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,] -0.6704371536
#> [2,] -0.5924970549
#> [3,] -0.2870207194
#> [4,] -0.3903305446
#> [5,] 0.1512494762
#> [6,] -0.3212221378
#> [7,] 0.0710794679
#> [8,] -0.0005961887
#> [9,] 0.6231365028
#> [10,] -0.3461443684
#> [11,] 0.6165738322
#> [12,] 0.2493729000
#> [13,] -0.4229340567
#> [14,] 1.3550204908
#> [15,] -0.3265509828
#> [16,] -0.5973892358
#> [17,] 1.4250527921
#> [18,] -0.8063875606
#> [19,] 0.6354045317
#> [20,] -0.5313145903
#> [21,] -0.5836658886
#> [22,] -0.2018558285
#> [23,] -1.5740622176
#> [24,] -0.2996736249
#> [25,] -0.2075267120
#> [26,] 0.4436835108
#> [27,] -0.5653261234
#> [28,] -1.2550228377
#> [29,] -0.5346095797
#> [30,] 0.4833898723
#> [31,] 0.2310958007
#> [32,] 0.2894397218
#> [33,] -0.0125271282
#> [34,] 0.7295520624
#> [35,] -0.8746838352
#> [36,] -0.3928786677
#> [37,] -0.1155639087
#> [38,] 1.1672097900
#> [39,] -0.7217220191
#> [40,] 0.0611228864
#> [41,] -0.6167469517
#> [42,] -0.0245098673
#> [43,] 0.6908016675
#> [44,] -0.8034209675
#> [45,] 0.8836838590
#> [46,] -1.0940286700
#> [47,] 0.0151098659
#> [48,] -0.0365081455
#> [49,] 0.1208070217
#> [50,] 0.0228325315
#> [51,] 0.0203843663
#> [52,] -0.4370748638
#> [53,] 0.0381300909
#> [54,] -0.0670253113
#> [55,] -0.5450317899
#> [56,] -0.1197466571
#> [57,] -0.1350384362
#> [58,] 0.1775410381
#> [59,] 1.1397581600
#> [60,] -0.4142450475
#> [61,] 0.3992870501
#> [62,] -0.4201999349
#> [63,] 0.0406908904
#> [64,] -0.6488893071
#> [65,] -0.9702623739
#> [66,] 0.1117415997
#> [67,] -0.1453520467
#> [68,] 0.0616511915
#> [69,] 0.0779089693
#> [70,] 0.4237295739
#> [71,] -0.4578180245
#> [72,] -0.2049643257
#> [73,] -0.2303823007
#> [74,] 0.1166922211
#> [75,] -0.3651839099
#> [76,] -0.2369421613
#> [77,] 0.1457184733
#> [78,] -1.0896100534
#> [79,] -0.1308667941
#> [80,] 0.2291608162
#> [81,] 0.1373206225
#> [82,] -0.0015645590
#> [83,] 0.3467469103
#> [84,] -0.1543835498
#> [85,] -0.2308938190
#> [86,] -0.5246963632
#> [87,] 0.4603606858
#> [88,] -0.3126381627
#> [89,] 0.2119984253
#> [90,] 0.3146859952
#> [91,] 0.4192903982
#> [92,] 0.6556585814
#> [93,] -0.5110961916
#> [94,] 1.3012866817
#> [95,] 0.8029894017
#> [96,] 0.2830272518
#> [97,] -0.6703772068
#> [98,] 0.6391863669
#> [99,] 0.0848818575
#> [100,] -0.0064332923
#> [101,] 0.1647413201
#> [102,] 0.2973037010
#> [103,] 0.3564079114
#> [104,] -0.8130206469
#> [105,] -0.5596398431
#> [106,] 0.2440550486
#> [107,] -0.5330370810
#> [108,] 0.4528272853
#> [109,] -0.5708769383
#> [110,] -0.4623841324
#> [111,] -0.2336821167
#> [112,] 0.1511168180
#> [113,] -0.0618989021
#> [114,] 0.5838774850
#> [115,] -0.0005897145
#> [116,] -0.7089513619
#> [117,] -0.3172602390
#> [118,] 0.3970471261
#> [119,] -1.5819421843
#> [120,] 0.5686097850
#> [121,] -0.3273318204
#> [122,] -0.8145712120
#> [123,] -0.0947952405
#> [124,] 0.3203346211
#> [125,] -0.4429004042
#> [126,] 0.1170302080
#> [127,] -0.7652000886
#> [128,] -0.0573301844
#> [129,] 0.0095936089
#> [130,] -0.1932077962
#> [131,] 0.1964147884
#> [132,] -0.3175516562
#> [133,] 0.4246079181
#> [134,] 0.1266855672
#> [135,] 0.3305523081
#> [136,] -0.0061834345
#> [137,] -0.5537455889
#> [138,] -0.1133659428
#> [139,] -0.7994346883
#> [140,] 0.8081345370
#> [141,] 0.4152951840
#> [142,] 0.8941963356
#> [143,] -0.3139351763
#> [144,] 0.1458335813
#> [145,] -0.2050217529
#> [146,] -0.0601875776
#> [147,] -1.1747708036
#> [148,] 0.5454530712
#> [149,] 0.2075616513
#> [150,] -0.2618668554
#> [151,] 0.8038631576
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#> [153,] 0.5741153650
#> [154,] 0.6919653211
#> [155,] 0.0716635518
#> [156,] -0.4965605133
#> [157,] 0.4423766989
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#> [159,] 0.5205855546
#> [160,] -0.1021902110
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#> [162,] 0.7098615761
#> [163,] 0.5765079241
#> [164,] 0.2450234845
#> [165,] -0.1737037973
#> [166,] 0.3589537727
#> [167,] -0.3289941328
#> [168,] -0.8993056792
#> [169,] -0.8217702772
#> [170,] -0.7797528629
#> [171,] -0.2137113010
#> [172,] 0.5276129313
#> [173,] -0.8487540548
#> [174,] 0.1034511834
#> [175,] -0.4103495194
#> [176,] -0.7528536716
#> [177,] -0.4402248633
#> [178,] -1.0685305792
#> [179,] 0.4078400388
#> [180,] 0.6313384527
#> [181,] 0.3750767342
#> [182,] -0.0151760713
#> [183,] -0.5310658138
#> [184,] 0.4077389424
#> [185,] 0.1571498830
#> [186,] -0.6328385157
#> [187,] -0.3822421104
#> [188,] 0.5204977222
#> [189,] 0.2562612439
#> [190,] 0.8532319796
#> [191,] -0.5648959945
#> [192,] 0.0370575608
#> [193,] -0.3390685700
#> [194,] -0.0375178322
#> [195,] 0.0474691628
#> [196,] -0.0326508613
#> [197,] 0.2159912492
#> [198,] -1.0662168263
#> [199,] -0.9549591875
#> [200,] -0.6453604072
#> [201,] 0.5183165577
#> [202,] -0.6994760335
#> [203,] 0.2180900675
#> [204,] 0.1893010887
#> [205,] 0.4929717779
#> [206,] 0.1844585902
#> [207,] 0.3573788914
#> [208,] -0.2500475107
#> [209,] 1.3916700683
#> [210,] -0.7617566067
#> [211,] 0.5279063041
#> [212,] -1.0117377264
#> [213,] -0.2423643713
#> [214,] -0.6133731964
#> [215,] -1.1655821251
#> [216,] 0.3821205590
#> [217,] -0.4501059373
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#> [219,] 0.8937038193
#> [220,] 0.3140554393
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#> [222,] -1.2230466787
#> [223,] 0.5678001497
#> [224,] 0.8463307286
#> [225,] 0.6348930242
#> [226,] 0.7005666356
#> [227,] -0.7991866479
#> [228,] 0.5683221791
#> [229,] 0.4112845264
#> [230,] 0.0902384990
#> [231,] -0.3665052768
#> [232,] 0.0127778808
#> [233,] 0.1629114679
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#> [236,] 0.0091703090
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#> [238,] 0.0657026892
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#> [241,] 0.0637630897
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#> [243,] 0.5475868321
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#> [246,] 0.6395072030
#> [247,] 0.3215850911
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#> [249,] 0.3975075566
#> [250,] 0.1215588503
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#> [253,] 0.3923042433
#> [254,] -0.1856373031
#> [255,] -0.0851580547
#> [256,] -0.0029478231
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#> [259,] -0.9567630443
#> [260,] 0.6395436832
#> [261,] 0.4795560341
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#> [264,] 0.3260846519
#> [265,] 0.1986533529
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#> [267,] 0.6809304320
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#> [271,] -0.4787051835
#> [272,] 0.6944439888
#> [273,] 0.3116084802
#> [274,] 0.6770165536
#> [275,] 0.0024186543
#> [276,] 0.1779699225
#> [277,] 0.1332607901
#> [278,] 0.2881507054
#> [279,] -0.8397962713
#> [280,] 0.8292775991
#> [281,] 0.3237814549
#> [282,] 0.3688578998
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