TP_REG
2025-01-28
Regression
Simulation
Regression 1
\[Y=10e^{-3X}+e^{-\frac{X}{2}}\epsilon, \] avec \(X \sim \mathcal{E}(1)\) et \(\epsilon \sim \mathcal{N}(0,1)\).
n=100
x=rexp(n,2)
e=rnorm(n,0,exp(-x/2))
y=10*exp(-3*x)+e
plot(function(x) 10*exp(-3*x),0,3,ylab='y')
lines(x,y,col="red",type="p")
sm.regression(x,y,h=0.01,col="blue",eval.points=sort(x),add=T,nbins=0)
sm.regression(x,y,h=.1,col="orange",eval.points=sort(x),add=T,nbins=0)
sm.regression(x,y,h=1,col="green",eval.points=sort(x),add=T,nbins=0)
legend(x="topright",leg=c('h=0.01','h=0.1','h=1'), col=c("blue","orange","green"),lty=1)
plot(function(x) 10*exp(-3*x),0,3)
lines(x,y,col="red",type="p")
reg3=sm.regression(x,y,method="cv",col="blue",eval.points=sort(x),add=T,nbins=0)
reg1=sm.regression(x,y,method="df",col="orange",add=T,eval.points=sort(x),nbins=0)
reg2=sm.regression(x,y,method="aicc",col="green",add=T,eval.points=sort(x),nbins=0)
legend(x="topright",leg=c('cv',"df",'aicc'), col=c("blue","orange","green"),lty=1)
plot(reg1$estimate,y[order(x)],col="orange")
lines(reg2$estimate,y[order(x)],col="green",type='p')
lines(reg3$estimate,y[order(x)],col="blue",type='p')
abline(0,1)
Erreur quadratique et Validation croisée
# Erreur quadratique
mean((reg1$estimate-y[order(x)])^2)## [1] 0.6127917mean((reg2$estimate-y[order(x)])^2)## [1] 0.5210248mean((reg3$estimate-y[order(x)])^2)## [1] 0.511677#Validation croisée
Compute_CV(x,y,'cv')/n## [1] 0.5936034Compute_CV(x,y,'df')/n## [1] 0.6760531Compute_CV(x,y,'aicc')/n## [1] 0.5967966# CV avec moyenne Y
n=length(x)
CV_y=0
for (j in 1:n)
{
CV_y=CV_y+(y[j]-mean(y[-j]))^2
}
CV_y/n## [1] 10.1484# Variance non corrigée e
var(e)*(n-1)/n## [1] 0.5281708Regression 2
\[Y=7cos(7X)+10e^{-3X}+3e^{-\frac{X}{2}}\epsilon, \] avec \(X \sim \mathcal{E}(1)\) et \(\epsilon \sim \mathcal{N}(0,1)\).
n=1000
x=rexp(n,2)
e=3*rnorm(n,0,exp(-x/2))
y=7*cos(7*x)+10*exp(-3*x)+e
plot(function(x) 10*exp(-3*x)+7*cos(7*x),0,3)
lines(x,y,col="red",type="p")
sm.regression(x,y,h=0.01,col="blue",eval.points=sort(x),add=T,nbins=0)
sm.regression(x,y,h=.1,col="orange",eval.points=sort(x),add=T,nbins=0)
sm.regression(x,y,h=1,col="green",eval.points=sort(x),add=T,nbins=0)
legend(x="topright",leg=c('h=0.01','h=0.1','h=1'), col=c("blue","orange","green"),lty=1)
plot(function(x) 10*exp(-3*x)+7*cos(7*x),0,3)
lines(x,y,col="red",type="p")
plot(function(x) 10*exp(-3*x)+7*cos(7*x),0,3)
lines(x,y,col="red",type="p")
reg3=sm.regression(x,y,method="cv",col="blue", eval.points=sort(x),add=T,nbins=0)
legend(x="topright",leg=c('cv',"df",'aicc'), col=c("blue","orange","green"),lty=1)
reg1=sm.regression(x,y,method="df",col="orange",eval.points=sort(x),add=T,nbins=0)
reg2=sm.regression(x,y,method="aicc",col="green", eval.points=sort(x),add=T,nbins=0)
plot(reg1$estimate,y[order(x)],col="orange")
lines(reg2$estimate,y[order(x)],col="green",type='p')
lines(reg3$estimate,y[order(x)],col="blue",type='p')
abline(0,1)
Erreur quadratique et Validation croisée
# Erreur quadratique
mean((reg1$estimate-y[order(x)])^2)## [1] 22.29401mean((reg2$estimate-y[order(x)])^2)## [1] 5.816735mean((reg3$estimate-y[order(x)])^2)## [1] 7.689503#Validation croisée
Compute_CV(x,y,'cv')/n## [1] NaNCompute_CV(x,y,'df')/n## [1] 22.60085Compute_CV(x,y,'aicc')/n## [1] 8.912584# CV avec moyenne Y
n=length(x)
CV_y=0
for (j in 1:n)
{
CV_y=CV_y+(y[j]-mean(y[-j]))^2
}
CV_y/n## [1] 53.00386# Variance non corrigée e
var(e)*(n-1)/n## [1] 5.884625Real world data
# load data
library(MASS)##
## Attachement du package : 'MASS'## L'objet suivant est masqué depuis 'package:sm':
##
## muscledata(mcycle)
head(mcycle)## times accel
## 1 2.4 0.0
## 2 2.6 -1.3
## 3 3.2 -2.7
## 4 3.6 0.0
## 5 4.0 -2.7
## 6 6.2 -2.7x=mcycle$times
y=mcycle$accel
n=length(x)# plot data
plot(x, y, xlab = "Time (ms)", ylab = "Acceleration (g)")
sm.regression(x,y,h=0.1,col="blue",eval.points=sort(x),add=T,nbins=0)
sm.regression(x,y,h=1,col="orange",eval.points=sort(x),add=T,nbins=0)
sm.regression(x,y,h=10,col="green",eval.points=sort(x),add=T,nbins=0)
legend(x="topright",leg=c('h=0.1','h=1','h=10'), col=c("blue","orange","green"),lty=1)
plot(x,y,col="red",type="p")
reg3=sm.regression(x,y,method="cv",col="blue", eval.points=sort(x),add=T,nbins=0)
legend(x="topright",leg=c('cv',"df",'aicc'), col=c("blue","orange","green"),lty=1)
reg1=sm.regression(x,y,method="df",col="orange",eval.points=sort(x),add=T,nbins=0)
reg2=sm.regression(x,y,method="aicc",col="green", eval.points=sort(x),add=T,nbins=0)
plot(reg1$estimate,y[order(x)],col="orange")
lines(reg2$estimate,y[order(x)],col="green",type='p')
lines(reg3$estimate,y[order(x)],col="blue",type='p')
abline(0,1)
Erreur quadratique et Validation croisée
# Erreur quadratique
mean((reg1$estimate-y[order(x)])^2)## [1] 987.5993mean((reg2$estimate-y[order(x)])^2)## [1] 472.0266mean((reg3$estimate-y[order(x)])^2)## [1] 459.8602#Validation croisée
Compute_CV(x,y,'cv')/n## [1] 570.7888Compute_CV(x,y,'df')/n## [1] 1027.242Compute_CV(x,y,'aicc')/n## [1] 742.0577# CV avec moyenne Y
n=length(x)
CV_y=0
for (j in 1:n)
{
CV_y=CV_y+(y[j]-mean(y[-j]))^2
}
CV_y/n## [1] 2352.71Classification supervisée
Simulation
rmixing2=function(n,alpha,l0,l1,p0,p1)
# Generate data from a mixing model
{
z=rbinom(n,1,alpha)
f1=eval(parse(text=paste('r',l1,'(',paste(c(n,p1),collapse=','),')',sep='')))
f0=eval(parse(text=paste('r',l0,'(',paste(c(n,p0),collapse=','),')',sep='')))
x=z*f1+(1-z)*f0
return(list(x=x,z=z))
}
dmixing2=function(t,alpha,l0,l1,p0,p1)
# draw the density of the mixing model
{
mix=alpha*eval(parse(text=paste('d',l1,'(t,',paste(p1,collapse=','),')',sep='')))+(1-alpha)*eval(parse(text=paste('d',l0,'(t,',paste(p0,collapse=','),')',sep='')))
p1_t=eval(parse(text=paste('d',l1,'(t,',paste(p1,collapse=','),')',sep='')))/mix
p0_t=eval(parse(text=paste('d',l0,'(t,',paste(p0,collapse=','),')',sep='')))/mix
return(list(mix=mix,p0_t=p0_t,p1_t=p1_t))
}
#Example
n=300
alpha=0.3
l0='norm'
p0=c(4,1)
l1='norm'
p1=c(0,2)
s=seq(-10,10,0.001)
r=rmixing2(n,alpha,l0,l1,p0,p1)
x=r$x
z=r$z
p0_x=dmixing2(x,alpha,l0,l1,p0,p1)$p0_t
p1_x=dmixing2(x,alpha,l0,l1,p0,p1)$p1_t
u=sort(x)
plot(u,p0_x[order(x)],ylab='p0_x',type='l')
plot(u,p1_x[order(x)],ylab='p1_x',type='l')
Classif_NP(x,z)
## $Class
## [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0
## [38] 1 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1
## [75] 1 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1
## [112] 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0
## [149] 0 1 1 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0
## [186] 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0
## [223] 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0
## [260] 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0
## [297] 0 0 0 1
##
## $Prob
## 0 1
## [1,] 9.592685e-01 0.04073146
## [2,] 9.504061e-01 0.04959385
## [3,] 8.438781e-01 0.15612187
## [4,] 9.642602e-01 0.03573982
## [5,] 8.570655e-01 0.14293453
## [6,] 8.575566e-01 0.14244343
## [7,] 8.275411e-01 0.17245888
## [8,] 9.507053e-01 0.04929473
## [9,] 8.788227e-01 0.12117731
## [10,] 7.636874e-01 0.23631258
## [11,] 9.075007e-01 0.09249931
## [12,] 9.089633e-01 0.09103674
## [13,] 9.614340e-01 0.03856603
## [14,] 9.589961e-01 0.04100387
## [15,] 9.956135e-01 0.00438652
## [16,] 9.465912e-01 0.05340878
## [17,] 9.645035e-01 0.03549652
## [18,] 9.651588e-01 0.03484115
## [19,] 3.439932e-03 0.99656007
## [20,] 1.214362e-01 0.87856375
## [21,] 7.245064e-02 0.92754936
## [22,] 9.082786e-01 0.09172140
## [23,] 7.977479e-01 0.20225209
## [24,] 7.785822e-01 0.22141777
## [25,] 9.605201e-01 0.03947990
## [26,] 4.295873e-01 0.57041268
## [27,] 9.408537e-01 0.05914631
## [28,] 3.845492e-01 0.61545080
## [29,] 9.557794e-01 0.04422055
## [30,] 4.145279e-01 0.58547211
## [31,] 9.614699e-01 0.03853012
## [32,] 9.618780e-01 0.03812197
## [33,] 4.549759e-01 0.54502411
## [34,] 9.582856e-01 0.04171437
## [35,] 9.148615e-01 0.08513849
## [36,] -4.270291e-03 1.00427029
## [37,] 9.647960e-01 0.03520398
## [38,] 3.300842e-02 0.96699158
## [39,] 9.601192e-01 0.03988077
## [40,] 6.890996e-01 0.31090043
## [41,] 9.576003e-01 0.04239967
## [42,] 9.214934e-01 0.07850661
## [43,] 8.975923e-01 0.10240772
## [44,] -4.539825e-03 1.00453983
## [45,] 8.321205e-02 0.91678795
## [46,] 9.634742e-01 0.03652584
## [47,] 9.432226e-01 0.05677744
## [48,] 9.540588e-01 0.04594115
## [49,] 8.210511e-02 0.91789489
## [50,] 7.549828e-01 0.24501720
## [51,] 1.157342e-01 0.88426577
## [52,] 9.610912e-01 0.03890879
## [53,] 8.654542e-01 0.13454577
## [54,] 4.226319e-01 0.57736806
## [55,] 5.720647e-01 0.42793528
## [56,] 9.458611e-01 0.05413894
## [57,] 8.478996e-01 0.15210044
## [58,] -4.473659e-03 1.00447366
## [59,] 3.560025e-01 0.64399745
## [60,] 7.704250e-01 0.22957502
## [61,] 3.639501e-01 0.63604989
## [62,] 6.363829e-01 0.36361705
## [63,] -4.412458e-03 1.00441246
## [64,] 9.216309e-01 0.07836913
## [65,] 9.582223e-01 0.04177769
## [66,] 9.544408e-01 0.04555925
## [67,] 8.863356e-01 0.11366436
## [68,] 1.513787e-01 0.84862126
## [69,] 7.652413e-01 0.23475874
## [70,] 7.635321e-01 0.23646789
## [71,] 9.423004e-01 0.05769965
## [72,] 8.480797e-01 0.15192033
## [73,] 9.354844e-01 0.06451563
## [74,] -4.100120e-03 1.00410012
## [75,] 2.318916e-01 0.76810839
## [76,] 3.541757e-01 0.64582431
## [77,] 1.374895e-01 0.86251049
## [78,] 9.595930e-01 0.04040702
## [79,] 2.173160e-01 0.78268396
## [80,] 9.622008e-01 0.03779921
## [81,] -2.715737e-03 1.00271574
## [82,] 9.463270e-01 0.05367300
## [83,] 7.372254e-03 0.99262775
## [84,] 9.640530e-01 0.03594702
## [85,] 9.550787e-01 0.04492133
## [86,] 2.120443e-03 0.99787956
## [87,] 9.301288e-01 0.06987122
## [88,] 9.570024e-01 0.04299758
## [89,] 6.472139e-01 0.35278609
## [90,] 9.646004e-01 0.03539957
## [91,] 9.504972e-01 0.04950285
## [92,] -1.544503e-03 1.00154450
## [93,] 9.125018e-01 0.08749817
## [94,] 8.785474e-01 0.12145262
## [95,] 9.078789e-01 0.09212109
## [96,] 9.379731e-01 0.06202693
## [97,] 9.496706e-01 0.05032937
## [98,] 7.419060e-01 0.25809397
## [99,] 9.583921e-01 0.04160786
## [100,] 9.614694e-01 0.03853059
## [101,] 9.650037e-01 0.03499627
## [102,] 9.488693e-01 0.05113073
## [103,] 9.643036e-01 0.03569641
## [104,] 9.628562e-01 0.03714376
## [105,] -9.005520e-04 1.00090055
## [106,] 9.597481e-01 0.04025185
## [107,] 8.708869e-01 0.12911310
## [108,] 8.428380e-02 0.91571620
## [109,] 9.638657e-01 0.03613430
## [110,] 9.052446e-01 0.09475538
## [111,] -5.602213e-05 1.00005602
## [112,] 9.434348e-01 0.05656523
## [113,] 9.641437e-01 0.03585631
## [114,] 9.583602e-01 0.04163979
## [115,] 9.461832e-01 0.05381678
## [116,] 9.463392e-01 0.05366085
## [117,] 9.647136e-01 0.03528636
## [118,] 9.566882e-01 0.04331182
## [119,] 9.646257e-01 0.03537428
## [120,] 2.452609e-01 0.75473912
## [121,] 9.416952e-01 0.05830483
## [122,] 9.472808e-01 0.05271919
## [123,] -4.471488e-03 1.00447149
## [124,] 7.258712e-01 0.27412877
## [125,] 9.170123e-01 0.08298769
## [126,] 9.650975e-01 0.03490248
## [127,] 9.591554e-01 0.04084456
## [128,] 8.689467e-01 0.13105329
## [129,] 2.043831e-01 0.79561688
## [130,] 8.371563e-01 0.16284366
## [131,] 9.651528e-01 0.03484720
## [132,] 9.648025e-01 0.03519750
## [133,] 8.432694e-01 0.15673059
## [134,] 7.871874e-01 0.21281256
## [135,] 6.781030e-01 0.32189702
## [136,] 3.740546e-01 0.62594543
## [137,] 9.118521e-01 0.08814795
## [138,] 9.104122e-01 0.08958776
## [139,] 8.395435e-01 0.16045653
## [140,] 9.612513e-01 0.03874866
## [141,] 7.442361e-01 0.25576388
## [142,] 5.645910e-01 0.43540897
## [143,] -4.330633e-03 1.00433063
## [144,] 7.787743e-01 0.22122575
## [145,] 9.264123e-01 0.07358765
## [146,] 8.588059e-01 0.14119407
## [147,] 3.455587e-01 0.65444125
## [148,] 9.567169e-01 0.04328312
## [149,] 9.651204e-01 0.03487963
## [150,] 5.166066e-02 0.94833934
## [151,] 2.529480e-02 0.97470520
## [152,] 9.418814e-01 0.05811863
## [153,] 9.497567e-01 0.05024333
## [154,] 5.852637e-01 0.41473632
## [155,] 9.551964e-01 0.04480355
## [156,] 8.204263e-01 0.17957371
## [157,] -4.001976e-03 1.00400198
## [158,] 9.558176e-01 0.04418236
## [159,] 3.009279e-01 0.69907215
## [160,] 9.651581e-01 0.03484187
## [161,] 9.172910e-03 0.99082709
## [162,] 9.547924e-01 0.04520757
## [163,] 8.569413e-01 0.14305873
## [164,] 9.552690e-01 0.04473103
## [165,] 5.263796e-01 0.47362038
## [166,] -4.539452e-03 1.00453945
## [167,] 8.461786e-01 0.15382137
## [168,] 9.457712e-01 0.05422879
## [169,] 9.273442e-01 0.07265583
## [170,] 3.390878e-03 0.99660912
## [171,] 8.017187e-01 0.19828127
## [172,] 8.274759e-01 0.17252409
## [173,] 1.134828e-02 0.98865172
## [174,] 9.423587e-01 0.05764130
## [175,] 8.150465e-01 0.18495349
## [176,] 9.476330e-01 0.05236700
## [177,] 8.603717e-01 0.13962833
## [178,] 6.495939e-01 0.35040605
## [179,] 5.340080e-01 0.46599195
## [180,] -1.978334e-03 1.00197833
## [181,] 9.485258e-01 0.05147421
## [182,] 3.899011e-01 0.61009893
## [183,] 9.430816e-01 0.05691836
## [184,] 9.750814e-01 0.02491858
## [185,] 9.182552e-01 0.08174483
## [186,] 9.647995e-01 0.03520052
## [187,] 9.504851e-01 0.04951489
## [188,] 4.258095e-01 0.57419051
## [189,] -2.796427e-03 1.00279643
## [190,] 4.205154e-01 0.57948460
## [191,] 9.638511e-01 0.03614895
## [192,] 8.114872e-01 0.18851281
## [193,] 8.923376e-01 0.10766243
## [194,] 8.572259e-01 0.14277406
## [195,] 9.625956e-01 0.03740440
## [196,] -1.552772e-03 1.00155277
## [197,] 9.609484e-01 0.03905161
## [198,] 9.556277e-01 0.04437234
## [199,] 8.887699e-01 0.11123006
## [200,] 9.640090e-01 0.03599105
## [201,] 9.645095e-01 0.03549046
## [202,] 2.084810e-01 0.79151904
## [203,] 9.529468e-01 0.04705315
## [204,] 2.615835e-02 0.97384165
## [205,] 9.402793e-01 0.05972069
## [206,] -1.291132e-04 1.00012911
## [207,] 9.489883e-01 0.05101170
## [208,] 3.675350e-02 0.96324650
## [209,] 9.346990e-01 0.06530098
## [210,] 8.618218e-01 0.13817817
## [211,] 8.911051e-01 0.10889489
## [212,] 3.282661e-02 0.96717339
## [213,] 9.386071e-01 0.06139290
## [214,] 9.253166e-01 0.07468338
## [215,] 3.295057e-02 0.96704943
## [216,] 9.821045e-01 0.01789554
## [217,] 6.928533e-01 0.30714674
## [218,] 7.543903e-03 0.99245610
## [219,] 5.712240e-01 0.42877600
## [220,] 9.647669e-01 0.03523310
## [221,] 3.213619e-03 0.99678638
## [222,] 9.442811e-01 0.05571893
## [223,] -4.169206e-03 1.00416921
## [224,] 6.334910e-01 0.36650898
## [225,] -2.257084e-03 1.00225708
## [226,] 9.651326e-01 0.03486740
## [227,] 9.534649e-01 0.04653511
## [228,] 9.651459e-01 0.03485406
## [229,] 5.531765e-01 0.44682346
## [230,] 9.647561e-01 0.03524385
## [231,] 9.645261e-01 0.03547392
## [232,] -4.391473e-03 1.00439147
## [233,] 9.625791e-01 0.03742090
## [234,] 9.447120e-01 0.05528800
## [235,] 1.655559e-01 0.83444414
## [236,] 8.212702e-01 0.17872978
## [237,] 9.074916e-01 0.09250836
## [238,] 2.206974e-02 0.97793026
## [239,] 9.344992e-01 0.06550081
## [240,] 8.300510e-02 0.91699490
## [241,] 8.965057e-01 0.10349429
## [242,] 9.749836e-01 0.02501640
## [243,] 9.650600e-01 0.03493996
## [244,] 8.918215e-01 0.10817846
## [245,] 9.377468e-01 0.06225317
## [246,] 9.651444e-01 0.03485565
## [247,] 9.503016e-01 0.04969837
## [248,] 9.557988e-01 0.04420122
## [249,] 9.373396e-01 0.06266037
## [250,] 8.582584e-01 0.14174157
## [251,] 9.621571e-01 0.03784293
## [252,] 9.604935e-01 0.03950652
## [253,] 9.539909e-01 0.04600912
## [254,] 9.651588e-01 0.03484118
## [255,] 2.187419e-02 0.97812581
## [256,] 6.138908e-02 0.93861092
## [257,] 1.932314e-01 0.80676858
## [258,] 3.241012e-01 0.67589881
## [259,] 6.424150e-01 0.35758503
## [260,] -4.397578e-03 1.00439758
## [261,] 3.865215e-03 0.99613479
## [262,] 1.247963e-01 0.87520368
## [263,] 9.650183e-01 0.03498170
## [264,] 9.133417e-01 0.08665829
## [265,] 9.607173e-01 0.03928267
## [266,] 5.956304e-01 0.40436957
## [267,] 9.511265e-01 0.04887347
## [268,] 4.681878e-01 0.53181222
## [269,] 9.532573e-01 0.04674273
## [270,] 8.943123e-01 0.10568773
## [271,] 9.612386e-01 0.03876139
## [272,] 9.650952e-01 0.03490483
## [273,] 9.448450e-01 0.05515503
## [274,] 8.849204e-01 0.11507959
## [275,] 8.313452e-01 0.16865482
## [276,] 7.750632e-01 0.22493679
## [277,] 9.633292e-01 0.03667082
## [278,] 9.645715e-01 0.03542846
## [279,] 9.544073e-01 0.04559274
## [280,] 9.605154e-01 0.03948460
## [281,] 4.679620e-01 0.53203803
## [282,] 9.223337e-01 0.07766626
## [283,] 4.292612e-01 0.57073882
## [284,] 9.580561e-01 0.04194392
## [285,] 9.626269e-01 0.03737314
## [286,] 4.919136e-02 0.95080864
## [287,] 3.141122e-03 0.99685888
## [288,] 9.477935e-01 0.05220647
## [289,] 9.648590e-01 0.03514103
## [290,] 2.401034e-02 0.97598966
## [291,] 8.659551e-01 0.13404487
## [292,] 9.602476e-01 0.03975236
## [293,] 4.974877e-01 0.50251229
## [294,] 6.154547e-01 0.38454530
## [295,] 8.232517e-01 0.17674827
## [296,] 8.408046e-01 0.15919542
## [297,] 9.628099e-01 0.03719013
## [298,] 6.690560e-01 0.33094396
## [299,] 6.574190e-01 0.34258102
## [300,] 2.801036e-01 0.71989636
##
## $M_table
## Class
## Y 0 1
## 0 204 7
## 1 16 73
##
## $err
## [1] 0.07666667ROC(z,p1_x)
## $ROC
## FPR TPR
## [1,] 0.995260664 1.00000000
## [2,] 0.990521327 1.00000000
## [3,] 0.985781991 1.00000000
## [4,] 0.981042654 1.00000000
## [5,] 0.976303318 1.00000000
## [6,] 0.971563981 1.00000000
## [7,] 0.966824645 1.00000000
## [8,] 0.962085308 1.00000000
## [9,] 0.957345972 1.00000000
## [10,] 0.952606635 1.00000000
## [11,] 0.947867299 1.00000000
## [12,] 0.943127962 1.00000000
## [13,] 0.938388626 1.00000000
## [14,] 0.933649289 1.00000000
## [15,] 0.928909953 1.00000000
## [16,] 0.924170616 1.00000000
## [17,] 0.919431280 1.00000000
## [18,] 0.914691943 1.00000000
## [19,] 0.909952607 1.00000000
## [20,] 0.905213270 1.00000000
## [21,] 0.905213270 0.98876404
## [22,] 0.900473934 0.98876404
## [23,] 0.895734597 0.98876404
## [24,] 0.890995261 0.98876404
## [25,] 0.886255924 0.98876404
## [26,] 0.881516588 0.98876404
## [27,] 0.876777251 0.98876404
## [28,] 0.876777251 0.97752809
## [29,] 0.872037915 0.97752809
## [30,] 0.867298578 0.97752809
## [31,] 0.862559242 0.97752809
## [32,] 0.857819905 0.97752809
## [33,] 0.853080569 0.97752809
## [34,] 0.848341232 0.97752809
## [35,] 0.843601896 0.97752809
## [36,] 0.838862559 0.97752809
## [37,] 0.834123223 0.97752809
## [38,] 0.829383886 0.97752809
## [39,] 0.824644550 0.97752809
## [40,] 0.824644550 0.96629213
## [41,] 0.819905213 0.96629213
## [42,] 0.815165877 0.96629213
## [43,] 0.810426540 0.96629213
## [44,] 0.805687204 0.96629213
## [45,] 0.800947867 0.96629213
## [46,] 0.796208531 0.96629213
## [47,] 0.791469194 0.96629213
## [48,] 0.786729858 0.96629213
## [49,] 0.781990521 0.96629213
## [50,] 0.777251185 0.96629213
## [51,] 0.772511848 0.96629213
## [52,] 0.767772512 0.96629213
## [53,] 0.763033175 0.96629213
## [54,] 0.758293839 0.96629213
## [55,] 0.753554502 0.96629213
## [56,] 0.748815166 0.96629213
## [57,] 0.744075829 0.96629213
## [58,] 0.739336493 0.96629213
## [59,] 0.734597156 0.96629213
## [60,] 0.729857820 0.96629213
## [61,] 0.725118483 0.96629213
## [62,] 0.720379147 0.96629213
## [63,] 0.715639810 0.96629213
## [64,] 0.710900474 0.96629213
## [65,] 0.706161137 0.96629213
## [66,] 0.701421801 0.96629213
## [67,] 0.696682464 0.96629213
## [68,] 0.691943128 0.96629213
## [69,] 0.687203791 0.96629213
## [70,] 0.682464455 0.96629213
## [71,] 0.677725118 0.96629213
## [72,] 0.672985782 0.96629213
## [73,] 0.668246445 0.96629213
## [74,] 0.663507109 0.96629213
## [75,] 0.658767773 0.96629213
## [76,] 0.654028436 0.96629213
## [77,] 0.649289100 0.96629213
## [78,] 0.644549763 0.96629213
## [79,] 0.639810427 0.96629213
## [80,] 0.635071090 0.96629213
## [81,] 0.630331754 0.96629213
## [82,] 0.625592417 0.96629213
## [83,] 0.620853081 0.96629213
## [84,] 0.616113744 0.96629213
## [85,] 0.611374408 0.96629213
## [86,] 0.606635071 0.96629213
## [87,] 0.601895735 0.96629213
## [88,] 0.597156398 0.96629213
## [89,] 0.592417062 0.96629213
## [90,] 0.587677725 0.96629213
## [91,] 0.582938389 0.96629213
## [92,] 0.578199052 0.96629213
## [93,] 0.573459716 0.96629213
## [94,] 0.568720379 0.96629213
## [95,] 0.563981043 0.96629213
## [96,] 0.559241706 0.96629213
## [97,] 0.554502370 0.96629213
## [98,] 0.549763033 0.96629213
## [99,] 0.545023697 0.96629213
## [100,] 0.540284360 0.96629213
## [101,] 0.535545024 0.96629213
## [102,] 0.530805687 0.96629213
## [103,] 0.526066351 0.96629213
## [104,] 0.521327014 0.96629213
## [105,] 0.516587678 0.96629213
## [106,] 0.511848341 0.96629213
## [107,] 0.507109005 0.96629213
## [108,] 0.502369668 0.96629213
## [109,] 0.497630332 0.96629213
## [110,] 0.492890995 0.96629213
## [111,] 0.488151659 0.96629213
## [112,] 0.483412322 0.96629213
## [113,] 0.478672986 0.96629213
## [114,] 0.478672986 0.95505618
## [115,] 0.473933649 0.95505618
## [116,] 0.469194313 0.95505618
## [117,] 0.464454976 0.95505618
## [118,] 0.459715640 0.95505618
## [119,] 0.454976303 0.95505618
## [120,] 0.450236967 0.95505618
## [121,] 0.445497630 0.95505618
## [122,] 0.440758294 0.95505618
## [123,] 0.436018957 0.95505618
## [124,] 0.431279621 0.95505618
## [125,] 0.426540284 0.95505618
## [126,] 0.421800948 0.95505618
## [127,] 0.417061611 0.95505618
## [128,] 0.412322275 0.95505618
## [129,] 0.407582938 0.95505618
## [130,] 0.402843602 0.95505618
## [131,] 0.398104265 0.95505618
## [132,] 0.393364929 0.95505618
## [133,] 0.388625592 0.95505618
## [134,] 0.383886256 0.95505618
## [135,] 0.379146919 0.95505618
## [136,] 0.374407583 0.95505618
## [137,] 0.369668246 0.95505618
## [138,] 0.364928910 0.95505618
## [139,] 0.360189573 0.95505618
## [140,] 0.355450237 0.95505618
## [141,] 0.350710900 0.95505618
## [142,] 0.345971564 0.95505618
## [143,] 0.341232227 0.95505618
## [144,] 0.336492891 0.95505618
## [145,] 0.331753555 0.95505618
## [146,] 0.331753555 0.94382022
## [147,] 0.327014218 0.94382022
## [148,] 0.322274882 0.94382022
## [149,] 0.317535545 0.94382022
## [150,] 0.312796209 0.94382022
## [151,] 0.308056872 0.94382022
## [152,] 0.303317536 0.94382022
## [153,] 0.298578199 0.94382022
## [154,] 0.293838863 0.94382022
## [155,] 0.289099526 0.94382022
## [156,] 0.284360190 0.94382022
## [157,] 0.284360190 0.93258427
## [158,] 0.279620853 0.93258427
## [159,] 0.274881517 0.93258427
## [160,] 0.270142180 0.93258427
## [161,] 0.265402844 0.93258427
## [162,] 0.260663507 0.93258427
## [163,] 0.255924171 0.93258427
## [164,] 0.251184834 0.93258427
## [165,] 0.246445498 0.93258427
## [166,] 0.241706161 0.93258427
## [167,] 0.236966825 0.93258427
## [168,] 0.232227488 0.93258427
## [169,] 0.227488152 0.93258427
## [170,] 0.222748815 0.93258427
## [171,] 0.222748815 0.92134831
## [172,] 0.218009479 0.92134831
## [173,] 0.213270142 0.92134831
## [174,] 0.208530806 0.92134831
## [175,] 0.203791469 0.92134831
## [176,] 0.199052133 0.92134831
## [177,] 0.194312796 0.92134831
## [178,] 0.189573460 0.92134831
## [179,] 0.184834123 0.92134831
## [180,] 0.180094787 0.92134831
## [181,] 0.175355450 0.92134831
## [182,] 0.170616114 0.92134831
## [183,] 0.165876777 0.92134831
## [184,] 0.161137441 0.92134831
## [185,] 0.156398104 0.92134831
## [186,] 0.151658768 0.92134831
## [187,] 0.151658768 0.91011236
## [188,] 0.146919431 0.91011236
## [189,] 0.142180095 0.91011236
## [190,] 0.137440758 0.91011236
## [191,] 0.132701422 0.91011236
## [192,] 0.132701422 0.89887640
## [193,] 0.127962085 0.89887640
## [194,] 0.123222749 0.89887640
## [195,] 0.118483412 0.89887640
## [196,] 0.113744076 0.89887640
## [197,] 0.113744076 0.88764045
## [198,] 0.109004739 0.88764045
## [199,] 0.104265403 0.88764045
## [200,] 0.099526066 0.88764045
## [201,] 0.094786730 0.88764045
## [202,] 0.090047393 0.88764045
## [203,] 0.085308057 0.88764045
## [204,] 0.080568720 0.88764045
## [205,] 0.075829384 0.88764045
## [206,] 0.075829384 0.87640449
## [207,] 0.071090047 0.87640449
## [208,] 0.066350711 0.87640449
## [209,] 0.061611374 0.87640449
## [210,] 0.056872038 0.87640449
## [211,] 0.052132701 0.87640449
## [212,] 0.047393365 0.87640449
## [213,] 0.042654028 0.87640449
## [214,] 0.042654028 0.86516854
## [215,] 0.037914692 0.86516854
## [216,] 0.037914692 0.85393258
## [217,] 0.037914692 0.84269663
## [218,] 0.037914692 0.83146067
## [219,] 0.033175355 0.83146067
## [220,] 0.033175355 0.82022472
## [221,] 0.033175355 0.80898876
## [222,] 0.028436019 0.80898876
## [223,] 0.028436019 0.79775281
## [224,] 0.028436019 0.78651685
## [225,] 0.023696682 0.78651685
## [226,] 0.018957346 0.78651685
## [227,] 0.018957346 0.77528090
## [228,] 0.018957346 0.76404494
## [229,] 0.018957346 0.75280899
## [230,] 0.018957346 0.74157303
## [231,] 0.014218009 0.74157303
## [232,] 0.014218009 0.73033708
## [233,] 0.014218009 0.71910112
## [234,] 0.009478673 0.71910112
## [235,] 0.004739336 0.71910112
## [236,] 0.004739336 0.70786517
## [237,] 0.004739336 0.69662921
## [238,] 0.004739336 0.68539326
## [239,] 0.000000000 0.68539326
## [240,] 0.000000000 0.67415730
## [241,] 0.000000000 0.66292135
## [242,] 0.000000000 0.65168539
## [243,] 0.000000000 0.64044944
## [244,] 0.000000000 0.62921348
## [245,] 0.000000000 0.61797753
## [246,] 0.000000000 0.60674157
## [247,] 0.000000000 0.59550562
## [248,] 0.000000000 0.58426966
## [249,] 0.000000000 0.57303371
## [250,] 0.000000000 0.56179775
## [251,] 0.000000000 0.55056180
## [252,] 0.000000000 0.53932584
## [253,] 0.000000000 0.52808989
## [254,] 0.000000000 0.51685393
## [255,] 0.000000000 0.50561798
## [256,] 0.000000000 0.49438202
## [257,] 0.000000000 0.48314607
## [258,] 0.000000000 0.47191011
## [259,] 0.000000000 0.46067416
## [260,] 0.000000000 0.44943820
## [261,] 0.000000000 0.43820225
## [262,] 0.000000000 0.42696629
## [263,] 0.000000000 0.41573034
## [264,] 0.000000000 0.40449438
## [265,] 0.000000000 0.39325843
## [266,] 0.000000000 0.38202247
## [267,] 0.000000000 0.37078652
## [268,] 0.000000000 0.35955056
## [269,] 0.000000000 0.34831461
## [270,] 0.000000000 0.33707865
## [271,] 0.000000000 0.32584270
## [272,] 0.000000000 0.31460674
## [273,] 0.000000000 0.30337079
## [274,] 0.000000000 0.29213483
## [275,] 0.000000000 0.28089888
## [276,] 0.000000000 0.26966292
## [277,] 0.000000000 0.25842697
## [278,] 0.000000000 0.24719101
## [279,] 0.000000000 0.23595506
## [280,] 0.000000000 0.22471910
## [281,] 0.000000000 0.21348315
## [282,] 0.000000000 0.20224719
## [283,] 0.000000000 0.19101124
## [284,] 0.000000000 0.17977528
## [285,] 0.000000000 0.16853933
## [286,] 0.000000000 0.15730337
## [287,] 0.000000000 0.14606742
## [288,] 0.000000000 0.13483146
## [289,] 0.000000000 0.12359551
## [290,] 0.000000000 0.11235955
## [291,] 0.000000000 0.10112360
## [292,] 0.000000000 0.08988764
## [293,] 0.000000000 0.07865169
## [294,] 0.000000000 0.06741573
## [295,] 0.000000000 0.05617978
## [296,] 0.000000000 0.04494382
## [297,] 0.000000000 0.03370787
## [298,] 0.000000000 0.02247191
## [299,] 0.000000000 0.01123596
## [300,] 0.000000000 0.00000000
##
## $AUC
## [1] 0.9413707Class_Bayes=as.numeric(p1_x>0.5)
(M_table=table(z,Class_Bayes))## Class_Bayes
## z 0 1
## 0 188 23
## 1 10 79(err=1-sum(diag(M_table))/n)## [1] 0.11Real world data
Dopage
load('Dopage.RData')
x=hema
z=test
Classif_NP(x,z)
## $Class
## [1] "negatif" "positif" "positif" "negatif" "positif" "positif" "negatif"
## [8] "positif" "negatif" "negatif" "negatif" "positif" "negatif" "negatif"
## [15] "negatif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
## [22] "negatif" "negatif" "negatif" "positif" "positif" "negatif" "negatif"
## [29] "positif" "positif" "negatif" "negatif" "negatif" "negatif" "negatif"
## [36] "positif" "negatif" "negatif" "positif" "negatif" "positif" "negatif"
## [43] "positif" "negatif" "positif" "positif" "negatif" "positif" "negatif"
## [50] "positif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
## [57] "negatif" "negatif" "negatif" "positif" "negatif" "negatif" "positif"
## [64] "positif" "negatif" "positif" "negatif" "negatif" "positif" "negatif"
## [71] "negatif" "negatif" "negatif" "negatif" "negatif"
##
## $Prob
## negatif positif
## [1,] 1.000016213 -1.621285e-05
## [2,] -0.015399975 1.015400e+00
## [3,] 0.131798629 8.682014e-01
## [4,] 0.913610113 8.638989e-02
## [5,] -0.007226770 1.007227e+00
## [6,] -0.007434607 1.007435e+00
## [7,] 0.822317428 1.776826e-01
## [8,] 0.452064700 5.479353e-01
## [9,] 1.000037060 -3.706033e-05
## [10,] 0.984403703 1.559630e-02
## [11,] 1.002079889 -2.079889e-03
## [12,] 0.063393131 9.366069e-01
## [13,] 0.766288803 2.337112e-01
## [14,] 0.998567461 1.432539e-03
## [15,] 0.981894532 1.810547e-02
## [16,] 0.870295392 1.297046e-01
## [17,] 0.990382634 9.617366e-03
## [18,] 0.923010966 7.698903e-02
## [19,] 1.002976953 -2.976953e-03
## [20,] 1.004961146 -4.961146e-03
## [21,] 0.851112730 1.488873e-01
## [22,] 0.933663838 6.633616e-02
## [23,] 0.884913425 1.150866e-01
## [24,] 1.004358978 -4.358978e-03
## [25,] 0.376311492 6.236885e-01
## [26,] -0.014582062 1.014582e+00
## [27,] 0.950271761 4.972824e-02
## [28,] 0.653951737 3.460483e-01
## [29,] 0.141132940 8.588671e-01
## [30,] -0.009277185 1.009277e+00
## [31,] 0.842818837 1.571812e-01
## [32,] 0.953618386 4.638161e-02
## [33,] 0.994551141 5.448859e-03
## [34,] 0.981510520 1.848948e-02
## [35,] 0.748594649 2.514054e-01
## [36,] 0.100112801 8.998872e-01
## [37,] 0.603680357 3.963196e-01
## [38,] 0.966419808 3.358019e-02
## [39,] 0.229610874 7.703891e-01
## [40,] 1.004793373 -4.793373e-03
## [41,] 0.331009187 6.689908e-01
## [42,] 0.999996640 3.359742e-06
## [43,] -0.007224877 1.007225e+00
## [44,] 0.913058111 8.694189e-02
## [45,] 0.022202558 9.777974e-01
## [46,] 0.019332617 9.806674e-01
## [47,] 0.938043481 6.195652e-02
## [48,] 0.010994495 9.890055e-01
## [49,] 0.936136018 6.386398e-02
## [50,] 0.076533578 9.234664e-01
## [51,] 1.003810698 -3.810698e-03
## [52,] 0.984586259 1.541374e-02
## [53,] 0.780585234 2.194148e-01
## [54,] 0.962360848 3.763915e-02
## [55,] 0.869140063 1.308599e-01
## [56,] 0.649572310 3.504277e-01
## [57,] 0.836751458 1.632485e-01
## [58,] 0.542609205 4.573908e-01
## [59,] 0.987977417 1.202258e-02
## [60,] -0.015773466 1.015773e+00
## [61,] 1.004855560 -4.855560e-03
## [62,] 0.782654530 2.173455e-01
## [63,] 0.199051930 8.009481e-01
## [64,] 0.008278253 9.917217e-01
## [65,] 1.001237547 -1.237547e-03
## [66,] 0.369378542 6.306215e-01
## [67,] 0.925590318 7.440968e-02
## [68,] 0.915724000 8.427600e-02
## [69,] 0.308905764 6.910942e-01
## [70,] 0.995717811 4.282189e-03
## [71,] 1.000003364 -3.363682e-06
## [72,] 0.710345424 2.896546e-01
## [73,] 0.522081041 4.779190e-01
## [74,] 1.001423773 -1.423773e-03
## [75,] 0.899719315 1.002807e-01
##
## $M_table
## Class
## Y negatif positif
## negatif 47 3
## positif 5 20
##
## $err
## [1] 0.1066667load('Dopage.RData')
x=hema
z=test
Classif_NP(x,z)
## $Class
## [1] "negatif" "positif" "positif" "negatif" "positif" "positif" "negatif"
## [8] "positif" "negatif" "negatif" "negatif" "positif" "negatif" "negatif"
## [15] "negatif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
## [22] "negatif" "negatif" "negatif" "positif" "positif" "negatif" "negatif"
## [29] "positif" "positif" "negatif" "negatif" "negatif" "negatif" "negatif"
## [36] "positif" "negatif" "negatif" "positif" "negatif" "positif" "negatif"
## [43] "positif" "negatif" "positif" "positif" "negatif" "positif" "negatif"
## [50] "positif" "negatif" "negatif" "negatif" "negatif" "negatif" "negatif"
## [57] "negatif" "negatif" "negatif" "positif" "negatif" "negatif" "positif"
## [64] "positif" "negatif" "positif" "negatif" "negatif" "positif" "negatif"
## [71] "negatif" "negatif" "negatif" "negatif" "negatif"
##
## $Prob
## negatif positif
## [1,] 1.000016213 -1.621285e-05
## [2,] -0.015399975 1.015400e+00
## [3,] 0.131798629 8.682014e-01
## [4,] 0.913610113 8.638989e-02
## [5,] -0.007226770 1.007227e+00
## [6,] -0.007434607 1.007435e+00
## [7,] 0.822317428 1.776826e-01
## [8,] 0.452064700 5.479353e-01
## [9,] 1.000037060 -3.706033e-05
## [10,] 0.984403703 1.559630e-02
## [11,] 1.002079889 -2.079889e-03
## [12,] 0.063393131 9.366069e-01
## [13,] 0.766288803 2.337112e-01
## [14,] 0.998567461 1.432539e-03
## [15,] 0.981894532 1.810547e-02
## [16,] 0.870295392 1.297046e-01
## [17,] 0.990382634 9.617366e-03
## [18,] 0.923010966 7.698903e-02
## [19,] 1.002976953 -2.976953e-03
## [20,] 1.004961146 -4.961146e-03
## [21,] 0.851112730 1.488873e-01
## [22,] 0.933663838 6.633616e-02
## [23,] 0.884913425 1.150866e-01
## [24,] 1.004358978 -4.358978e-03
## [25,] 0.376311492 6.236885e-01
## [26,] -0.014582062 1.014582e+00
## [27,] 0.950271761 4.972824e-02
## [28,] 0.653951737 3.460483e-01
## [29,] 0.141132940 8.588671e-01
## [30,] -0.009277185 1.009277e+00
## [31,] 0.842818837 1.571812e-01
## [32,] 0.953618386 4.638161e-02
## [33,] 0.994551141 5.448859e-03
## [34,] 0.981510520 1.848948e-02
## [35,] 0.748594649 2.514054e-01
## [36,] 0.100112801 8.998872e-01
## [37,] 0.603680357 3.963196e-01
## [38,] 0.966419808 3.358019e-02
## [39,] 0.229610874 7.703891e-01
## [40,] 1.004793373 -4.793373e-03
## [41,] 0.331009187 6.689908e-01
## [42,] 0.999996640 3.359742e-06
## [43,] -0.007224877 1.007225e+00
## [44,] 0.913058111 8.694189e-02
## [45,] 0.022202558 9.777974e-01
## [46,] 0.019332617 9.806674e-01
## [47,] 0.938043481 6.195652e-02
## [48,] 0.010994495 9.890055e-01
## [49,] 0.936136018 6.386398e-02
## [50,] 0.076533578 9.234664e-01
## [51,] 1.003810698 -3.810698e-03
## [52,] 0.984586259 1.541374e-02
## [53,] 0.780585234 2.194148e-01
## [54,] 0.962360848 3.763915e-02
## [55,] 0.869140063 1.308599e-01
## [56,] 0.649572310 3.504277e-01
## [57,] 0.836751458 1.632485e-01
## [58,] 0.542609205 4.573908e-01
## [59,] 0.987977417 1.202258e-02
## [60,] -0.015773466 1.015773e+00
## [61,] 1.004855560 -4.855560e-03
## [62,] 0.782654530 2.173455e-01
## [63,] 0.199051930 8.009481e-01
## [64,] 0.008278253 9.917217e-01
## [65,] 1.001237547 -1.237547e-03
## [66,] 0.369378542 6.306215e-01
## [67,] 0.925590318 7.440968e-02
## [68,] 0.915724000 8.427600e-02
## [69,] 0.308905764 6.910942e-01
## [70,] 0.995717811 4.282189e-03
## [71,] 1.000003364 -3.363682e-06
## [72,] 0.710345424 2.896546e-01
## [73,] 0.522081041 4.779190e-01
## [74,] 1.001423773 -1.423773e-03
## [75,] 0.899719315 1.002807e-01
##
## $M_table
## Class
## Y negatif positif
## negatif 47 3
## positif 5 20
##
## $err
## [1] 0.1066667Iris
data('iris')
attach(iris)
for (j in colnames(iris)[1:4])
{
print(j)
x=get(j)
z=Species
r=Classif_NP(x,z)
print(r$M_table)
print(r$err)
}## [1] "Sepal.Length"
## Class
## Y setosa versicolor virginica
## setosa 45 5 0
## versicolor 6 28 16
## virginica 1 10 39
## [1] 0.2533333
## [1] "Sepal.Width"
## Class
## Y setosa versicolor virginica
## setosa 38 2 10
## versicolor 5 27 18
## virginica 13 21 16
## [1] 0.46
## [1] "Petal.Length"
## Class
## Y setosa versicolor virginica
## setosa 50 0 0
## versicolor 0 46 4
## virginica 0 3 47
## [1] 0.04666667
## [1] "Petal.Width"
## Class
## Y setosa versicolor virginica
## setosa 50 0 0
## versicolor 0 48 2
## virginica 0 4 46
## [1] 0.04