.3337 edf 9.57  eps 0.0068 iteration  88 qsel 4
#> AIC 119.7236 logLik -49.2884 edf 10.5  eps 0.0092 iteration  89 qsel 5
#> AIC 118.3341 logLik -48.5937 edf 10.5  eps 0.0081 iteration  90 qsel 5
#> AIC 117.4665 logLik -48.1599 edf 10.5  eps 0.0069 iteration  91 qsel 5
#> AIC 116.7648 logLik -47.6714 edf 10.7  eps 0.1396 iteration  92 qsel 5
#> AIC 116.1922 logLik -47.3637 edf 10.7  eps 0.0261 iteration  93 qsel 5
#> AIC 115.6583 logLik -47.0968 edf 10.7  eps 0.0060 iteration  94 qsel 5
#> AIC 115.2587 logLik -46.8812 edf 10.7  eps 0.0362 iteration  95 qsel 5
#> AIC 114.9798 logLik -46.7417 edf 10.7  eps 0.0051 iteration  96 qsel 5
#> AIC 114.7844 logLik -46.6418 edf 10.7  eps 0.0444 iteration  97 qsel 5
#> AIC 114.6732 logLik -46.5862 edf 10.7  eps 0.0041 iteration  98 qsel 5
#> AIC 114.5974 logLik -46.5483 edf 10.7  eps 0.0115 iteration  99 qsel 5
#> AIC 114.5443 logLik -46.5217 edf 10.7  eps 0.0052 iteration 100 qsel 5
#> AIC 114.5066 logLik -46.5029 edf 10.7  eps 0.0034 iteration 101 qsel 5
#> AIC 114.4795 logLik -46.4894 edf 10.7  eps 0.0025 iteration 102 qsel 5
#> AIC 114.4578 logLik -46.4785 edf 10.7  eps 0.0032 iteration 103 qsel 5
#> AIC 114.4372 logLik -46.4682 edf 10.7  eps 0.0020 iteration 104 qsel 5
#> AIC 114.4222 logLik -46.4607 edf 10.7  eps 0.0016 iteration 105 qsel 5
#> AIC 114.4112 logLik -46.4552 edf 10.7  eps 0.0013 iteration 106 qsel 5
#> AIC 114.4032 logLik -46.4512 edf 10.7  eps 0.0011 iteration 107 qsel 5
#> AIC 114.3973 logLik -46.4482 edf 10.7  eps 0.0011 iteration 108 qsel 5
#> AIC 114.3930 logLik -46.4461 edf 10.7  eps 0.0013 iteration 109 qsel 5
#> AIC 114.3898 logLik -46.4445 edf 10.7  eps 0.0030 iteration 110 qsel 5
#> AIC 114.3874 logLik -46.4433 edf 10.7  eps 0.0021 iteration 111 qsel 5
#> AIC 114.3857 logLik -46.4424 edf 10.7  eps 0.0007 iteration 112 qsel 5
#> AIC 114.3844 logLik -46.4418 edf 10.7  eps 0.0004 iteration 113 qsel 5
#> AIC 114.3834 logLik -46.4413 edf 10.7  eps 0.0002 iteration 114 qsel 5
#> AIC 114.3827 logLik -46.4409 edf 10.7  eps 0.0001 iteration 115 qsel 5
#> AIC 114.3822 logLik -46.4407 edf 10.7  eps 0.0001 iteration 116 qsel 5
#> AIC 114.3818 logLik -46.4405 edf 10.7  eps 0.0000 iteration 117 qsel 5
#> AIC 114.3815 logLik -46.4403 edf 10.7  eps 0.0000 iteration 118 qsel 5
#> AIC 114.3813 logLik -46.4402 edf 10.7  eps 0.0000 iteration 119 qsel 5
#> AIC 114.3811 logLik -46.4402 edf 10.7  eps 0.0000 iteration 120 qsel 5
#> AIC 114.3810 logLik -46.4401 edf 10.7  eps 0.0000 iteration 121 qsel 5
#> AIC 114.3809 logLik -46.4401 edf 10.7  eps 0.0000 iteration 122 qsel 5
#> AIC 114.3809 logLik -46.4400 edf 10.7  eps 0.0000 iteration 123 qsel 5
#> AIC 114.3808 logLik -46.4400 edf 10.7  eps 0.0000 iteration 124 qsel 5
#> AIC 114.3808 logLik -46.4400 edf 10.7  eps 0.0000 iteration 125 qsel 5
#> AIC 114.3808 logLik -46.4400 edf 10.7  eps 0.0000 iteration 126 qsel 5
#> AIC 114.3808 logLik -46.4400 edf 10.7  eps 0.0000 iteration 127 qsel 5
#> AIC 114.3807 logLik -46.4400 edf 10.7  eps 0.0000 iteration 128 qsel 5
#> AIC 114.3807 logLik -46.4400 edf 10.7  eps 0.0000 iteration 129 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 130 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 131 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 132 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 133 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 134 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 135 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 136 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 137 qsel 5
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#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 170 qsel 5
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#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 210 qsel 5
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#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 330 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 331 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 332 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 333 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 334 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 335 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 336 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 337 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 338 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 339 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 340 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 341 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 342 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 343 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 344 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 345 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 346 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 347 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 348 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 349 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 350 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 351 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 352 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 353 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 354 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 355 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 356 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 357 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 358 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 359 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 360 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 361 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 362 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 363 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 364 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 365 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 366 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 367 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 368 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 369 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 370 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 371 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 372 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 373 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 374 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 375 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 376 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 377 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 378 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 379 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 380 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 381 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 382 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 383 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 384 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 385 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 386 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 387 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 388 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 389 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 390 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 391 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 392 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 393 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 394 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 395 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 396 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 397 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 398 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 399 qsel 5
#> AIC 114.3807 logLik -46.4399 edf 10.7  eps 0.0000 iteration 400 qsel 5
#> 
#>  elapsed time: 35.89sec


## Plot estimated effects.
## plot(b)

## Plot AIC and log-lik contributions.
## boost_plot(b, "AIC")
## boost_plot(b, "loglik.contrib")

## Out-of-sample selection of model terms.
set.seed(123)
d <- GAMart(n = 5000)

## Split data into training and testing
i <- sample(1:2, size = nrow(d), replace = TRUE)
dtest <- subset(d, i == 1)
dtrain <- subset(d, i == 2)

## Model formula
f <- list(
  num ~ s(x1) + s(x2) + s(x3),
  sigma ~ s(x1) + s(x2) + s(x3)
)

## Create model frame for out-of-sample selection.
sm <- boost_frame(f, train = dtrain, test = dtest, family = "gaussian")

## Out-of-sample selection function.
sfun <- function(parameters) {
  sm$parameters <- parameters
  p <- predict(sm, type = "parameter")
  -1 * sum(sm$family$d(dtest$num, p, log = TRUE))
}

## Start boosting with out-of-sample negative
## log-likelihood selection of model terms.
b <- bamlss(f, data = dtrain, sampler = FALSE, optimizer = opt_boost,
  selectfun = sfun, always = "best")
#> 
#> userIC 2413.338 logLik -598.545 eps 0.0531 iteration   2 qsel 1
#> userIC 2409.204 logLik -546.484 eps 0.0509 iteration   3 qsel 2
#> userIC 2408.146 logLik -501.945 eps 0.0545 iteration   4 qsel 2
#> userIC 2404.738 logLik -459.498 eps 0.0536 iteration   5 qsel 2
#> userIC 2403.927 logLik -423.168 eps 0.1060 iteration   6 qsel 2
#> userIC 2401.114 logLik -388.559 eps 0.1721 iteration   7 qsel 2
#> userIC 2399.574 logLik -356.674 eps 0.1006 iteration   8 qsel 3
#> userIC 2397.478 logLik -327.295 eps 0.3657 iteration   9 qsel 3
#> userIC 2395.112 logLik -299.251 eps 0.1390 iteration  10 qsel 3
#> userIC 2393.894 logLik -273.542 eps 0.1068 iteration  11 qsel 3
#> userIC 2392.253 logLik -249.784 eps 0.0981 iteration  12 qsel 3
#> userIC 2390.262 logLik -227.060 eps 0.2394 iteration  13 qsel 3
#> userIC 2389.281 logLik -206.297 eps 0.1422 iteration  14 qsel 3
#> userIC 2388.016 logLik -187.084 eps 0.1092 iteration  15 qsel 3
#> userIC 2386.337 logLik -168.671 eps 0.1048 iteration  16 qsel 3
#> userIC 2385.532 logLik -151.868 eps 0.1188 iteration  17 qsel 3
#> userIC 2384.575 logLik -136.330 eps 0.0938 iteration  18 qsel 3
#> userIC 2383.158 logLik -121.410 eps 0.1196 iteration  19 qsel 3
#> userIC 2382.483 logLik -107.780 eps 0.1400 iteration  20 qsel 3
#> userIC 2381.776 logLik -95.2136 eps 0.0898 iteration  21 qsel 3
#> userIC 2380.580 logLik -83.1257 eps 0.1321 iteration  22 qsel 3
#> userIC 2380.001 logLik -72.0359 eps 0.0879 iteration  23 qsel 3
#> userIC 2379.490 logLik -62.3061 eps 0.0778 iteration  24 qsel 3
#> userIC 2378.523 logLik -52.0815 eps 0.1159 iteration  25 qsel 3
#> userIC 2377.979 logLik -43.0269 eps 0.1050 iteration  26 qsel 3
#> userIC 2377.587 logLik -35.1386 eps 0.0663 iteration  27 qsel 3
#> userIC 2376.848 logLik -26.8749 eps 0.1179 iteration  28 qsel 3
#> userIC 2376.330 logLik -19.4503 eps 0.0809 iteration  29 qsel 3
#> userIC 2376.036 logLik -13.0555 eps 0.0874 iteration  30 qsel 3
#> userIC 2375.477 logLik  -6.3765 eps 0.0890 iteration  31 qsel 3
#> userIC 2374.982 logLik  -0.2570 eps 0.0854 iteration  32 qsel 3
#> userIC 2374.769 logLik   4.9264 eps 0.0690 iteration  33 qsel 3
#> userIC 2374.349 logLik  10.3245 eps 0.3250 iteration  34 qsel 3
#> userIC 2373.878 logLik  15.4001 eps 0.0592 iteration  35 qsel 3
#> userIC 2373.729 logLik  19.6011 eps 0.0460 iteration  36 qsel 3
#> userIC 2373.383 logLik  23.8714 eps 0.0804 iteration  37 qsel 3
#> userIC 2372.992 logLik  28.1978 eps 0.0558 iteration  38 qsel 3
#> userIC 2372.874 logLik  31.6019 eps 0.0490 iteration  39 qsel 3
#> userIC 2372.559 logLik  35.1998 eps 0.0411 iteration  40 qsel 3
#> userIC 2372.284 logLik  38.6987 eps 0.0569 iteration  41 qsel 3
#> userIC 2372.152 logLik  41.7811 eps 0.0983 iteration  42 qsel 3
#> userIC 2371.852 logLik  44.5202 eps 0.0783 iteration  43 qsel 3
#> userIC 2371.692 logLik  47.3496 eps 0.0628 iteration  44 qsel 3
#> userIC 2371.539 logLik  50.0094 eps 0.0344 iteration  45 qsel 3
#> userIC 2371.304 logLik  52.2288 eps 0.1278 iteration  46 qsel 3
#> userIC 2371.194 logLik  54.5166 eps 0.0387 iteration  47 qsel 3
#> userIC 2371.029 logLik  56.8489 eps 0.0669 iteration  48 qsel 3
#> userIC 2370.842 logLik  58.6465 eps 0.0471 iteration  49 qsel 3
#> userIC 2370.769 logLik  60.4962 eps 0.0331 iteration  50 qsel 3
#> userIC 2370.603 logLik  62.5801 eps 0.0328 iteration  51 qsel 3
#> userIC 2370.449 logLik  64.0356 eps 0.0312 iteration  52 qsel 3
#> userIC 2370.382 logLik  65.9383 eps 0.6300 iteration  53 qsel 3
#> userIC 2370.210 logLik  67.4205 eps 0.0266 iteration  54 qsel 3
#> userIC 2370.110 logLik  68.5985 eps 0.0424 iteration  55 qsel 3
#> userIC 2370.049 logLik  70.3715 eps 0.0226 iteration  56 qsel 3
#> userIC 2369.907 logLik  71.5704 eps 0.0226 iteration  57 qsel 3
#> userIC 2369.815 logLik  72.5233 eps 0.0275 iteration  58 qsel 3
#> userIC 2369.763 logLik  74.2077 eps 0.0460 iteration  59 qsel 3
#> userIC 2369.637 logLik  75.1778 eps 0.0180 iteration  60 qsel 3
#> userIC 2369.553 logLik  75.9481 eps 0.0152 iteration  61 qsel 3
#> userIC 2369.515 logLik  77.5642 eps 0.0875 iteration  62 qsel 3
#> userIC 2369.396 logLik  78.1818 eps 0.0530 iteration  63 qsel 3
#> userIC 2369.331 logLik  78.9716 eps 0.0240 iteration  64 qsel 3
#> userIC 2369.299 logLik  80.5106 eps 0.0273 iteration  65 qsel 3
#> userIC 2369.177 logLik  81.0100 eps 0.0129 iteration  66 qsel 3
#> userIC 2369.131 logLik  81.6499 eps 0.0393 iteration  67 qsel 3
#> userIC 2369.110 logLik  83.0792 eps 0.0206 iteration  68 qsel 3
#> userIC 2368.988 logLik  83.4832 eps 0.0116 iteration  69 qsel 3
#> userIC 2368.958 logLik  84.0026 eps 0.0171 iteration  70 qsel 3
#> userIC 2368.939 logLik  84.3331 eps 0.0104 iteration  71 qsel 3
#> userIC 2368.912 logLik  85.6200 eps 0.0154 iteration  72 qsel 3
#> userIC 2368.811 logLik  86.0426 eps 0.0104 iteration  73 qsel 3
#> userIC 2368.791 logLik  86.3101 eps 0.0350 iteration  74 qsel 3
#> userIC 2368.781 logLik  87.4468 eps 0.0227 iteration  75 qsel 3
#> userIC 2368.691 logLik  87.7915 eps 0.0118 iteration  76 qsel 3
#> userIC 2368.670 logLik  88.0082 eps 0.0117 iteration  77 qsel 3
#> userIC 2368.666 logLik  88.2900 eps 0.0087 iteration  78 qsel 3
#> userIC 2368.644 logLik 172.9726 eps 0.0244 iteration  79 qsel 4
#> userIC 2368.571 logLik 174.0924 eps 0.0188 iteration  80 qsel 4
#> userIC 2368.507 logLik 244.7876 eps 0.0214 iteration  81 qsel 4
#> userIC 2368.435 logLik 302.3209 eps 0.0186 iteration  82 qsel 4
#> userIC 2368.353 logLik 303.5135 eps 0.0124 iteration  83 qsel 4
#> userIC 2368.299 logLik 349.4761 eps 0.0161 iteration  84 qsel 4
#> userIC 2368.214 logLik 385.2245 eps 0.0138 iteration  85 qsel 4
#> userIC 2368.111 logLik 386.4442 eps 0.0161 iteration  86 qsel 4
#> userIC 2368.060 logLik 386.7164 eps 0.0133 iteration  87 qsel 4
#> userIC 2368.041 logLik 414.0993 eps 0.0118 iteration  88 qsel 4
#> userIC 2367.931 logLik 415.2377 eps 0.0097 iteration  89 qsel 4
#> userIC 2367.889 logLik 435.7674 eps 0.0100 iteration  90 qsel 4
#> userIC 2367.772 logLik 436.8224 eps 0.0081 iteration  91 qsel 4
#> userIC 2367.739 logLik 437.0671 eps 0.0070 iteration  92 qsel 4
#> userIC 2367.724 logLik 452.1933 eps 0.0085 iteration  93 qsel 4
#> userIC 2367.602 logLik 453.1626 eps 0.0091 iteration  94 qsel 4
#> userIC 2367.575 logLik 464.1367 eps 0.0071 iteration  95 qsel 5
#> userIC 2367.476 logLik 465.0218 eps 0.0185 iteration  96 qsel 5
#> userIC 2367.450 logLik 465.8041 eps 0.0086 iteration  97 qsel 5
#> userIC 2367.428 logLik 466.4965 eps 0.0114 iteration  98 qsel 5
#> userIC 2367.407 logLik 467.1109 eps 0.0099 iteration  99 qsel 5
#> userIC 2367.387 logLik 467.6570 eps 0.0289 iteration 100 qsel 5
#> userIC 2367.367 logLik 468.1428 eps 0.0119 iteration 101 qsel 5
#> userIC 2367.348 logLik 468.5742 eps 0.0086 iteration 102 qsel 5
#> userIC 2367.327 logLik 468.9557 eps 0.0120 iteration 103 qsel 5
#> userIC 2367.307 logLik 469.2909 eps 0.0072 iteration 104 qsel 5
#> userIC 2367.285 logLik 469.5800 eps 0.0056 iteration 105 qsel 5
#> userIC 2367.266 logLik 469.8162 eps 0.0048 iteration 106 qsel 5
#> userIC 2367.247 logLik 470.0114 eps 0.0046 iteration 107 qsel 5
#> userIC 2367.232 logLik 478.1570 eps 0.0060 iteration 108 qsel 5
#> userIC 2367.113 logLik 478.3300 eps 0.0316 iteration 109 qsel 5
#> userIC 2367.097 logLik 484.0327 eps 0.0050 iteration 110 qsel 5
#> userIC 2366.983 logLik 484.1843 eps 0.0473 iteration 111 qsel 5
#> userIC 2366.969 logLik 488.1785 eps 0.0041 iteration 112 qsel 5
#> userIC 2366.881 logLik 490.9084 eps 0.0033 iteration 113 qsel 5
#> userIC 2366.768 logLik 491.0446 eps 0.0092 iteration 114 qsel 5
#> userIC 2366.753 logLik 492.9112 eps 0.0027 iteration 115 qsel 5
#> userIC 2366.646 logLik 493.0268 eps 0.0043 iteration 116 qsel 5
#> userIC 2366.639 logLik 494.2997 eps 0.0022 iteration 117 qsel 5
#> userIC 2366.535 logLik 495.2359 eps 0.0018 iteration 118 qsel 5
#> userIC 2366.463 logLik 495.8433 eps 0.0014 iteration 119 qsel 5
#> userIC 2366.368 logLik 496.2647 eps 0.0011 iteration 120 qsel 5
#> userIC 2366.280 logLik 496.6283 eps 0.0009 iteration 121 qsel 5
#> userIC 2366.211 logLik 496.8505 eps 0.0007 iteration 122 qsel 5
#> userIC 2366.126 logLik 497.0148 eps 0.0006 iteration 123 qsel 5
#> userIC 2366.048 logLik 497.1397 eps 0.0005 iteration 124 qsel 5
#> userIC 2365.974 logLik 497.3073 eps 0.0005 iteration 125 qsel 5
#> userIC 2365.916 logLik 497.3918 eps 0.0003 iteration 126 qsel 5
#> userIC 2365.846 logLik 497.4619 eps 0.0003 iteration 127 qsel 5
#> userIC 2365.783 logLik 497.5215 eps 0.0002 iteration 128 qsel 5
#> userIC 2365.724 logLik 497.6429 eps 0.0004 iteration 129 qsel 5
#> userIC 2365.673 logLik 497.6923 eps 0.0002 iteration 130 qsel 5
#> userIC 2365.617 logLik 497.7365 eps 0.0001 iteration 131 qsel 5
#> userIC 2365.565 logLik 497.7763 eps 0.0001 iteration 132 qsel 5
#> userIC 2365.519 logLik 497.8126 eps 0.0001 iteration 133 qsel 5
#> userIC 2365.474 logLik 497.9173 eps 0.0003 iteration 134 qsel 5
#> userIC 2365.432 logLik 497.9503 eps 0.0001 iteration 135 qsel 5
#> userIC 2365.390 logLik 497.9755 eps 0.0106 iteration 136 qsel 5
#> userIC 2365.380 logLik 498.0168 eps 0.0233 iteration 137 qsel 5
#> 
#>  elapsed time:  2.93sec


## Plot curve of negative out-of-sample log-likelihood.
## boost_plot(b, which = "user")