library(SmoothPLS)
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 4.4.3
library(pls)
#> Warning: package 'pls' was built under R version 4.4.3
#>
#> Attaching package: 'pls'
#> The following object is masked from 'package:stats':
#>
#> loadingsThis vignette / notebook show how to mix a one state CFD, a multi-state CFD and a SFD into the same multivariate functional PLS model.
Parameters
N_states = 3
nind = 50 # number of individuals (train set)
start = 0 # First time
end = 100 # end time
curve_type = 'cat'
TTRatio = 0.2 # Train Test Ratio means we have floor(nind*TTRatio/(1-TTRatio))
NotS_ratio = 0.2 # noise variance over total variance for Y
beta_0_real=65.4321 # Intercept value for the link between X(t) and Y
nbasis = 7 # number of basis functions
norder = 4 # 4 for cubic splines basis
regul_time = seq(start, end, 1) # regularisation time sequence
regul_time_0 = seq(start, end, 1)
all_curves_in_pls = TRUE #Keep all or (all - 1) states in PLS method if FALSE.
int_mode = 1 # in case of integration errors.CFD One state data generation
df_cfd_os
df_cfd_os = generate_X_df(nind = nind,
start = start, end = end,
curve_type = 'cat')
head(df_cfd_os)
#> id time state
#> 1 1 0.000000 0
#> 2 1 2.883051 1
#> 3 1 16.173600 0
#> 4 1 16.331487 1
#> 5 1 16.893597 0
#> 6 1 18.476103 1Y_df_cfd_os
beta_func_cfd_os = beta_5_real_func
Y_df_cfd_os = generate_Y_df(df_cfd_os, curve_type = 'cat',
beta_real_func_or_list = beta_func_cfd_os,
beta_0_real = beta_0_real,
NotS_ratio, id_col = 'id', time_col = 'time')
#> Warning: package 'future' was built under R version 4.4.3
Y_cfd_os = Y_df_cfd_os$Y_noised
plot(regul_time, beta_5_real_func(regul_time))
CFD Multistates Data generation
lambda_determination
# Initialized the lambdas values
lambdas = lambda_determination(N_states)
lambdas
#> [1] 0.1477226 0.2408948 0.1465805tranfer_probabilities
# Initialized the transition matrix
transition_df = transfer_probabilities(N_states)
transition_df
#> dir1 dir2 dir3
#> state_1 0.000000000 0.7096725 0.2903275
#> state_2 0.006384883 0.0000000 0.9936151
#> state_3 0.874851402 0.1251486 0.0000000df_cfd
df_cfd = generate_X_df_multistates(nind = nind, N_states, start, end,
lambdas, transition_df)
head(df_cfd)
#> id time state
#> 1 1 0.0000000 3
#> 2 1 0.2154268 2
#> 3 1 0.6424598 3
#> 4 1 2.7861784 1
#> 5 1 21.2412850 3
#> 6 1 30.8977401 2
plot_CFD_individuals(df_cfd)
plot_CFD_individuals(df_cfd, by_cfda = TRUE)
beta list
##### beta_real #####
###### beta_0_real ######
beta_0_real
#> [1] 65.4321
beta_func_list = beta_list_generation(N_states = N_states)
for(i in 1:N_states){
plot(0:end, beta_func_list[[i]](0:end, end_time = end),
ylab=paste0("Beta(t) n°=", i), type = 'l')
title(paste0("Beta(t) n°=", i))
}
Y evaluation
Y generation is based on the following equation : $Y = 0 + {i=1}^K _0^T _i(t) ind_i(t) dt $ with the indicator function of the state .
We link with the .
df_processed = cat_data_to_indicator(data = df_cfd)
Y_df_cfd = generate_Y_df(df = df_processed, curve_type = curve_type,
beta_real_func_or_list = beta_func_list,
beta_0_real = beta_0_real,
NotS_ratio = NotS_ratio)
Y_cfd = Y_df_cfd$Y_noised
names(Y_df_cfd)
#> [1] "id" "Y_beta1" "Y_beta2" "Y_beta3" "Y_real" "Y_noised"
head(Y_df_cfd)
#> id Y_beta1 Y_beta2 Y_beta3 Y_real Y_noised
#> 1 1 3.922839 21.13217 -9.664221 80.82289 82.142844
#> 2 2 -6.876623 35.10004 -15.902251 77.75327 80.173596
#> 3 3 13.876119 -10.40496 -10.057427 58.84583 90.952695
#> 4 4 22.578203 63.42320 -1.395864 150.03764 158.666223
#> 5 5 -11.374676 -8.55571 -16.846493 28.65522 4.972648
#> 6 6 8.290573 25.71019 -22.329097 77.10377 64.245545SFD data generation
For SFD for X_df two new arguments are important: the noise added to the signal and the seed for repeatability.
df_sfd
df_sfd = generate_X_df(nind = nind, start = start, end = end,
curve_type = 'num', noise_sd = 0.15, seed = 123)
head(df_sfd)
#> id time value
#> 1 1 0 1.2591356
#> 2 1 1 0.7193661
#> 3 1 2 1.0470795
#> 4 1 3 0.7297674
#> 5 1 4 0.6105385
#> 6 1 5 0.5351208
# Visualisation
ggplot(df_sfd, aes(x = time, y = value, group = id, color = factor(id))) +
geom_line(alpha = 0.8) +
labs(title = "Noised cosinus curves",
x = "Time", y = "Value",
color = "Individual") +
theme_minimal() +
theme(legend.position = "none")
Data manipulation
df_sfd_regul = regularize_time_series(df_sfd, time_seq = regul_time,
curve_type = 'num')
df_sfd_regul
#> id time value
#> 1 1 0 1.2591356058
#> 2 1 1 0.7193661352
#> 3 1 2 1.0470795456
#> 4 1 3 0.7297673587
#> 5 1 4 0.6105384880
#> 6 1 5 0.5351207804
#> 7 1 6 0.5772717305
#> 8 1 7 0.0021078518
#> 9 1 8 0.3897052156
#> 10 1 9 0.0861911155
#> 11 1 10 0.2642695075
#> 12 1 11 -0.1577629109
#> 13 1 12 -0.3285942560
#> 14 1 13 -0.6444211095
#> 15 1 14 -0.4137112833
#> 16 1 15 -0.6025342230
#> 17 1 16 -0.8502908980
#> 18 1 17 -1.0718453808
#> 19 1 18 -1.1726978392
#> 20 1 19 -1.1993425902
#> 21 1 20 -1.3168846512
#> 22 1 21 -1.5241886843
#> 23 1 22 -1.4634608174
#> 24 1 23 -1.3736442186
#> 25 1 24 -1.6335783757
#> 26 1 25 -1.8577736968
#> 27 1 26 -1.8702501514
#> 28 1 27 -1.7023667280
#> 29 1 28 -1.9036260161
#> 30 1 29 -2.0955330536
#> 31 1 30 -2.0244393652
#> 32 1 31 -1.9819685631
#> 33 1 32 -1.8498600658
#> 34 1 33 -2.0180679264
#> 35 1 34 -1.9505031276
#> 36 1 35 -2.4807905328
#> 37 1 36 -2.1013011431
#> 38 1 37 -1.9235543721
#> 39 1 38 -2.1228567127
#> 40 1 39 -1.8401851918
#> 41 1 40 -1.7434094354
#> 42 1 41 -1.8387396971
#> 43 1 42 -1.5712667007
#> 44 1 43 -1.8344798840
#> 45 1 44 -1.5651967205
#> 46 1 45 -1.4872290083
#> 47 1 46 -1.5981515868
#> 48 1 47 -1.5746566524
#> 49 1 48 -1.2786856943
#> 50 1 49 -1.2489645550
#> 51 1 50 -0.8271237339
#> 52 1 51 -0.7885405674
#> 53 1 52 -0.8197516409
#> 54 1 53 -0.9034585802
#> 55 1 54 -0.7062551838
#> 56 1 55 -0.2641780101
#> 57 1 56 -0.5456987332
#> 58 1 57 -0.0083153595
#> 59 1 58 -0.1724310277
#> 60 1 59 -0.0808493202
#> 61 1 60 -0.0009657591
#> 62 1 61 0.5626153216
#> 63 1 62 0.1641731499
#> 64 1 63 0.5614677100
#> 65 1 64 0.7930222075
#> 66 1 65 0.8215195183
#> 67 1 66 0.9037413374
#> 68 1 67 1.0732258443
#> 69 1 68 1.0398107608
#> 70 1 69 1.1326284089
#> 71 1 70 1.1315289749
#> 72 1 71 1.2510798906
#> 73 1 72 1.2364944602
#> 74 1 73 1.6271283295
#> 75 1 74 1.6108396038
#> 76 1 75 1.5800859428
#> 77 1 76 1.7055727639
#> 78 1 77 1.6876975984
#> 79 1 78 1.7387679672
#> 80 1 79 1.8425846779
#> 81 1 80 1.8865890447
#> 82 1 81 1.9752385250
#> 83 1 82 1.8675994474
#> 84 1 83 1.9014718951
#> 85 1 84 1.8648411794
#> 86 1 85 2.0962514088
#> 87 1 86 2.0305742451
#> 88 1 87 1.9777651808
#> 89 1 88 1.9707358197
#> 90 1 89 1.8320293230
#> 91 1 90 1.7692432166
#> 92 1 91 1.8071125429
#> 93 1 92 1.7820972342
#> 94 1 93 1.8881680125
#> 95 1 94 1.5547195431
#> 96 1 95 1.5935932108
#> 97 1 96 1.4525877723
#> 98 1 97 1.4383705292
#> 99 1 98 1.3105640166
#> 100 1 99 1.4509563287
#> 101 1 100 1.0862570388
#> 102 2 0 0.9378618266
#> 103 2 1 0.9660453260
#> 104 2 2 0.7434194922
#> 105 2 3 0.4959209641
#> 106 2 4 0.5710908042
#> 107 2 5 0.6455078797
#> 108 2 6 0.2988864544
#> 109 2 7 0.3523930945
#> 110 2 8 -0.1065048437
#> 111 2 9 0.0022849536
#> 112 2 10 -0.0370698945
#> 113 2 11 -0.1949544169
#> 114 2 12 -0.3484747650
#> 115 2 13 -0.5831930392
#> 116 2 14 -0.7353814234
#> 117 2 15 -0.8799845182
#> 118 2 16 -0.8242910066
#> 119 2 17 -1.0963092403
#> 120 2 18 -1.1362559723
#> 121 2 19 -1.2053766100
#> 122 2 20 -0.9900684367
#> 123 2 21 -1.4591262992
#> 124 2 22 -1.4153393419
#> 125 2 23 -1.5225416719
#> 126 2 24 -1.7560478382
#> 127 2 25 -1.6936381825
#> 128 2 26 -1.5307901643
#> 129 2 27 -1.7373815317
#> 130 2 28 -1.8494326149
#> 131 2 29 -1.9621792167
#> 132 2 30 -2.2424851992
#> 133 2 31 -1.7928563778
#> 134 2 32 -2.2019664985
#> 135 2 33 -1.8843664054
#> 136 2 34 -1.7136062723
#> 137 2 35 -2.2132760824
#> 138 2 36 -1.8802647271
#> 139 2 37 -2.0058662806
#> 140 2 38 -2.1756015392
#> 141 2 39 -2.1325678964
#> 142 2 40 -2.1036663913
#> 143 2 41 -1.8937860302
#> 144 2 42 -1.9769678547
#> 145 2 43 -1.5911346093
#> 146 2 44 -1.3092366772
#> 147 2 45 -1.7408282981
#> 148 2 46 -1.3470252522
#> 149 2 47 -1.2614596757
#> 150 2 48 -1.2331818937
#> 151 2 49 -1.3354015772
#> 152 2 50 -1.0985225027
#> 153 2 51 -1.0148587850
#> 154 2 52 -0.7767067327
#> 155 2 53 -0.8019780680
#> 156 2 54 -0.4815787742
#> 157 2 55 -0.5638455170
#> 158 2 56 -0.2272817789
#> 159 2 57 -0.4185749972
#> 160 2 58 -0.3252008493
#> 161 2 59 0.4755367418
#> 162 2 60 0.0524523369
#> 163 2 61 0.2848615600
#> 164 2 62 0.4598116452
#> 165 2 63 0.4145200441
#> 166 2 64 0.6854550781
#> 167 2 65 0.7817098787
#> 168 2 66 0.8096309201
#> 169 2 67 0.9639820032
#> 170 2 68 1.0575622677
#> 171 2 69 1.4862305660
#> 172 2 70 1.1554473231
#> 173 2 71 1.1969343739
#> 174 2 72 1.4563155877
#> 175 2 73 1.5808079117
#> 176 2 74 1.6772478649
#> 177 2 75 1.6141871697
#> 178 2 76 1.5879738730
#> 179 2 77 1.9945849161
#> 180 2 78 1.8031699950
#> 181 2 79 1.7689777625
#> 182 2 80 1.8990561806
#> 183 2 81 1.9329805756
#> 184 2 82 2.1493585313
#> 185 2 83 2.0080691259
#> 186 2 84 2.1130798755
#> 187 2 85 1.9217983057
#> 188 2 86 2.0176991738
#> 189 2 87 1.9178337705
#> 190 2 88 1.9539674446
#> 191 2 89 1.7710632446
#> 192 2 90 1.6668157353
#> 193 2 91 2.1137320595
#> 194 2 92 1.8478108405
#> 195 2 93 1.5066314210
#> 196 2 94 1.5325781308
#> 197 2 95 1.3699517140
#> 198 2 96 1.7950076316
#> 199 2 97 1.5736779583
#> 200 2 98 1.2432405221
#> 201 2 99 1.2656241949
#> 202 2 100 1.0184536195
#> 203 3 0 1.0798334185
#> 204 3 1 0.8422298185
#> 205 3 2 0.7917233066
#> 206 3 3 0.4594395663
#> 207 3 4 0.6835971888
#> 208 3 5 0.4383151798
#> 209 3 6 0.4334818825
#> 210 3 7 0.2185982377
#> 211 3 8 0.2999560291
#> 212 3 9 0.0346517028
#> 213 3 10 0.2912442676
#> 214 3 11 -0.1971839318
#> 215 3 12 -0.3692027318
#> 216 3 13 -0.6355388409
#> 217 3 14 -0.5761542822
#> 218 3 15 -0.8721678297
#> 219 3 16 -0.7595543941
#> 220 3 17 -1.1115412776
#> 221 3 18 -0.9953022656
#> 222 3 19 -1.2248411290
#> 223 3 20 -1.5021680660
#> 224 3 21 -1.1772924238
#> 225 3 22 -1.3506431684
#> 226 3 23 -1.7069762738
#> 227 3 24 -1.6358876156
#> 228 3 25 -1.8288790360
#> 229 3 26 -1.8390420419
#> 230 3 27 -1.7302156084
#> 231 3 28 -1.7237129323
#> 232 3 29 -1.7603353060
#> 233 3 30 -1.8305280202
#> 234 3 31 -1.9834820085
#> 235 3 32 -2.4794722969
#> 236 3 33 -1.9145886622
#> 237 3 34 -1.8660989277
#> 238 3 35 -1.9232728029
#> 239 3 36 -2.1649851394
#> 240 3 37 -1.8971259793
#> 241 3 38 -1.7940243789
#> 242 3 39 -2.1261915930
#> 243 3 40 -1.7840912242
#> 244 3 41 -1.4459899989
#> 245 3 42 -2.0051063389
#> 246 3 43 -1.5749513520
#> 247 3 44 -1.6754469933
#> 248 3 45 -1.7585617966
#> 249 3 46 -1.6036302016
#> 250 3 47 -1.3753312924
#> 251 3 48 -1.3443412466
#> 252 3 49 -1.3923818793
#> 253 3 50 -1.1202938975
#> 254 3 51 -1.1148942266
#> 255 3 52 -0.7502269635
#> 256 3 53 -0.6115954483
#> 257 3 54 -0.6800249153
#> 258 3 55 -0.7749669486
#> 259 3 56 -0.3154472358
#> 260 3 57 -0.5538530376
#> 261 3 58 -0.2135945637
#> 262 3 59 0.0627427992
#> 263 3 60 0.2502846840
#> 264 3 61 0.3361818705
#> 265 3 62 0.5070075260
#> 266 3 63 0.3972186565
#> 267 3 64 0.4083215225
#> 268 3 65 0.6375337377
#> 269 3 66 1.1120956246
#> 270 3 67 1.1124888368
#> 271 3 68 1.0188842423
#> 272 3 69 1.0433463747
#> 273 3 70 1.4490852733
#> 274 3 71 1.3942930746
#> 275 3 72 1.4618972568
#> 276 3 73 1.2131730267
#> 277 3 74 1.8324151786
#> 278 3 75 1.5572768287
#> 279 3 76 1.8067992732
#> 280 3 77 1.9380703912
#> 281 3 78 2.0357739359
#> 282 3 79 2.0963255441
#> 283 3 80 1.9055420533
#> 284 3 81 2.0451433972
#> 285 3 82 1.6695545463
#> 286 3 83 1.9916220630
#> 287 3 84 2.1332404554
#> 288 3 85 1.9460774356
#> 289 3 86 1.8309257192
#> 290 3 87 2.0311616331
#> 291 3 88 1.9711160256
#> 292 3 89 1.6731317098
#> 293 3 90 1.6873656325
#> 294 3 91 1.9909723325
#> 295 3 92 1.6948081006
#> 296 3 93 1.4164358303
#> 297 3 94 1.6971419893
#> 298 3 95 1.4769868377
#> 299 3 96 1.5921968680
#> 300 3 97 1.5156816006
#> 301 3 98 1.2348876934
#> 302 3 99 0.9889990409
#> 303 3 100 1.4495398133
#> 304 4 0 1.3862407145
#> 305 4 1 1.1679758836
#> 306 4 2 0.9746713772
#> 307 4 3 0.4871026947
#> 308 4 4 0.5378987760
#> 309 4 5 0.4548514199
#> 310 4 6 0.4907170842
#> 311 4 7 0.2453477460
#> 312 4 8 -0.0526197316
#> 313 4 9 0.2632846046
#> 314 4 10 0.0217277187
#> 315 4 11 -0.2045128804
#> 316 4 12 -0.1816099026
#> 317 4 13 -0.6879032811
#> 318 4 14 -0.5088027268
#> 319 4 15 -0.8048020561
#> 320 4 16 -0.7393761679
#> 321 4 17 -0.9633113413
#> 322 4 18 -0.9677282488
#> 323 4 19 -0.9666351389
#> 324 4 20 -1.2655542240
#> 325 4 21 -1.2087000184
#> 326 4 22 -1.6289124330
#> 327 4 23 -1.6424764654
#> 328 4 24 -1.3838866864
#> 329 4 25 -1.6263337737
#> 330 4 26 -2.0553062161
#> 331 4 27 -2.0097127575
#> 332 4 28 -1.8857347055
#> 333 4 29 -1.7689377812
#> 334 4 30 -1.9497806043
#> 335 4 31 -1.8689288390
#> 336 4 32 -1.8390196812
#> 337 4 33 -1.7447003077
#> 338 4 34 -1.9915692977
#> 339 4 35 -2.0044893942
#> 340 4 36 -2.2485179812
#> 341 4 37 -1.9516375181
#> 342 4 38 -2.0255574240
#> 343 4 39 -2.0514691858
#> 344 4 40 -1.8904219000
#> 345 4 41 -1.6619085759
#> 346 4 42 -2.0566167902
#> 347 4 43 -1.7584140184
#> 348 4 44 -1.6067574258
#> 349 4 45 -1.6817548622
#> 350 4 46 -1.4151006379
#> 351 4 47 -1.3151015237
#> 352 4 48 -1.2879677045
#> 353 4 49 -1.5540298150
#> 354 4 50 -0.6948858899
#> 355 4 51 -1.0035943734
#> 356 4 52 -0.7634761704
#> 357 4 53 -0.7050472809
#> 358 4 54 -0.4744237970
#> 359 4 55 -0.3850094714
#> 360 4 56 -0.4166574745
#> 361 4 57 -0.2044732803
#> 362 4 58 -0.2779888873
#> 363 4 59 0.1179192032
#> 364 4 60 0.0458252243
#> 365 4 61 0.6026434243
#> 366 4 62 0.1166688598
#> 367 4 63 0.4174890516
#> 368 4 64 0.7317327509
#> 369 4 65 0.8028850817
#> 370 4 66 0.7535158404
#> 371 4 67 0.8046709368
#> 372 4 68 1.0843437115
#> 373 4 69 1.1648166692
#> 374 4 70 0.9981055519
#> 375 4 71 1.3665164740
#> 376 4 72 1.4791818751
#> 377 4 73 1.5604447589
#> 378 4 74 1.4535167867
#> 379 4 75 1.7543619614
#> 380 4 76 1.9542583136
#> 381 4 77 1.8735426002
#> 382 4 78 1.6852792826
#> 383 4 79 1.8334578714
#> 384 4 80 1.9864136589
#> 385 4 81 1.8655001151
#> 386 4 82 1.6592235376
#> 387 4 83 2.1279961551
#> 388 4 84 1.8755501659
#> 389 4 85 1.9106580677
#> 390 4 86 2.2111174687
#> 391 4 87 1.8504149178
#> 392 4 88 2.0666396464
#> 393 4 89 1.7162653165
#> 394 4 90 1.8102546048
#> 395 4 91 1.8031166490
#> 396 4 92 1.5824068032
#> 397 4 93 1.5991098856
#> 398 4 94 1.6199267854
#> 399 4 95 1.6483781220
#> 400 4 96 1.2176040978
#> 401 4 97 1.3243528759
#> 402 4 98 1.3964732463
#> 403 4 99 1.1033237120
#> 404 4 100 1.1146984000
#> 405 5 0 1.4356594782
#> 406 5 1 0.7577740952
#> 407 5 2 0.6194322814
#> 408 5 3 0.8398337663
#> 409 5 4 0.7398972830
#> 410 5 5 0.5954593512
#> 411 5 6 0.4124369274
#> 412 5 7 0.3219320455
#> 413 5 8 -0.0584388402
#> 414 5 9 0.1054318600
#> 415 5 10 -0.2912823356
#> 416 5 11 -0.3353580695
#> 417 5 12 -0.7180680445
#> 418 5 13 -0.6560141889
#> 419 5 14 -0.5176320984
#> 420 5 15 -0.6410984717
#> 421 5 16 -0.8660876258
#> 422 5 17 -1.1303000520
#> 423 5 18 -0.8794712397
#> 424 5 19 -1.4255515454
#> 425 5 20 -1.2784589448
#> 426 5 21 -1.4528861136
#> 427 5 22 -1.6312787821
#> 428 5 23 -1.5161320816
#> 429 5 24 -1.7550310860
#> 430 5 25 -1.6726335208
#> 431 5 26 -1.6800101500
#> 432 5 27 -1.7293663990
#> 433 5 28 -1.8051039179
#> 434 5 29 -1.6869637363
#> 435 5 30 -2.0908706871
#> 436 5 31 -1.7260113631
#> 437 5 32 -2.0625145614
#> 438 5 33 -2.1097332845
#> 439 5 34 -1.8956366850
#> 440 5 35 -1.9791599689
#> 441 5 36 -1.8799886424
#> 442 5 37 -2.0120028887
#> 443 5 38 -1.8146567911
#> 444 5 39 -1.8893204472
#> 445 5 40 -1.8317834667
#> 446 5 41 -1.8098952573
#> 447 5 42 -1.5625619532
#> 448 5 43 -1.9141035930
#> 449 5 44 -1.8678379602
#> 450 5 45 -1.5189291948
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#> 1895 19 76 1.8309409707
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#> 1912 19 93 1.8330770184
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#> 1914 19 95 1.6718230418
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#> 1920 20 0 1.5030172531
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#> 1929 20 9 -0.0541393134
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#> 1971 20 51 -1.0495400431
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#> 1992 20 72 1.6171035400
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#> 1994 20 74 1.6328676729
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#> 2010 20 90 1.8165938611
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#> 2012 20 92 1.8556129089
#> 2013 20 93 1.4462982298
#> 2014 20 94 1.5777123735
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#> 2017 20 97 1.3678282816
#> 2018 20 98 1.2798611502
#> 2019 20 99 1.0755971038
#> 2020 20 100 0.9314326363
#> 2021 21 0 1.5332478270
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#> 4883 49 34 -2.1210153603
#> 4884 49 35 -1.8081866689
#> 4885 49 36 -1.9345465245
#> 4886 49 37 -2.0844892331
#> 4887 49 38 -1.8414319874
#> 4888 49 39 -1.9289222649
#> 4889 49 40 -1.7624879347
#> 4890 49 41 -1.6276378254
#> 4891 49 42 -1.5980025939
#> 4892 49 43 -1.5497109083
#> 4893 49 44 -1.7852326414
#> 4894 49 45 -1.7848833128
#> 4895 49 46 -1.3901940490
#> 4896 49 47 -1.5673739524
#> 4897 49 48 -1.3244307441
#> 4898 49 49 -1.0710064282
#> 4899 49 50 -0.8245332763
#> 4900 49 51 -0.9019834977
#> 4901 49 52 -0.8926376346
#> 4902 49 53 -0.5889024387
#> 4903 49 54 -0.8535626867
#> 4904 49 55 -0.5900171321
#> 4905 49 56 -0.5233547078
#> 4906 49 57 -0.2437603560
#> 4907 49 58 -0.2160484758
#> 4908 49 59 -0.1640847311
#> 4909 49 60 -0.0254943392
#> 4910 49 61 0.1716343146
#> 4911 49 62 0.3385936663
#> 4912 49 63 0.6089063739
#> 4913 49 64 0.5633369604
#> 4914 49 65 0.8435457324
#> 4915 49 66 1.0683188756
#> 4916 49 67 0.9329061149
#> 4917 49 68 1.1519839364
#> 4918 49 69 1.1843373442
#> 4919 49 70 1.3372943533
#> 4920 49 71 1.5052568130
#> 4921 49 72 1.7809612362
#> 4922 49 73 1.4669809308
#> 4923 49 74 1.7700439691
#> 4924 49 75 1.5056090019
#> 4925 49 76 1.7348064196
#> 4926 49 77 1.6239158832
#> 4927 49 78 2.0483514782
#> 4928 49 79 1.8305402794
#> 4929 49 80 1.8679613812
#> 4930 49 81 1.9072703760
#> 4931 49 82 2.1555530659
#> 4932 49 83 1.6925905016
#> 4933 49 84 2.1162655412
#> 4934 49 85 1.8626621192
#> 4935 49 86 1.9528608996
#> 4936 49 87 1.9365699446
#> 4937 49 88 2.1092408218
#> 4938 49 89 1.8647672352
#> 4939 49 90 2.0024993689
#> 4940 49 91 1.7914402968
#> 4941 49 92 1.7503451737
#> 4942 49 93 1.6095925552
#> 4943 49 94 1.6979057957
#> 4944 49 95 1.6740638781
#> 4945 49 96 1.4799869950
#> 4946 49 97 1.3453892408
#> 4947 49 98 1.1397794144
#> 4948 49 99 0.8997809898
#> 4949 49 100 1.0284243658
#> 4950 50 0 1.0524457884
#> 4951 50 1 0.8170931783
#> 4952 50 2 1.0625242446
#> 4953 50 3 0.7646391933
#> 4954 50 4 0.7568469508
#> 4955 50 5 0.2968441999
#> 4956 50 6 0.3830199342
#> 4957 50 7 0.3430347983
#> 4958 50 8 0.1508943759
#> 4959 50 9 0.0132587428
#> 4960 50 10 -0.2701229931
#> 4961 50 11 -0.3344349907
#> 4962 50 12 -0.4250614052
#> 4963 50 13 -0.6074428204
#> 4964 50 14 -0.4933546980
#> 4965 50 15 -0.4624232592
#> 4966 50 16 -0.6446609839
#> 4967 50 17 -0.8907620138
#> 4968 50 18 -1.0804185093
#> 4969 50 19 -1.0805619219
#> 4970 50 20 -1.3849398686
#> 4971 50 21 -1.3215962471
#> 4972 50 22 -1.4256773981
#> 4973 50 23 -1.8859892815
#> 4974 50 24 -1.3272737902
#> 4975 50 25 -1.8826761848
#> 4976 50 26 -2.1413544390
#> 4977 50 27 -1.8051585105
#> 4978 50 28 -1.8395057090
#> 4979 50 29 -1.9000055066
#> 4980 50 30 -1.9134134239
#> 4981 50 31 -2.1402960605
#> 4982 50 32 -1.8939959223
#> 4983 50 33 -1.7882553949
#> 4984 50 34 -2.1257810952
#> 4985 50 35 -1.9508109729
#> 4986 50 36 -2.0261674250
#> 4987 50 37 -1.9756545429
#> 4988 50 38 -1.7934236471
#> 4989 50 39 -1.8637025169
#> 4990 50 40 -1.5736598054
#> 4991 50 41 -1.8639936428
#> 4992 50 42 -1.5354130229
#> 4993 50 43 -1.7626704599
#> 4994 50 44 -1.6589513785
#> 4995 50 45 -1.5968413708
#> 4996 50 46 -1.4220007748
#> 4997 50 47 -1.3068358778
#> 4998 50 48 -1.2612381175
#> 4999 50 49 -1.0942462859
#> 5000 50 50 -1.1978944631
#> 5001 50 51 -1.0086312622
#> 5002 50 52 -0.7633348606
#> 5003 50 53 -0.5904004689
#> 5004 50 54 -0.5773736168
#> 5005 50 55 -0.4012499145
#> 5006 50 56 -0.2591793250
#> 5007 50 57 -0.1698020969
#> 5008 50 58 -0.1697352127
#> 5009 50 59 -0.0352708361
#> 5010 50 60 0.2082800500
#> 5011 50 61 0.1718198477
#> 5012 50 62 0.3445286306
#> 5013 50 63 0.4733160868
#> 5014 50 64 0.3699044204
#> 5015 50 65 0.7764935343
#> 5016 50 66 0.9274390226
#> 5017 50 67 0.9450225431
#> 5018 50 68 1.3317824358
#> 5019 50 69 1.1405954258
#> 5020 50 70 1.3534676230
#> 5021 50 71 1.4412235332
#> 5022 50 72 1.5683491865
#> 5023 50 73 1.5968926123
#> 5024 50 74 1.5830772560
#> 5025 50 75 1.7674449570
#> 5026 50 76 1.7855011442
#> 5027 50 77 1.8416354607
#> 5028 50 78 1.9635560907
#> 5029 50 79 2.0147146389
#> 5030 50 80 1.9332196863
#> 5031 50 81 1.9041965865
#> 5032 50 82 2.1821054910
#> 5033 50 83 2.0033104149
#> 5034 50 84 1.9435320340
#> 5035 50 85 1.8547563563
#> 5036 50 86 2.0260307999
#> 5037 50 87 2.0246092453
#> 5038 50 88 1.7690720252
#> 5039 50 89 1.7031145749
#> 5040 50 90 1.8910655332
#> 5041 50 91 1.6913151035
#> 5042 50 92 1.9599968119
#> 5043 50 93 1.5282422147
#> 5044 50 94 1.3919175511
#> 5045 50 95 1.5372965357
#> 5046 50 96 1.5353868429
#> 5047 50 97 1.4003481837
#> 5048 50 98 1.2648833350
#> 5049 50 99 1.2409652098
#> 5050 50 100 0.9653467651
df_sfd_long = convert_to_wide_format(df_sfd_regul)
df_sfd_long
#> # A tibble: 50 × 102
#> id `0` `1` `2` `3` `4` `5` `6` `7` `8` `9`
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1.26 0.719 1.05 0.730 0.611 0.535 0.577 0.00211 0.390 0.0862
#> 2 2 0.938 0.966 0.743 0.496 0.571 0.646 0.299 0.352 -0.107 0.00228
#> 3 3 1.08 0.842 0.792 0.459 0.684 0.438 0.433 0.219 0.300 0.0347
#> 4 4 1.39 1.17 0.975 0.487 0.538 0.455 0.491 0.245 -0.0526 0.263
#> 5 5 1.44 0.758 0.619 0.840 0.740 0.595 0.412 0.322 -0.0584 0.105
#> 6 6 0.988 0.863 0.841 0.793 0.472 0.480 0.530 0.245 0.0314 -0.0308
#> 7 7 1.11 0.715 0.941 0.672 0.559 0.485 0.297 0.00222 0.227 0.0147
#> 8 8 1.14 0.817 0.602 0.842 0.399 0.508 0.423 0.346 0.165 -0.0993
#> 9 9 1.32 1.21 1.03 0.554 0.717 0.463 0.393 0.441 0.254 -0.257
#> 10 10 1.18 1.17 0.847 0.776 1.00 0.572 0.414 0.0599 0.137 -0.0226
#> # ℹ 40 more rows
#> # ℹ 91 more variables: `10` <dbl>, `11` <dbl>, `12` <dbl>, `13` <dbl>,
#> # `14` <dbl>, `15` <dbl>, `16` <dbl>, `17` <dbl>, `18` <dbl>, `19` <dbl>,
#> # `20` <dbl>, `21` <dbl>, `22` <dbl>, `23` <dbl>, `24` <dbl>, `25` <dbl>,
#> # `26` <dbl>, `27` <dbl>, `28` <dbl>, `29` <dbl>, `30` <dbl>, `31` <dbl>,
#> # `32` <dbl>, `33` <dbl>, `34` <dbl>, `35` <dbl>, `36` <dbl>, `37` <dbl>,
#> # `38` <dbl>, `39` <dbl>, `40` <dbl>, `41` <dbl>, `42` <dbl>, `43` <dbl>, …generate_Y_df
WARNING! Here we have to regularize X(t) before evaluating Y!
beta_func_sfd = beta_1_real_func
Y_df_sfd = generate_Y_df(df = df_sfd_regul, curve_type = 'num',
beta_real_func_or_list = beta_func_sfd,
beta_0_real = beta_0_real, NotS_ratio = NotS_ratio,
seed = 123)
Y_sfd = Y_df_sfd$Y_noised
head(Y_df_sfd)
#> id Y_real Y_noised
#> 1 1 271.9966 271.4010
#> 2 2 274.7040 274.4594
#> 3 3 273.1712 274.8276
#> 4 4 270.1414 270.2163
#> 5 5 268.3050 268.4424
#> 6 6 268.4381 270.2606beta_func_list_tot
beta_func_list_tot = append(beta_list_generation(N_states = N_states),
append(beta_func_sfd, beta_func_cfd_os))
par(mfrow=c(1, 3))
hist(Y_df_sfd$Y_real)
hist(Y_df_sfd$Y_noised)
plot(regul_time, beta_4_real_func(regul_time))
Test set
CFD one state
df_cfd_os_test
nind_test = floor(nind*TTRatio/(1-TTRatio))
df_cfd_os_test = generate_X_df(nind = nind_test,
start = start, end = end,
curve_type = 'cat')Y_df_cfd_os_test
Y_df_cfd_os_test = generate_Y_df(df_cfd_os_test, curve_type = 'cat',
beta_real_func_or_list = beta_5_real_func,
beta_0_real = beta_0_real,
NotS_ratio = NotS_ratio)
Y_cfd_os_test = Y_df_cfd_os_test$Y_noisedCFD multistates
df_cfd_test
nind_test = floor(nind*TTRatio/(1-TTRatio))
df_cfd_test = generate_X_df_multistates(nind = nind_test, N_states, start, end,
lambdas, transition_df)Y_df_cfd_test
df_cfd_test_processed = cat_data_to_indicator(df_cfd_test)
Y_df_cfd_test = generate_Y_df(df_cfd_test_processed, curve_type = 'cat',
beta_real_func_or_list = beta_func_list,
beta_0_real = beta_0_real,
NotS_ratio= NotS_ratio)
Y_cfd_test = Y_df_cfd_test$Y_noisedSFD
df_sfd_test
df_sfd_test = generate_X_df(nind = nind_test, start = start, end = end,
curve_type = 'num', noise_sd = 0.15, seed = 123)Y_df_cfd_test
df_sfd_regul_test = regularize_time_series(df_sfd_test, time_seq = regul_time,
curve_type = 'num')
Y_df_sfd_test = generate_Y_df(df = df_sfd_regul_test, curve_type = 'num',
beta_real_func_or_list = beta_func_sfd,
beta_0_real = beta_0_real, NotS_ratio = NotS_ratio,
seed = 123)
Y_sfd_test = Y_df_sfd_test$Y_noisedBasis creation
All the states will share the same basis.
basis = create_bspline_basis(start, end, nbasis, norder)
#basis = fda::create.fourier.basis(c(start,end), nbasis = nbasis)
# All the states will share the same basis.
basis_list = obj_list_creation(N_rep = N_states, obj = basis)
plot(basis, main=paste0(nbasis, " ", basis$type," functions basis"))
SmoothPLS
Multivariate
spls_obj = smoothPLS(df_list = list(df_cfd, df_sfd, df_cfd_os), Y = Y,
basis_obj = basis,
regul_time_obj = regul_time,
curve_type_obj = list('cat', 'num', 'cat'),
orth_obj = c(TRUE, TRUE, TRUE),
id_col_obj = 'id',
time_col_obj = 'time',
print_steps = TRUE, plot_rmsep = TRUE,
print_nbComp = TRUE, plot_reg_curves = FALSE)
#> ### Smooth PLS ###
#> ## Use parallelization in case of heavy computational load. ##
#> ## Threshold can be manualy adjusted : (default 2500) ##
#> ## >options(SmoothPLS.parallel_threshold = 500) ##
#> => Input format assertions.
#> => Input format assertions OK.
#> => Orthonormalize basis.
#> => Data objects formatting.
#> => Evaluate Lambda matrix.
#> ==> Lambda for : CatFD_1_state_1.
#> ==> Lambda for : CatFD_1_state_2.
#> ==> Lambda for : CatFD_1_state_3.
#> ==> Lambda for : NumFD_2_value.
#> evaluate_lambda_SFD() : int_mode to 2 for pracma::trapz for
#> integration stability.
#> ==> Lambda for : CatFD_3_state_1.
#> => PLSR model.
#> => Optimal number of PLS components : 6
#> => Evaluate SmoothPLS functions and <w_i, p_j> coef.
#> => Build regression functions and intercept.
#> ==> Build regression curve for : CatFD_1_state_1
#> ==> Build regression curve for : CatFD_1_state_2
#> ==> Build regression curve for : CatFD_1_state_3
#> ==> Build regression curve for : NumFD_2_value
#> ==> Build regression curve for : CatFD_3_state_1
for(k in 1:(length(spls_obj$reg_obj)-1)){
y_lim = eval_max_min_y(f_list = list(beta_func_list_tot[[k]],
spls_obj$reg_obj[[k+1]]),
regul_time = regul_time_0)
plot(regul_time_0, beta_func_list_tot[[k]](regul_time_0), ylim = y_lim)
plot(spls_obj$reg_obj[[k+1]], add = TRUE, col = 'blue')
title(paste0("Delta - ", names(spls_obj$reg_obj)[k+1]))
}
basis_2 = create_bspline_basis(start, end, (2*nbasis), norder)
spls_obj_0 = smoothPLS(df_list = list(df_cfd, df_sfd, df_cfd_os),
Y = Y_cfd + Y_sfd,
basis_obj = list(basis_2, basis, basis),
regul_time_obj = start:end,
curve_type_obj = list('cat', 'num', 'cat'),
orth_obj = c(TRUE, FALSE, TRUE),
id_col_obj = 'id',
time_col_obj = 'time', plot_reg_curves = FALSE)
#> ### Smooth PLS ###
#> ## Use parallelization in case of heavy computational load. ##
#> ## Threshold can be manualy adjusted : (default 2500) ##
#> ## >options(SmoothPLS.parallel_threshold = 500) ##
#> evaluate_lambda_SFD() : int_mode to 2 for pracma::trapz for
#> integration stability.
#> => Optimal number of PLS components : 3
for(k in 1:(length(spls_obj_0$reg_obj)-1)){
y_lim = eval_max_min_y(f_list = list(beta_func_list_tot[[k]],
spls_obj_0$reg_obj[[k+1]]),
regul_time = regul_time_0)
plot(regul_time_0, beta_func_list_tot[[k]](regul_time_0), ylim = y_lim)
plot(spls_obj_0$reg_obj[[k+1]], add = TRUE, col = 'blue')
title(paste0("Delta - ", names(spls_obj_0$reg_obj)[k+1]))
}
Predictions Multivariate
Y_hat = smoothPLS_predict(df_predict_list = list(df_cfd, df_sfd, df_cfd_os),
delta_list = spls_obj_0$reg_obj,
curve_type_obj = list('cat', 'num', 'cat'),
id_col_obj = 'id',
time_col_obj = 'time',
regul_time_obj = 0:100,
int_mode = 1,
nb_pt = 10,
subdivision = 100)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
hist(Y_hat)
only SFD
spls_obj_2 = smoothPLS(df_list = df_sfd, Y = Y_df_sfd$Y_noised,
basis_obj = basis,
regul_time_obj = start:end,
curve_type_obj = 'num',
orth_obj = c(TRUE),
id_col_obj = 'id',
time_col_obj = 'time')
#> ### Smooth PLS ###
#> ## Use parallelization in case of heavy computational load. ##
#> ## Threshold can be manualy adjusted : (default 2500) ##
#> ## >options(SmoothPLS.parallel_threshold = 500) ##
#> evaluate_lambda_SFD() : int_mode to 2 for pracma::trapz for
#> integration stability.
#> => Optimal number of PLS components : 7
for(k in 1:(length(spls_obj_2$reg_obj)-1)){
y_lim = eval_max_min_y(f_list = list(beta_func_sfd,
spls_obj_2$reg_obj[[k+1]]),
regul_time = regul_time_0)
plot(regul_time_0, beta_func_sfd(regul_time_0), ylim = y_lim)
plot(spls_obj_2$reg_obj[[k+1]], add = TRUE, col = 'blue')
title(paste0("delta - ", names(spls_obj_2$reg_obj)[k+1]))
}
Prediction SFD
Y_hat_2 = smoothPLS_predict(df_predict_list = df_sfd,
delta_list = spls_obj_2$reg_obj,
curve_type_obj = 'num',
id_col_obj = 'id',
time_col_obj = 'time',
regul_time_obj = regul_time,
int_mode = 1,
nb_pt = 10,
subdivision = 100)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
hist(Y_hat_2)
only CFD
spls_obj_3 = smoothPLS(df_list = df_cfd, Y = Y_df_cfd$Y_noised,
basis_obj = basis,
regul_time_obj = regul_time,
curve_type_obj = 'cat',
orth_obj = c(TRUE),
id_col_obj = 'id', time_col_obj = 'time')
#> ### Smooth PLS ###
#> ## Use parallelization in case of heavy computational load. ##
#> ## Threshold can be manualy adjusted : (default 2500) ##
#> ## >options(SmoothPLS.parallel_threshold = 500) ##
#> => Optimal number of PLS components : 3
for(k in 1:(length(spls_obj_3$reg_obj)-1)){
y_lim = eval_max_min_y(f_list = list(beta_func_list_tot[[k]],
spls_obj_3$reg_obj[[k+1]]),
regul_time = regul_time_0)
plot(regul_time_0, beta_func_list_tot[[k]](regul_time_0), ylim = y_lim)
plot(spls_obj_3$reg_obj[[k+1]], add = TRUE, col = 'blue')
title(paste0("delta - ", names(spls_obj_3$reg_obj)[k+1]))
}
Prediction CFD
Y_hat_3 = smoothPLS_predict(df_predict_list = df_sfd,
delta_list = spls_obj_3$reg_obj,
curve_type_obj = 'num',
id_col_obj = 'id',
time_col_obj = 'time',
regul_time_obj = 0:100,
int_mode = 1,
nb_pt = 10,
subdivision = 100)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
hist(Y_hat_3)
only CFD one state
spls_obj_4 = smoothPLS(df_list = df_cfd_os, Y = Y_df_cfd_os$Y_noised,
basis_obj = basis,
regul_time_obj = regul_time,
curve_type_obj = 'cat',
orth_obj = c(TRUE),
id_col_obj = 'id', time_col_obj = 'time')
#> ### Smooth PLS ###
#> ## Use parallelization in case of heavy computational load. ##
#> ## Threshold can be manualy adjusted : (default 2500) ##
#> ## >options(SmoothPLS.parallel_threshold = 500) ##
#> => Optimal number of PLS components : 2
for(k in 1:(length(spls_obj_4$reg_obj)-1)){
y_lim = eval_max_min_y(f_list = list(beta_func_cfd_os,
spls_obj_4$reg_obj[[k+1]]),
regul_time = regul_time_0)
plot(regul_time_0, beta_func_cfd_os(regul_time_0), ylim = y_lim)
plot(spls_obj_4$reg_obj[[k+1]], add = TRUE, col = 'blue')
title(paste0("delta - ", names(spls_obj_4$reg_obj)[k+1]))
}
Prediction CFD
Y_hat_4 = smoothPLS_predict(df_predict_list = df_sfd,
delta_list = spls_obj_4$reg_obj,
curve_type_obj = 'num',
id_col_obj = 'id',
time_col_obj = 'time',
regul_time_obj = 0:100,
int_mode = 1,
nb_pt = 10,
subdivision = 100)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
hist(Y_hat_4)
Global PLS functions
Naive PLS
naive_pls_obj = naivePLS(df_list = list(df_cfd, df_sfd, df_cfd_os), Y = Y,
regul_time_obj = regul_time,
curve_type_obj = list('cat', 'num', 'cat'),
id_col_obj = 'id',
time_col_obj = 'time',
print_steps = TRUE,
plot_rmsep = TRUE,
print_nbComp = TRUE,
plot_reg_curves = TRUE)
#> ### Naive PLS ###
#> => Input format assertions.
#> => Input format assertions OK.
#> => Data formatting.
#> => PLS model.
#> [1] "Optimal number of PLS components : 3"
Functional PLS
fpls_obj = funcPLS(df_list = list(df_cfd, df_sfd, df_cfd_os), Y = Y,
basis_obj = basis,
curve_type_obj = list('cat', 'num', 'cat'),
regul_time_obj = regul_time,
id_col_obj = 'id', time_col_obj = 'time',
print_steps = TRUE, plot_rmsep = TRUE,
print_nbComp = TRUE, plot_reg_curves = TRUE)
#> ### Functional PLS ###
#> => Input format assertions.
#> => Input format assertions OK.
#> => Building alpha matrix.
#> => Building curve names.
#> ==> Evaluating alpha for : CatFD_1_1.
#> ==> Evaluating alpha for : CatFD_1_2.
#> ==> Evaluating alpha for : CatFD_1_3.
#> ==> Evaluating alpha for : NumFD_2.
#> ==> Evaluating alpha for : CatFD_3_state_1.
#> => Evaluate metrix and root_metric.
#> => plsr(Y ~ trans_alphas).
#> Optimal number of PLS components : 5 .
#> => Build Intercept and regression curves for optimal number of components.
#> ==> Build regression curve for : CatFD_1_1
#> ==> Build regression curve for : CatFD_1_2
#> ==> Build regression curve for : CatFD_1_3
#> ==> Build regression curve for : NumFD_2
#> ==> Build regression curve for : CatFD_3_state_1
Smooth PLS
spls_obj = smoothPLS(df_list = list(df_cfd, df_sfd, df_cfd_os), Y = Y,
basis_obj = basis, int_mode = 1,
regul_time_obj = regul_time,
curve_type_obj = list('cat', 'num', 'cat'),
orth_obj = c(TRUE, TRUE, TRUE),
id_col_obj = 'id',
time_col_obj = 'time',
print_steps = TRUE, plot_rmsep = TRUE,
print_nbComp = TRUE, plot_reg_curves = TRUE)
#> ### Smooth PLS ###
#> ## Use parallelization in case of heavy computational load. ##
#> ## Threshold can be manualy adjusted : (default 2500) ##
#> ## >options(SmoothPLS.parallel_threshold = 500) ##
#> => Input format assertions.
#> => Input format assertions OK.
#> => Orthonormalize basis.
#> => Data objects formatting.
#> => Evaluate Lambda matrix.
#> ==> Lambda for : CatFD_1_state_1.
#> ==> Lambda for : CatFD_1_state_2.
#> ==> Lambda for : CatFD_1_state_3.
#> ==> Lambda for : NumFD_2_value.
#> evaluate_lambda_SFD() : int_mode to 2 for pracma::trapz for
#> integration stability.
#> ==> Lambda for : CatFD_3_state_1.
#> => PLSR model.
#> => Optimal number of PLS components : 6
#> => Evaluate SmoothPLS functions and <w_i, p_j> coef.
#> => Build regression functions and intercept.
#> ==> Build regression curve for : CatFD_1_state_1
#> ==> Build regression curve for : CatFD_1_state_2
#> ==> Build regression curve for : CatFD_1_state_3
#> ==> Build regression curve for : NumFD_2_value
#> ==> Build regression curve for : CatFD_3_state_1
Curves comparison
# Warning ms_spls_obj$delta_ms_list[[1]] is the intercept!
cat("curve_1 : smooth PLS regression curve.\n")
#> curve_1 : smooth PLS regression curve.
cat("curve_2 : functional PLS regression curve.\n")
#> curve_2 : functional PLS regression curve.
cat("curve_3 : naive PLS regression coefficients\n")
#> curve_3 : naive PLS regression coefficients
N_curves = N_states + 2 # CFD multistate + sfd + cfd_one_state
for(i in 1:N_curves){
start = 0
print(paste0("Curve_", i, " : ", names(spls_obj$reg_obj)[i+1]))
evaluate_curves_distances(real_f = beta_func_list_tot[[i]],
regul_time = regul_time,
fun_fd_list = list(spls_obj$reg_obj[[i+1]],
fpls_obj$reg_obj[[i+1]],
approxfun(
x = regul_time,
y = naive_pls_obj$opti_reg_coef[
start:(start+length(regul_time)
)])
)
)
start = start + length(regul_time)
}
#> [1] "Curve_1 : CatFD_1_state_1"
#> [1] "real_f -> curve_1 / INPROD : 19.6256778376969 / DIST : 14.701284134194"
#> [1] "real_f -> curve_2 / INPROD : 14.2271254889424 / DIST : 14.667316608678"
#> [1] "real_f -> curve_3 / INPROD : 36.476847428572 / DIST : 17.9076926628246"
#> [1] "Curve_2 : CatFD_1_state_2"
#> [1] "real_f -> curve_1 / INPROD : -32.6163432849567 / DIST : 12.0046811666242"
#> [1] "real_f -> curve_2 / INPROD : 18.3631337710772 / DIST : 12.1727866853296"
#> [1] "real_f -> curve_3 / INPROD : 53.913979094139 / DIST : 29.4533502519748"
#> [1] "Curve_3 : CatFD_1_state_3"
#> [1] "real_f -> curve_1 / INPROD : 109.824547585968 / DIST : 32.6881019240843"
#> [1] "real_f -> curve_2 / INPROD : 64.2436222399201 / DIST : 16.4282047274178"
#> [1] "real_f -> curve_3 / INPROD : -41.3465274886144 / DIST : 12.1174090254037"
#> [1] "Curve_4 : NumFD_2_value"
#> [1] "real_f -> curve_1 / INPROD : 51.778012692118 / DIST : 17.3677778322172"
#> [1] "real_f -> curve_2 / INPROD : 53.1160754470434 / DIST : 17.4917430546858"
#> [1] "real_f -> curve_3 / INPROD : 36.476847428572 / DIST : 17.9076926628246"
#> [1] "Curve_5 : CatFD_3_state_1"
#> [1] "real_f -> curve_1 / INPROD : 20.7063873288566 / DIST : 27.2607692067541"
#> [1] "real_f -> curve_2 / INPROD : 35.4038276184738 / DIST : 13.2090328503943"
#> [1] "real_f -> curve_3 / INPROD : 53.9139790941392 / DIST : 32.8910080032406"
for(i in 1:N_curves){
start = 0
y_lim = eval_max_min_y(f_list = list(spls_obj$reg_ob[[i+1]],
fpls_obj$reg_ob[[i+1]],
approxfun(
x = regul_time,
y = naive_pls_obj$opti_reg_coef[
start:(start+length(regul_time))]),
beta_func_list_tot[[i]]
),
regul_time = regul_time_0)
plot(regul_time_0, beta_func_list_tot[[i]](regul_time_0), col = 'black',
ylim = y_lim, xlab = 'Time', ylab = 'Value', type = 'l')
lines(regul_time_0, approxfun(x = regul_time,
y = naive_pls_obj$opti_reg_coef[
start:(start+
length(regul_time))])(regul_time_0),
col = 'green')
title(paste0(names(spls_obj$reg_obj)[i+1], " regression curves"))
plot(spls_obj$reg_obj[[i+1]], col = 'blue', add = TRUE)
plot(fpls_obj$reg_obj[[i+1]], col = 'red', add = TRUE)
legend("topleft",
legend = c("Real curve", "NaivePLS coef",
"SmoothPLS reg curve", "FunctionalPLS reg curve"),
col = c("black", "green", "blue", "red"),
lty = 1,
lwd = 1)
start = start + length(regul_time)
}
Results
train_results = data.frame(matrix(ncol = 5, nrow = 3))
colnames(train_results) = c("PRESS", "RMSE", "MAE", "R2", "var_Y")
rownames(train_results) = c("NaivePLS", "FPLS", "SmoothPLS")
test_results = train_resultsTrain set
Y_train = Y
# Naive
Y_hat = predict(naive_pls_obj$plsr_model,
ncomp = naive_pls_obj$nbCP_opti,
newdata = naive_pls_obj$plsr_model$model$`as.matrix(df_mod_wide)`)
train_results["NaivePLS", ] = evaluate_results(Y_train, Y_hat)
# FPLS
Y_hat_fpls = (predict(fpls_obj$plsr_model, ncomp = fpls_obj$nbCP_opti,
newdata = fpls_obj$trans_alphas)
+ fpls_obj$reg_obj$Intercept
+ mean(Y))
Y_hat_fpls = smoothPLS_predict(df_predict_list = list(df_cfd,
df_sfd,
df_cfd_os),
delta_list = fpls_obj$reg_obj,
curve_type_obj = list('cat', 'num', 'cat'),
int_mode = int_mode,
regul_time_obj = regul_time)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
train_results["FPLS", ] = evaluate_results(Y_train, Y_hat_fpls)
# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict_list = list(df_cfd,
df_sfd,
df_cfd_os),
delta_list = spls_obj$reg_obj,
curve_type_obj = list('cat', 'num', 'cat'),
int_mode = int_mode,
regul_time_obj = regul_time)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
train_results["SmoothPLS", ] = evaluate_results(Y_train, Y_hat_spls)
train_results["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
train_results["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
train_results["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti
train_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 3587.445 8.470472 6.889787 0.9784226 97.84226 3
#> FPLS 8618.399 13.128899 11.036135 0.9481629 92.43060 5
#> SmoothPLS 85717.700 41.404758 33.131182 0.4844331 266.23140 6Test set
Y_test = Y_cfd_test + Y_sfd_test + Y_cfd_os_test
# Naive
df_test_wide = naivePLS_formatting(df_list = list(df_cfd_test,
df_sfd_test,
df_cfd_os_test),
regul_time_obj = regul_time,
curve_type_obj = list('cat', 'num', 'cat'),
id_col_obj = 'id', time_col_obj = 'time')
Y_hat = predict(naive_pls_obj$plsr_model,
ncomp = naive_pls_obj$nbCP_opti,
newdata = as.matrix(df_test_wide))
test_results["NaivePLS", ] = evaluate_results(Y_test, Y_hat)
# FPLS
Y_hat_fpls = smoothPLS_predict(df_predict_list = list(df_cfd_test,
df_sfd_test,
df_cfd_os_test),
delta_list = fpls_obj$reg_obj,
curve_type_obj = list('cat', 'num', 'cat'),
int_mode = int_mode,
regul_time_obj = regul_time)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
test_results["FPLS", ] = evaluate_results(Y_test, Y_hat_fpls)
# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict_list = list(df_cfd_test,
df_sfd_test,
df_cfd_os_test),
delta_list = spls_obj$reg_obj,
curve_type_obj = list('cat', 'num', 'cat'),
int_mode = int_mode,
regul_time_obj = regul_time)
#> smoothPLS_SFD_predict() : Unstable integration with int_mode = 1,
#> switch to int_mode = 2 to use pracma::trapz for integration stability.
#>
test_results["SmoothPLS", ] = evaluate_results(Y_test, Y_hat_spls)
test_results["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
test_results["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
test_results["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti
test_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 1138.896 9.742075 8.223849 0.9292952 106.45002 3
#> FPLS 1062.372 9.409093 8.551631 0.9340460 91.63868 5
#> SmoothPLS 13676.857 33.760007 27.075352 0.1509159 309.08982 6Plot results
train_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 3587.445 8.470472 6.889787 0.9784226 97.84226 3
#> FPLS 8618.399 13.128899 11.036135 0.9481629 92.43060 5
#> SmoothPLS 85717.700 41.404758 33.131182 0.4844331 266.23140 6
test_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 1138.896 9.742075 8.223849 0.9292952 106.45002 3
#> FPLS 1062.372 9.409093 8.551631 0.9340460 91.63868 5
#> SmoothPLS 13676.857 33.760007 27.075352 0.1509159 309.08982 6
plot_model_metrics_base(train_results, test_results)
plot_model_metrics_base(train_results, test_results,
models_to_plot = c('FPLS', 'SmoothPLS'))
