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,] -0.6704566601
#> [2,] -0.5925155914
#> [3,] -0.2870297658
#> [4,] -0.3903425916
#> [5,] 0.1512533989
#> [6,] -0.3212308442
#> [7,] 0.0710815720
#> [8,] -0.0005972517
#> [9,] 0.6231543856
#> [10,] -0.3461542128
#> [11,] 0.6165907888
#> [12,] 0.2493802797
#> [13,] -0.4229470194
#> [14,] 1.3550590126
#> [15,] -0.3265597137
#> [16,] -0.5974060590
#> [17,] 1.4250937991
#> [18,] -0.8064117254
#> [19,] 0.6354245008
#> [20,] -0.5313297468
#> [21,] -0.5836826542
#> [22,] -0.2018604692
#> [23,] -1.5741079507
#> [24,] -0.2996817503
#> [25,] -0.2075326459
#> [26,] 0.4436962967
#> [27,] -0.5653426412
#> [28,] -1.2550595374
#> [29,] -0.5346239907
#> [30,] 0.4834049559
#> [31,] 0.2311018280
#> [32,] 0.2894463877
#> [33,] -0.0125268284
#> [34,] 0.7295741839
#> [35,] -0.8747089801
#> [36,] -0.3928902742
#> [37,] -0.1155668459
#> [38,] 1.1672435760
#> [39,] -0.7217417178
#> [40,] 0.0611243125
#> [41,] -0.6167645485
#> [42,] -0.0245103839
#> [43,] 0.6908204543
#> [44,] -0.8034455356
#> [45,] 0.8837094798
#> [46,] -1.0940587657
#> [47,] 0.0151093307
#> [48,] -0.0365091373
#> [49,] 0.1208098298
#> [50,] 0.0228335289
#> [51,] 0.0203841255
#> [52,] -0.4370865446
#> [53,] 0.0381300050
#> [54,] -0.0670260414
#> [55,] -0.5450479974
#> [56,] -0.1197495178
#> [57,] -0.1350421079
#> [58,] 0.1775461764
#> [59,] 1.1397934859
#> [60,] -0.4142561404
#> [61,] 0.3992984051
#> [62,] -0.4202125247
#> [63,] 0.0406907572
#> [64,] -0.6489089858
#> [65,] -0.9702903642
#> [66,] 0.1117445633
#> [67,] -0.1453568149
#> [68,] 0.0616516205
#> [69,] 0.0779096420
#> [70,] 0.4237417182
#> [71,] -0.4578309643
#> [72,] -0.2049702780
#> [73,] -0.2303885529
#> [74,] 0.1166963282
#> [75,] -0.3651955569
#> [76,] -0.2369500750
#> [77,] 0.1457228397
#> [78,] -1.0896406573
#> [79,] -0.1308710754
#> [80,] 0.2291674619
#> [81,] 0.1373238859
#> [82,] -0.0015643758
#> [83,] 0.3467565323
#> [84,] -0.1543888962
#> [85,] -0.2309014974
#> [86,] -0.5247106391
#> [87,] 0.4603747857
#> [88,] -0.3126465765
#> [89,] 0.2120047116
#> [90,] 0.3146963593
#> [91,] 0.4193015146
#> [92,] 0.6556778133
#> [93,] -0.5111104188
#> [94,] 1.3013236680
#> [95,] 0.8030124821
#> [96,] 0.2830361899
#> [97,] -0.6703954799
#> [98,] 0.6392057972
#> [99,] 0.0848836974
#> [100,] -0.0064337716
#> [101,] 0.1647458661
#> [102,] 0.2973106680
#> [103,] 0.3564182328
#> [104,] -0.8130441051
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#> [106,] 0.2440618391
#> [107,] -0.5330512912
#> [108,] 0.4528402173
#> [109,] -0.5708931835
#> [110,] -0.4623969739
#> [111,] -0.2336890208
#> [112,] 0.1511207911
#> [113,] -0.0618991731
#> [114,] 0.5838949464
#> [115,] -0.0005892470
#> [116,] -0.7089720216
#> [117,] -0.3172697223
#> [118,] 0.3970567787
#> [119,] -1.5819880428
#> [120,] 0.5686251944
#> [121,] -0.3273432678
#> [122,] -0.8145940559
#> [123,] -0.0947979896
#> [124,] 0.3203428780
#> [125,] -0.4429133655
#> [126,] 0.1170332022
#> [127,] -0.7652234333
#> [128,] -0.0573318811
#> [129,] 0.0095928844
#> [130,] -0.1932131076
#> [131,] 0.1964228615
#> [132,] -0.3175599181
#> [133,] 0.4246197779
#> [134,] 0.1266881215
#> [135,] 0.3305602671
#> [136,] -0.0061834939
#> [137,] -0.5537621931
#> [138,] -0.1133697510
#> [139,] -0.7994572391
#> [140,] 0.8081578245
#> [141,] 0.4153083028
#> [142,] 0.8942222160
#> [143,] -0.3139444517
#> [144,] 0.1458380321
#> [145,] -0.2050259510
#> [146,] -0.0601892036
#> [147,] -1.1748051406
#> [148,] 0.5454688323
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#> [150,] -0.2618746549
#> [151,] 0.8038868939
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#> [155,] 0.0716646406
#> [156,] -0.4965733924
#> [157,] 0.4423892111
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#> [159,] 0.5205994919
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#> [162,] 0.7098824842
#> [163,] 0.5765239949
#> [164,] 0.2450293204
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#> [166,] 0.3589634540
#> [167,] -0.3290028521
#> [168,] -0.8993322171
#> [169,] -0.8217942301
#> [170,] -0.7797747655
#> [171,] -0.2137166776
#> [172,] 0.5276279942
#> [173,] -0.8487795398
#> [174,] 0.1034542895
#> [175,] -0.4103611024
#> [176,] -0.7528761525
#> [177,] -0.4402384001
#> [178,] -1.0685618040
#> [179,] 0.4078520134
#> [180,] 0.6313571340
#> [181,] 0.3750879398
#> [182,] -0.0151754002
#> [183,] -0.5310802005
#> [184,] 0.4077498342
#> [185,] 0.1571536758
#> [186,] -0.6328579544
#> [187,] -0.3822521507
#> [188,] 0.5205127750
#> [189,] 0.2562676001
#> [190,] 0.8532572121
#> [191,] -0.5649117264
#> [192,] 0.0370585167
#> [193,] -0.3390790595
#> [194,] -0.0375169486
#> [195,] 0.0474707447
#> [196,] -0.0326514547
#> [197,] 0.2159972774
#> [198,] -1.0662461286
#> [199,] -0.9549865987
#> [200,] -0.6453789741
#> [201,] 0.5183307748
#> [202,] -0.6994981183
#> [203,] 0.2180974130
#> [204,] 0.1893054841
#> [205,] 0.4929863051
#> [206,] 0.1844648176
#> [207,] 0.3573890378
#> [208,] -0.2500557609
#> [209,] 1.3917106836
#> [210,] -0.7617778892
#> [211,] 0.5279206489
#> [212,] -1.0117658159
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#> [215,] -1.1656157013
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#> [219,] 0.8937308100
#> [220,] 0.3140650093
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#> [222,] -1.2230817731
#> [223,] 0.5678172666
#> [224,] 0.8463547383
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#> [232,] 0.0127784696
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#> [243,] 0.5476027637
#> [244,] 0.5265563483
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#> [247,] 0.3215942360
#> [248,] -0.4795886634
#> [249,] 0.3975190764
#> [250,] 0.1215631023
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#> [256,] -0.0029482127
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#> [264,] 0.3260938617
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#> [272,] 0.6944639345
#> [273,] 0.3116161602
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#> [275,] 0.0024198961
#> [276,] 0.1779762817
#> [277,] 0.1332637066
#> [278,] 0.2881592259
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#> [280,] 0.8293027203
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