The elementwise logistic function, \(\log(1 + e^x)\). This is a special case of log(sum(exp)) that evaluates to a vector rather than to a scalar, which is useful for logistic regression.
logistic(x)An Expression, vector, or matrix.
An Expression representing the logistic function evaluated at the input.
set.seed(92)
n <- 20
m <- 1000
sigma <- 45
beta_true <- stats::rnorm(n)
idxs <- sample(n, size = 0.8*n, replace = FALSE)
beta_true[idxs] <- 0
X <- matrix(stats::rnorm(m*n, 0, 5), nrow = m, ncol = n)
y <- sign(X %*% beta_true + stats::rnorm(m, 0, sigma))
beta <- Variable(n)
X_sign <- apply(X, 2, function(x) { ifelse(y <= 0, -1, 1) * x })
obj <- -sum(logistic(-X[y <= 0,] %*% beta)) - sum(logistic(X[y == 1,] %*% beta))
prob <- Problem(Maximize(obj))
result <- solve(prob)
log_odds <- result$getValue(X %*% beta)
beta_res <- result$getValue(beta)
y_probs <- 1/(1 + exp(-X %*% beta_res))
log(y_probs/(1 - y_probs))
#> [,1]
#> [1,] -0.6704747453
#> [2,] -0.5925328212
#> [3,] -0.2870377968
#> [4,] -0.3903535369
#> [5,] 0.1512570887
#> [6,] -0.3212394186
#> [7,] 0.0710834791
#> [8,] -0.0005976271
#> [9,] 0.6231703117
#> [10,] -0.3461630253
#> [11,] 0.6166059988
#> [12,] 0.2493867405
#> [13,] -0.4229590165
#> [14,] 1.3550948223
#> [15,] -0.3265674802
#> [16,] -0.5974214291
#> [17,] 1.4251319269
#> [18,] -0.8064347421
#> [19,] 0.6354415476
#> [20,] -0.5313438902
#> [21,] -0.5836979792
#> [22,] -0.2018653764
#> [23,] -1.5741498252
#> [24,] -0.2996895657
#> [25,] -0.2075379701
#> [26,] 0.4437075976
#> [27,] -0.5653584061
#> [28,] -1.2550929261
#> [29,] -0.5346377291
#> [30,] 0.4834186388
#> [31,] 0.2311073293
#> [32,] 0.2894531798
#> [33,] -0.0125271013
#> [34,] 0.7295945149
#> [35,] -0.8747328120
#> [36,] -0.3929007100
#> [37,] -0.1155697899
#> [38,] 1.1672745037
#> [39,] -0.7217610157
#> [40,] 0.0611259460
#> [41,] -0.6167812678
#> [42,] -0.0245112095
#> [43,] 0.6908383315
#> [44,] -0.8034683028
#> [45,] 0.8837321215
#> [46,] -1.0940881168
#> [47,] 0.0151087256
#> [48,] -0.0365100536
#> [49,] 0.1208122471
#> [50,] 0.0228343539
#> [51,] 0.0203843954
#> [52,] -0.4370977832
#> [53,] 0.0381296246
#> [54,] -0.0670272720
#> [55,] -0.5450630415
#> [56,] -0.1197518068
#> [57,] -0.1350460388
#> [58,] 0.1775514401
#> [59,] 1.1398260247
#> [60,] -0.4142674984
#> [61,] 0.3993092330
#> [62,] -0.4202249437
#> [63,] 0.0406900070
#> [64,] -0.6489266545
#> [65,] -0.9703157831
#> [66,] 0.1117470893
#> [67,] -0.1453609166
#> [68,] 0.0616521968
#> [69,] 0.0779098757
#> [70,] 0.4237529659
#> [71,] -0.4578431809
#> [72,] -0.2049760543
#> [73,] -0.2303945316
#> [74,] 0.1166998759
#> [75,] -0.3652053517
#> [76,] -0.2369567192
#> [77,] 0.1457272538
#> [78,] -1.0896686258
#> [79,] -0.1308746810
#> [80,] 0.2291736953
#> [81,] 0.1373271433
#> [82,] -0.0015643759
#> [83,] 0.3467661311
#> [84,] -0.1543936115
#> [85,] -0.2309079599
#> [86,] -0.5247239950
#> [87,] 0.4603874797
#> [88,] -0.3126546162
#> [89,] 0.2120101364
#> [90,] 0.3147059544
#> [91,] 0.4193116299
#> [92,] 0.6556946429
#> [93,] -0.5111240660
#> [94,] 1.3013586628
#> [95,] 0.8030343104
#> [96,] 0.2830436450
#> [97,] -0.6704129231
#> [98,] 0.6392222750
#> [99,] 0.0848846684
#> [100,] -0.0064339648
#> [101,] 0.1647498071
#> [102,] 0.2973181065
#> [103,] 0.3564271017
#> [104,] -0.8130651251
#> [105,] -0.5596709529
#> [106,] 0.2440681383
#> [107,] -0.5330643786
#> [108,] 0.4528529740
#> [109,] -0.5709081712
#> [110,] -0.4624088876
#> [111,] -0.2336950084
#> [112,] 0.1511247448
#> [113,] -0.0619001744
#> [114,] 0.5839107079
#> [115,] -0.0005887716
#> [116,] -0.7089905383
#> [117,] -0.3172780305
#> [118,] 0.3970662275
#> [119,] -1.5820303785
#> [120,] 0.5686395206
#> [121,] -0.3273532649
#> [122,] -0.8146151770
#> [123,] -0.0948010100
#> [124,] 0.3203504916
#> [125,] -0.4429258729
#> [126,] 0.1170359830
#> [127,] -0.7652443479
#> [128,] -0.0573330291
#> [129,] 0.0095923205
#> [130,] -0.1932187132
#> [131,] 0.1964295918
#> [132,] -0.3175673688
#> [133,] 0.4246307440
#> [134,] 0.1266911131
#> [135,] 0.3305676080
#> [136,] -0.0061833793
#> [137,] -0.5537778127
#> [138,] -0.1133729598
#> [139,] -0.7994784829
#> [140,] 0.8081791592
#> [141,] 0.4153194889
#> [142,] 0.8942464415
#> [143,] -0.3139527223
#> [144,] 0.1458417356
#> [145,] -0.2050302408
#> [146,] -0.0601911319
#> [147,] -1.1748369016
#> [148,] 0.5454838585
#> [149,] 0.2075718762
#> [150,] -0.2618829301
#> [151,] 0.8039082164
#> [152,] -0.0455086160
#> [153,] 0.5741459944
#> [154,] 0.6920029468
#> [155,] 0.0716658788
#> [156,] -0.4965852192
#> [157,] 0.4424012961
#> [158,] -0.3816940147
#> [159,] 0.5206130555
#> [160,] -0.1021958137
#> [161,] -0.2226467066
#> [162,] 0.7099016303
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#> [164,] 0.2450351330
#> [165,] -0.1737110973
#> [166,] 0.3589718972
#> [167,] -0.3290109210
#> [168,] -0.8993571740
#> [169,] -0.8218169271
#> [170,] -0.7797947156
#> [171,] -0.2137223959
#> [172,] 0.5276414892
#> [173,] -0.8488026286
#> [174,] 0.1034571399
#> [175,] -0.4103722955
#> [176,] -0.7528964425
#> [177,] -0.4402503001
#> [178,] -1.0685897810
#> [179,] 0.4078631608
#> [180,] 0.6313743728
#> [181,] 0.3750977960
#> [182,] -0.0151761111
#> [183,] -0.5310943750
#> [184,] 0.4077601021
#> [185,] 0.1571578122
#> [186,] -0.6328755783
#> [187,] -0.3822625490
#> [188,] 0.5205264608
#> [189,] 0.2562736494
#> [190,] 0.8532803165
#> [191,] -0.5649272190
#> [192,] 0.0370599525
#> [193,] -0.3390879441
#> [194,] -0.0375167676
#> [195,] 0.0474717908
#> [196,] -0.0326523828
#> [197,] 0.2160030272
#> [198,] -1.0662726662
#> [199,] -0.9550123054
#> [200,] -0.6453962911
#> [201,] 0.5183437663
#> [202,] -0.6995172274
#> [203,] 0.2181032498
#> [204,] 0.1893102213
#> [205,] 0.4929995215
#> [206,] 0.1844709863
#> [207,] 0.3573983187
#> [208,] -0.2500617709
#> [209,] 1.3917463231
#> [210,] -0.7617971564
#> [211,] 0.5279346337
#> [212,] -1.0117924511
#> [213,] -0.2423777791
#> [214,] -0.6134068322
#> [215,] -1.1656471094
#> [216,] 0.3821435128
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#> [218,] -1.0973564770
#> [219,] 0.8937549140
#> [220,] 0.3140736705
#> [221,] 0.1340535416
#> [222,] -1.2231142137
#> [223,] 0.5678335252
#> [224,] 0.8463775306
#> [225,] 0.6349311266
#> [226,] 0.7006064459
#> [227,] -0.7992302457
#> [228,] 0.5683533931
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#> [230,] 0.0902430997
#> [231,] -0.3665262918
#> [232,] 0.0127791973
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#> [236,] 0.0091714254
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#> [238,] 0.0657049711
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#> [241,] 0.0637695497
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#> [243,] 0.5476184607
#> [244,] 0.5265704966
#> [245,] -0.8598340525
#> [246,] 0.6395416471
#> [247,] 0.3216020007
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#> [249,] 0.3975296388
#> [250,] 0.1215660180
#> [251,] -0.3140333609
#> [252,] -0.3046537339
#> [253,] 0.3923267337
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#> [255,] -0.0851623037
#> [256,] -0.0029482542
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#> [258,] -0.0359994195
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#> [260,] 0.6395786993
#> [261,] 0.4795818681
#> [262,] 0.1872640071
#> [263,] -0.2498943726
#> [264,] 0.3261025397
#> [265,] 0.1986625843
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#> [267,] 0.6809690638
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#> [269,] 0.5265890631
#> [270,] 0.6813044039
#> [271,] -0.4787301999
#> [272,] 0.6944828574
#> [273,] 0.3116230615
#> [274,] 0.6770526435
#> [275,] 0.0024198299
#> [276,] 0.1779808418
#> [277,] 0.1332661721
#> [278,] 0.2881665987
#> [279,] -0.8398431590
#> [280,] 0.8293255980
#> [281,] 0.3237992271
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