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Last data update: 2014.03.03

R: CV for lb

cv.lb

R Documentation

CV for lb

Description

Cross-validation method to tuning the parameter t for lb.

Usage

cv.lb(X, y, kappa, alpha, K = 5, tlist, nt = 100, trate = 100,
  family = c("gaussian", "binomial", "multinomial"), group = FALSE,
  intercept = TRUE, normalize = TRUE, plot.it = TRUE, se = TRUE, ...)

Arguments

`X`	An n-by-p matrix of predictors
`y`	Response Variable
`kappa`	The damping factor of the Linearized Bregman Algorithm that is defined in the reference paper. See details.
`alpha`	Parameter in Linearized Bregman algorithm which controls the step-length of the discretized solver for the Bregman Inverse Scale Space. See details.
`K`	Folds number for CV. Default is 5.
`tlist`	Parameters t along the path.
`nt`	Number of t. Used only if tlist is missing. Default is 100.
`trate`	tmax/tmin. Used only if tlist is missing. Default is 100.
`family`	Response type
`group`	Whether to use a group penalty, Default is FALSE.
`intercept`	If TRUE, an intercept is included in the model (and not penalized), otherwise no intercept is included. Default is TRUE.
`normalize`	if TRUE, each variable is scaled to have L2 norm square-root n. Default is TRUE.
`plot.it`	Plot it? Default is TRUE
`se`	Include standard error bands? Default is TRUE
`...`	Additonal arguments passing to lb

Details

K-fold cross-validation method is used to tuning the parameter t for ISS. Mean square error is used for linear model. Miss-classification error is used for binomial and multinomial model.

Value

A list is returned. The list contains a vector of parameter t, crossvalidation error cv.error, and the estimated standard deviation for it cv.sd

Author(s)

Feng Ruan, Jiechao Xiong and Yuan Yao

References

Ohser, Ruan, Xiong, Yao and Yin, Sparse Recovery via Differential Inclusions, http://arxiv.org/abs/1406.7728

Examples

#Examples in the reference paper
library(MASS)
n = 200;p = 100;k = 30;sigma = 1
Sigma = 1/(3*p)*matrix(rep(1,p^2),p,p)
diag(Sigma) = 1
A = mvrnorm(n, rep(0, p), Sigma)
u_ref = rep(0,p)
supp_ref = 1:k
u_ref[supp_ref] = rnorm(k)
u_ref[supp_ref] = u_ref[supp_ref]+sign(u_ref[supp_ref])
b = as.vector(A%*%u_ref + sigma*rnorm(n))
cv.lb(A,b,10,1/20,intercept = FALSE,normalize = FALSE)

#Simulated data, binomial case
X <- matrix(rnorm(500*100), nrow=500, ncol=100)
alpha <- c(rep(1,30), rep(0,70))
y <- 2*as.numeric(runif(500)<1/(1+exp(-X %*% alpha)))-1
cv.lb(X,y,kappa=5,alpha=1,family="binomial",
             intercept=FALSE,normalize = FALSE)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'license()' or 'licence()' for distribution details.

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Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Libra)
Loading required package: nnls
Loaded Libra 1.5

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Libra/cv.lb.Rd_%03d_medium.png", width=480, height=480)
> ### Name: cv.lb
> ### Title: CV for lb
> ### Aliases: cv.lb
> ### Keywords: Cross-validation
> 
> ### ** Examples
> 
> #Examples in the reference paper
> library(MASS)
> n = 200;p = 100;k = 30;sigma = 1
> Sigma = 1/(3*p)*matrix(rep(1,p^2),p,p)
> diag(Sigma) = 1
> A = mvrnorm(n, rep(0, p), Sigma)
> u_ref = rep(0,p)
> supp_ref = 1:k
> u_ref[supp_ref] = rnorm(k)
> u_ref[supp_ref] = u_ref[supp_ref]+sign(u_ref[supp_ref])
> b = as.vector(A%*%u_ref + sigma*rnorm(n))
> cv.lb(A,b,10,1/20,intercept = FALSE,normalize = FALSE)
$t
  [1]  0.2523626  0.2643791  0.2769677  0.2901557  0.3039717  0.3184455
  [7]  0.3336086  0.3494936  0.3661350  0.3835688  0.4018327  0.4209663
 [13]  0.4410109  0.4620099  0.4840089  0.5070553  0.5311992  0.5564926
 [19]  0.5829904  0.6107500  0.6398313  0.6702973  0.7022140  0.7356505
 [25]  0.7706790  0.8073755  0.8458193  0.8860936  0.9282856  0.9724867
 [31]  1.0187923  1.0673029  1.1181233  1.1713636  1.2271390  1.2855701
 [37]  1.3467835  1.4109116  1.4780932  1.5484738  1.6222055  1.6994481
 [43]  1.7803686  1.8651421  1.9539523  2.0469912  2.1444602  2.2465703
 [49]  2.3535424  2.4656081  2.5830099  2.7060019  2.8348502  2.9698337
 [55]  3.1112446  3.2593889  3.4145871  3.5771752  3.7475051  3.9259454
 [61]  4.1128823  4.3087203  4.5138832  4.7288152  4.9539813  5.1898688
 [67]  5.4369883  5.6958746  5.9670880  6.2512153  6.5488717  6.8607011
 [73]  7.1873786  7.5296110  7.8881391  8.2637388  8.6572229  9.0694431
 [79]  9.5012915  9.9537026 10.4276557 10.9241763 11.4443392 11.9892700
 [85] 12.5601482 13.1582091 13.7847471 14.4411182 15.1287429 15.8491094
 [91] 16.6037767 17.3943780 18.2226244 19.0903084 19.9993078 20.9515899
 [97] 21.9492156 22.9943441 24.0892371 25.2362642

$cv.erroe
  [1] 104.712736 101.784566  98.052820  95.054531  92.698070  90.083815
  [7]  87.284639  84.516695  80.712229  76.982747  74.274930  71.066785
 [13]  67.262324  64.005580  61.150352  58.447498  54.879844  51.425946
 [19]  47.813554  42.923796  37.894836  34.346578  31.596836  29.624455
 [25]  28.200974  26.967204  26.018538  24.679697  22.176077  19.315565
 [31]  16.899280  15.303606  13.842156  12.297016  10.955972   9.760491
 [37]   8.222686   7.004394   6.041693   5.398641   4.279262   3.493932
 [43]   2.998576   2.633723   2.444422   2.315812   2.147801   1.966060
 [49]   1.778623   1.673769   1.641720   1.620664   1.617192   1.612369
 [55]   1.604392   1.598660   1.595456   1.598252   1.601753   1.637065
 [61]   1.658787   1.654317   1.636348   1.636291   1.654309   1.662730
 [67]   1.679145   1.690478   1.687726   1.687490   1.684090   1.677448
 [73]   1.676405   1.681560   1.697018   1.702904   1.702105   1.728972
 [79]   1.749012   1.765516   1.796589   1.868502   1.853434   1.839077
 [85]   1.849818   1.886774   1.928899   1.970608   2.002887   2.028296
 [91]   2.073326   2.119235   2.168391   2.210397   2.265024   2.375731
 [97]   2.433977   2.488238   2.495640   2.505449

$cv.sd
  [1] 16.62208543 16.68303859 16.74297442 16.61238403 16.24927925 15.70632680
  [7] 15.62608487 15.72565586 14.97825728 14.36985436 14.09277920 13.79473528
 [13] 13.56021157 13.32635863 13.01326587 12.63934624 11.93653526 11.77758071
 [19] 11.32280419 10.18902898  8.80152025  7.54843591  6.36954414  5.53498542
 [25]  5.09188533  4.85683059  4.77107420  4.62049123  4.24865738  4.13405758
 [31]  4.18913352  4.27743549  4.04910173  3.56361725  3.03432043  2.45647652
 [37]  1.66221988  1.15315178  0.84627660  0.68944615  0.31711013  0.28148847
 [43]  0.35281318  0.43189929  0.48558936  0.49568902  0.46114448  0.38929794
 [49]  0.25978612  0.19095224  0.16552227  0.15756261  0.15200305  0.14497286
 [55]  0.13645817  0.13010530  0.12983105  0.13503011  0.14508433  0.14025339
 [61]  0.13897591  0.13703774  0.13371909  0.13693140  0.13555310  0.13582506
 [67]  0.13863193  0.14397508  0.14937896  0.15058743  0.13990525  0.13739697
 [73]  0.13661281  0.13189917  0.12002795  0.10057141  0.08140745  0.07244043
 [79]  0.08677410  0.09919874  0.09991463  0.09797437  0.09958440  0.10063272
 [85]  0.09972147  0.10751108  0.12674909  0.12922841  0.12551451  0.11427084
 [91]  0.11069609  0.10778147  0.10290944  0.09443625  0.08816807  0.10511478
 [97]  0.12589715  0.12887218  0.14410223  0.14684595

> 
> #Simulated data, binomial case
> X <- matrix(rnorm(500*100), nrow=500, ncol=100)
> alpha <- c(rep(1,30), rep(0,70))
> y <- 2*as.numeric(runif(500)<1/(1+exp(-X %*% alpha)))-1
> cv.lb(X,y,kappa=5,alpha=1,family="binomial",
+              intercept=FALSE,normalize = FALSE)
$t
  [1]   7.983111   8.363233   8.761455   9.178638   9.615686  10.073544
  [7]  10.553203  11.055702  11.582128  12.133619  12.711371  13.316632
 [13]  13.950714  14.614987  15.310891  16.039931  16.803684  17.603804
 [19]  18.442022  19.320153  20.240097  21.203844  22.213481  23.271193
 [25]  24.379268  25.540105  26.756217  28.030234  29.364915  30.763147
 [31]  32.227958  33.762516  35.370144  37.054320  38.818689  40.667070
 [37]  42.603464  44.632060  46.757249  48.983630  51.316023  53.759474
 [43]  56.319272  59.000956  61.810331  64.753477  67.836762  71.066861
 [49]  74.450763  77.995792  81.709620  85.600285  89.676207  93.946207
 [55]  98.419527 103.105847 108.015309 113.158539 118.546668 124.191357
 [61] 130.104822 136.299861 142.789882 149.588929 156.711719 164.173665
 [67] 171.990918 180.180395 188.759820 197.747761 207.163670 217.027924
 [73] 227.361872 238.187878 249.529373 261.410902 273.858179 286.898143
 [79] 300.559014 314.870357 329.863146 345.569829 362.024396 379.262460
 [85] 397.321328 416.240082 436.059667 456.822976 478.574946 501.362652
 [91] 525.235412 550.244892 576.445217 603.893089 632.647914 662.771920
 [97] 694.330304 727.391364 762.026652 798.311124

$cv.erroe
  [1] 0.452 0.432 0.422 0.406 0.384 0.356 0.344 0.340 0.334 0.314 0.310 0.306
 [13] 0.304 0.300 0.282 0.276 0.270 0.268 0.258 0.240 0.222 0.208 0.218 0.210
 [25] 0.200 0.196 0.194 0.194 0.192 0.180 0.170 0.172 0.166 0.168 0.168 0.164
 [37] 0.166 0.172 0.178 0.176 0.170 0.168 0.156 0.156 0.154 0.160 0.160 0.162
 [49] 0.166 0.168 0.168 0.168 0.170 0.172 0.170 0.174 0.180 0.174 0.182 0.188
 [61] 0.188 0.186 0.184 0.184 0.186 0.186 0.190 0.190 0.188 0.194 0.196 0.192
 [73] 0.190 0.194 0.194 0.196 0.202 0.192 0.194 0.194 0.198 0.196 0.204 0.208
 [85] 0.212 0.208 0.206 0.204 0.202 0.202 0.200 0.198 0.198 0.200 0.198 0.200
 [97] 0.198 0.200 0.202 0.202

$cv.sd
  [1] 0.012409674 0.016552945 0.016852300 0.022934690 0.017492856 0.016309506
  [7] 0.021118712 0.018973666 0.009273618 0.017492856 0.020000000 0.025806976
 [13] 0.021587033 0.020736441 0.015937377 0.016309506 0.018708287 0.013564660
 [19] 0.018814888 0.008366600 0.004898979 0.005830952 0.010198039 0.011832160
 [25] 0.010488088 0.010770330 0.012489996 0.014352700 0.014628739 0.017029386
 [31] 0.015165751 0.015937377 0.011661904 0.008000000 0.006633250 0.007483315
 [37] 0.008124038 0.009695360 0.011575837 0.012083046 0.012247449 0.013564660
 [43] 0.016911535 0.016911535 0.015362291 0.015165751 0.013784049 0.014282857
 [49] 0.016309506 0.017435596 0.019849433 0.019849433 0.018973666 0.016552945
 [55] 0.017606817 0.018055470 0.021679483 0.020396078 0.015297059 0.012409674
 [61] 0.012000000 0.012884099 0.015033296 0.014352700 0.014000000 0.012083046
 [67] 0.010954451 0.010954451 0.010677078 0.009273618 0.008717798 0.009695360
 [73] 0.009486833 0.009797959 0.009797959 0.011224972 0.008602325 0.010677078
 [79] 0.010295630 0.012489996 0.011135529 0.009273618 0.010295630 0.008000000
 [85] 0.007348469 0.012000000 0.012083046 0.012083046 0.012409674 0.012409674
 [91] 0.016431677 0.016852300 0.016852300 0.016733201 0.016852300 0.015811388
 [97] 0.016552945 0.015811388 0.015937377 0.015937377

> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>