# binaryClassificationLoss: Loss functions for binary classification In bmrm: Bundle Methods for Regularized Risk Minimization Package

## Description

Loss functions for binary classification

## Usage

 ```1 2 3 4 5 6 7``` ```logisticLoss(x, y, loss.weights = 1) rocLoss(x, y) fbetaLoss(x, y, beta = 1) hingeLoss(x, y, loss.weights = 1) ```

## Arguments

 `x` matrix of training instances (one instance by row) `y` a logical vector representing the training labels for each instance in x `loss.weights` numeric vector of loss weights to incure for each instance of x. Vector length should match length(y), but values are cycled if not of identical size. `beta` a numeric value setting the beta parameter is the f-beta score

## Value

a function taking one argument w and computing the loss value and the gradient at point w

## Functions

• `logisticLoss`: logistic regression

• `rocLoss`: Find linear weights maximize area under its ROC curve

• `fbetaLoss`: F-beta score loss function

• `hingeLoss`: Hinge Loss for Linear Support Vector Machine (SVM)

## References

Teo et al. A Scalable Modular Convex Solver for Regularized Risk Minimization. KDD 2007

nrbm

## Examples

 ```1 2 3 4 5``` ``` x <- cbind(intercept=100,data.matrix(iris[1:2])) w <- nrbm(hingeLoss(x,iris\$Species=="setosa"));predict(w,x) w <- nrbm(logisticLoss(x,iris\$Species=="setosa"));predict(w,x) w <- nrbm(rocLoss(x,iris\$Species=="setosa"));predict(w,x) w <- nrbm(fbetaLoss(x,iris\$Species=="setosa"));predict(w,x) ```

### Example output

```Run nrbm with convex loss
LowRankQP CONVERGED IN 10 ITERATIONS

Primal Feasibility    =   1.7800712e-16
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   9.6827444e-13
Duality Gap           =   9.6827447e-13
Termination Condition =   9.6784159e-13
1:ncall=2 gap=0.999553 obj=1 reg=0 risk=1 w=[0,0]
LowRankQP CONVERGED IN 10 ITERATIONS

Primal Feasibility    =   1.3921589e-13
Dual Feasibility      =   3.3306691e-16
Complementarity Value =   9.1850983e-13
Duality Gap           =   8.9050989e-13
Termination Condition =   5.8806811e-13
2:ncall=3 gap=0.0659427 obj=0.627853 reg=0.104648 risk=0.523206 w=[-0.417988,0.185645]
LowRankQP CONVERGED IN 11 ITERATIONS

Primal Feasibility    =   2.7761488e-15
Dual Feasibility      =   3.3306691e-16
Complementarity Value =   9.0158540e-13
Duality Gap           =   9.0161212e-13
Termination Condition =   5.5899984e-13
3:ncall=4 gap=0.00909986 obj=0.621954 reg=0.0538237 risk=0.568131 w=[-0.254275,0.20734]
LowRankQP CONVERGED IN 16 ITERATIONS

Primal Feasibility    =   6.6906247e-15
Dual Feasibility      =   2.4424907e-15
Complementarity Value =   7.2126145e-11
Duality Gap           =   7.2127415e-11
Termination Condition =   4.4710588e-11
4:ncall=5 gap=0.00241997 obj=0.615598 reg=0.0534959 risk=0.562102 w=[-0.252949,0.207384]
w
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attr(,"decision.value")
w
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Run nrbm with convex loss
LowRankQP CONVERGED IN 10 ITERATIONS

Primal Feasibility    =   6.9964791e-17
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   4.4743485e-12
Duality Gap           =   4.4743485e-12
Termination Condition =   4.4705061e-12
1:ncall=2 gap=0.692288 obj=0.693147 reg=0 risk=0.693147 w=[0,0]
LowRankQP CONVERGED IN 13 ITERATIONS

Primal Feasibility    =   3.4250922e-14
Dual Feasibility      =   4.4408921e-16
Complementarity Value =   5.4373475e-11
Duality Gap           =   5.4393379e-11
Termination Condition =   3.7875446e-11
2:ncall=3 gap=0.193216 obj=0.628802 reg=0.0465831 risk=0.582219 w=[-0.279108,0.123552]
LowRankQP CONVERGED IN 18 ITERATIONS

Primal Feasibility    =   1.8637764e-14
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   1.2891627e-12
Duality Gap           =   1.2834178e-12
Termination Condition =   8.3088394e-13
3:ncall=4 gap=0.046114 obj=0.59767 reg=0.0407285 risk=0.556941 w=[-0.25892,0.119934]
LowRankQP CONVERGED IN 17 ITERATIONS

Primal Feasibility    =   9.2121199e-15
Dual Feasibility      =   4.4408921e-16
Complementarity Value =   5.9960173e-12
Duality Gap           =   5.9958705e-12
Termination Condition =   3.7762537e-12
4:ncall=5 gap=0.00984807 obj=0.59767 reg=0.0407285 risk=0.556941 w=[-0.25892,0.119934]
LowRankQP CONVERGED IN 17 ITERATIONS

Primal Feasibility    =   6.9105782e-15
Dual Feasibility      =   3.3306691e-16
Complementarity Value =   5.5576981e-12
Duality Gap           =   5.5576654e-12
Termination Condition =   3.4893883e-12
5:ncall=6 gap=0.00296106 obj=0.595704 reg=0.0356982 risk=0.560006 w=[-0.240576,0.11623]
w
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attr(,"decision.value")
w
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attr(,"probability")
w
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[60,] 0.3500910
[61,] 0.3425649
[62,] 0.3203478
[63,] 0.2954176
[64,] 0.3074832
[65,] 0.3336719
[66,] 0.2823140
[67,] 0.3362611
[68,] 0.3179985
[69,] 0.2855021
[70,] 0.3234163
[71,] 0.3254300
[72,] 0.3050138
[73,] 0.2877126
[74,] 0.3050138
[75,] 0.2923320
[76,] 0.2848403
[77,] 0.2705293
[78,] 0.2799650
[79,] 0.3126295
[80,] 0.3207013
[81,] 0.3261432
[82,] 0.3261432
[83,] 0.3179985
[84,] 0.3076560
[85,] 0.3470830
[86,] 0.3252518
[87,] 0.2823140
[88,] 0.2829723
[89,] 0.3362611
[90,] 0.3287027
[91,] 0.3312725
[92,] 0.3099636
[93,] 0.3154831
[94,] 0.3504604
[95,] 0.3285236
[96,] 0.3309130
[97,] 0.3283446
[98,] 0.3023843
[99,] 0.3502757
[100,] 0.3257865
[101,] 0.3071376
[102,] 0.3179985
[103,] 0.2609830
[104,] 0.2973336
[105,] 0.2897662
[106,] 0.2384577
[107,] 0.3613032
[108,] 0.2496268
[109,] 0.2684011
[110,] 0.2698891
[111,] 0.2945735
[112,] 0.2875463
[113,] 0.2751411
[114,] 0.3181746
[115,] 0.3205245
[116,] 0.2995973
[117,] 0.2897662
[118,] 0.2511990
[119,] 0.2258835
[120,] 0.2954176
[121,] 0.2749793
[122,] 0.3310927
[123,] 0.2299741
[124,] 0.2924999
[125,] 0.2870477
[126,] 0.2608265
[127,] 0.2999381
[128,] 0.3099636
[129,] 0.2899333
[130,] 0.2563697
[131,] 0.2430032
[132,] 0.2422574
[133,] 0.2899333
[134,] 0.2949110
[135,] 0.3001085
[136,] 0.2341165
[137,] 0.3096165
[138,] 0.2971640
[139,] 0.3151326
[140,] 0.2726681
[141,] 0.2823140
[142,] 0.2726681
[143,] 0.3179985
[144,] 0.2798014
[145,] 0.2870477
[146,] 0.2799650
[147,] 0.2877126
[148,] 0.2897662
[149,] 0.3147823
[150,] 0.3203478
Run nrbm with convex loss
LowRankQP CONVERGED IN 11 ITERATIONS

Primal Feasibility    =   4.3444753e-16
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   1.2644897e-12
Duality Gap           =   1.2645145e-12
Termination Condition =   9.9958325e-13
1:ncall=2 gap=0.17031 obj=0.435327 reg=0.265017 risk=0.17031 w=[-0.665722,0.294699]
LowRankQP CONVERGED IN 14 ITERATIONS

Primal Feasibility    =   1.7661691e-16
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   7.8774848e-13
Duality Gap           =   7.8775875e-13
Termination Condition =   5.6536745e-13
2:ncall=3 gap=0.0372012 obj=0.43054 reg=0.173322 risk=0.257219 w=[-0.456302,0.372065]
LowRankQP CONVERGED IN 12 ITERATIONS

Primal Feasibility    =   3.5647736e-16
Dual Feasibility      =   3.3306691e-15
Complementarity Value =   1.3845608e-12
Duality Gap           =   1.3851142e-12
Termination Condition =   9.8631916e-13
3:ncall=4 gap=0.0107409 obj=0.414506 reg=0.218508 risk=0.195998 w=[-0.533752,0.390032]
LowRankQP CONVERGED IN 11 ITERATIONS

Primal Feasibility    =   1.1141041e-15
Dual Feasibility      =   1.9984014e-14
Complementarity Value =   7.2686195e-12
Duality Gap           =   7.2718220e-12
Termination Condition =   5.1425610e-12
4:ncall=5 gap=0.00108233 obj=0.414506 reg=0.218508 risk=0.195998 w=[-0.533752,0.390032]
[,1]
[1,] -1.357021
[2,] -1.445287
[3,] -1.260530
[4,] -1.246158
[5,] -1.264643
[6,] -1.361134
[7,] -1.129148
[8,] -1.342649
[9,] -1.217414
[10,] -1.406284
[11,] -1.439140
[12,] -1.235899
[13,] -1.391912
[14,] -1.125036
[15,] -1.535631
[16,] -1.326243
[17,] -1.361134
[18,] -1.357021
[19,] -1.560262
[20,] -1.240011
[21,] -1.556150
[22,] -1.279015
[23,] -1.051142
[24,] -1.435028
[25,] -1.235899
[26,] -1.498662
[27,] -1.342649
[28,] -1.410396
[29,] -1.449400
[30,] -1.260530
[31,] -1.352908
[32,] -1.556150
[33,] -1.176377
[34,] -1.297499
[35,] -1.406284
[36,] -1.420656
[37,] -1.570522
[38,] -1.211268
[39,] -1.178411
[40,] -1.396024
[41,] -1.303646
[42,] -1.504809
[43,] -1.100405
[44,] -1.303646
[45,] -1.240011
[46,] -1.391912
[47,] -1.240011
[48,] -1.207155
[49,] -1.385765
[50,] -1.381652
[51,] -2.488159
[52,] -2.167908
[53,] -2.473787
[54,] -2.038560
[55,] -2.377296
[56,] -1.950295
[57,] -2.075530
[58,] -1.679306
[59,] -2.391668
[60,] -1.722422
[61,] -1.888694
[62,] -1.979039
[63,] -2.344440
[64,] -2.124792
[65,] -1.857916
[66,] -2.367037
[67,] -1.818913
[68,] -2.042673
[69,] -2.451190
[70,] -2.013929
[71,] -1.901032
[72,] -2.163795
[73,] -2.387555
[74,] -2.163795
[75,] -2.284918
[76,] -2.352665
[77,] -2.537422
[78,] -2.406040
[79,] -2.071417
[80,] -2.028301
[81,] -1.999557
[82,] -1.999557
[83,] -2.042673
[84,] -2.149423
[85,] -1.712163
[86,] -1.876401
[87,] -2.367037
[88,] -2.465562
[89,] -1.818913
[90,] -1.960554
[91,] -1.921551
[92,] -2.085789
[93,] -2.081676
[94,] -1.771685
[95,] -1.935923
[96,] -1.872288
[97,] -1.911291
[98,] -2.178167
[99,] -1.747053
[100,] -1.950295
[101,] -2.075530
[102,] -2.042673
[103,] -2.619541
[104,] -2.231543
[105,] -2.299290
[106,] -2.886417
[107,] -1.640303
[108,] -2.765294
[109,] -2.601056
[110,] -2.438897
[111,] -2.221283
[112,] -2.362924
[113,] -2.459415
[114,] -2.067304
[115,] -2.003670
[116,] -2.167908
[117,] -2.299290
[118,] -2.627766
[119,] -3.095805
[120,] -2.344440
[121,] -2.434784
[122,] -1.896920
[123,] -3.017798
[124,] -2.309549
[125,] -2.289030
[126,] -2.594909
[127,] -2.217171
[128,] -2.085789
[129,] -2.323921
[130,] -2.672916
[131,] -2.857673
[132,] -2.734516
[133,] -2.323921
[134,] -2.270546
[135,] -2.241802
[136,] -2.939792
[137,] -2.036526
[138,] -2.206911
[139,] -2.032414
[140,] -2.473787
[141,] -2.367037
[142,] -2.473787
[143,] -2.042673
[144,] -2.381409
[145,] -2.289030
[146,] -2.406040
[147,] -2.387555
[148,] -2.299290
[149,] -1.983151
[150,] -1.979039
Run nrbm with convex loss
LowRankQP CONVERGED IN 18 ITERATIONS

Primal Feasibility    =   1.9517854e-17
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   1.9333766e-11
Duality Gap           =   1.9333766e-11
Termination Condition =   1.9333766e-11
1:ncall=2 gap=1 obj=1 reg=0 risk=1 w=[0,0]
LowRankQP CONVERGED IN 12 ITERATIONS

Primal Feasibility    =   2.3908367e-14
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   3.2022979e-12
Duality Gap           =   3.2023019e-12
Termination Condition =   3.2022129e-12
2:ncall=3 gap=0.689532 obj=0.689559 reg=2.65567e-05 risk=0.689532 w=[-0.0066503,0.00296263]
LowRankQP CONVERGED IN 21 ITERATIONS

Primal Feasibility    =   2.7238794e-12
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   1.8019420e-11
Duality Gap           =   1.8019256e-11
Termination Condition =   1.8018212e-11
3:ncall=4 gap=0.251596 obj=0.251663 reg=6.70608e-05 risk=0.251596 w=[-0.00958544,0.00648947]
LowRankQP CONVERGED IN 21 ITERATIONS

Primal Feasibility    =   3.2977870e-12
Dual Feasibility      =   1.1102230e-16
Complementarity Value =   9.7458032e-12
Duality Gap           =   9.7458638e-12
Termination Condition =   9.7446944e-12
4:ncall=5 gap=0.100004 obj=0.100118 reg=0.000113787 risk=0.100004 w=[-0.0100571,0.011242]
LowRankQP CONVERGED IN 22 ITERATIONS

Primal Feasibility    =   6.2549231e-12
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   2.6076103e-12
Duality Gap           =   2.6092917e-12
Termination Condition =   2.6071316e-12
5:ncall=6 gap=0.0561003 obj=0.0562839 reg=0.000183647 risk=0.0561003 w=[-0.01492,0.0120208]
LowRankQP CONVERGED IN 26 ITERATIONS

Primal Feasibility    =   1.7317929e-11
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   3.7369053e-11
Duality Gap           =   3.7369791e-11
Termination Condition =   3.7361498e-11
6:ncall=7 gap=0.0480279 obj=0.0482301 reg=0.000202214 risk=0.0480279 w=[-0.0111095,0.016763]
LowRankQP CONVERGED IN 24 ITERATIONS

Primal Feasibility    =   5.4300317e-12
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   6.8865874e-13
Duality Gap           =   6.8849401e-13
Termination Condition =   6.8847964e-13
7:ncall=8 gap=0.0354716 obj=0.0357318 reg=0.000260138 risk=0.0354716 w=[-0.0145094,0.0175981]
LowRankQP CONVERGED IN 25 ITERATIONS

Primal Feasibility    =   3.4922701e-12
Dual Feasibility      =   2.2204460e-16
Complementarity Value =   1.5876541e-12
Duality Gap           =   1.5876102e-12
Termination Condition =   1.5871980e-12
8:ncall=9 gap=0.0354444 obj=0.0357318 reg=0.000260138 risk=0.0354716 w=[-0.0145094,0.0175981]
LowRankQP CONVERGED IN 26 ITERATIONS

Primal Feasibility    =   2.1567826e-11
Dual Feasibility      =   1.1102230e-16
Complementarity Value =   1.3521845e-12
Duality Gap           =   1.3518423e-12
Termination Condition =   1.3517188e-12
9:ncall=10 gap=0.0262886 obj=0.0266331 reg=0.000344543 risk=0.0262886 w=[-0.0190909,0.0180115]
LowRankQP CONVERGED IN 24 ITERATIONS

Primal Feasibility    =   1.2748913e-11
Dual Feasibility      =   2.2204460e-16
Complementarity Value =   8.9070616e-12
Duality Gap           =   8.9088318e-12
Termination Condition =   8.9034020e-12
10:ncall=11 gap=0.0262221 obj=0.0266331 reg=0.000344543 risk=0.0262886 w=[-0.0190909,0.0180115]
LowRankQP CONVERGED IN 23 ITERATIONS

Primal Feasibility    =   9.8084847e-12
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   1.5448578e-12
Duality Gap           =   1.5459364e-12
Termination Condition =   1.5441055e-12
11:ncall=12 gap=0.0163421 obj=0.0168293 reg=0.000487208 risk=0.0163421 w=[-0.0217831,0.0223536]
LowRankQP CONVERGED IN 24 ITERATIONS

Primal Feasibility    =   2.8225792e-11
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   4.9629042e-11
Duality Gap           =   4.9630768e-11
Termination Condition =   4.9584347e-11
12:ncall=13 gap=0.0159279 obj=0.0168293 reg=0.000487208 risk=0.0163421 w=[-0.0217831,0.0223536]
LowRankQP CONVERGED IN 24 ITERATIONS

Primal Feasibility    =   3.7455833e-11
Dual Feasibility      =   2.2204460e-16
Complementarity Value =   7.0933512e-13
Duality Gap           =   6.9898077e-13
Termination Condition =   7.0864790e-13
13:ncall=14 gap=0.0112716 obj=0.0122414 reg=0.00096976 risk=0.0112716 w=[-0.0336702,0.0283732]
LowRankQP CONVERGED IN 23 ITERATIONS

Primal Feasibility    =   3.8778226e-11
Dual Feasibility      =   3.3306691e-16
Complementarity Value =   1.9698655e-11
Duality Gap           =   1.9707300e-11
Termination Condition =   1.9677701e-11
14:ncall=15 gap=0.0111765 obj=0.0122414 reg=0.00096976 risk=0.0112716 w=[-0.0336702,0.0283732]
LowRankQP CONVERGED IN 22 ITERATIONS

Primal Feasibility    =   3.8731554e-11
Dual Feasibility      =   0.0000000e+00
Complementarity Value =   5.0804142e-12
Duality Gap           =   5.0574358e-12
Termination Condition =   5.0747227e-12
15:ncall=16 gap=0.00565734 obj=0.00677888 reg=0.00112154 risk=0.00565734 w=[-0.0370628,0.0294669]
LowRankQP CONVERGED IN 22 ITERATIONS

Primal Feasibility    =   5.3830944e-11
Dual Feasibility      =   1.1102230e-16
Complementarity Value =   2.3264717e-11
Duality Gap           =   2.3253108e-11
Termination Condition =   2.3237430e-11
16:ncall=17 gap=0.00402432 obj=0.00519856 reg=0.00117424 risk=0.00402432 w=[-0.0361199,0.0322956]
LowRankQP CONVERGED IN 22 ITERATIONS

Primal Feasibility    =   5.7866389e-11
Dual Feasibility      =   5.5511151e-16
Complementarity Value =   1.5948706e-12
Duality Gap           =   1.4588097e-12
Termination Condition =   1.5924276e-12
17:ncall=18 gap=0.000771767 obj=0.00230588 reg=0.00153412 risk=0.000771767 w=[-0.0426594,0.0353138]
LowRankQP CONVERGED IN 21 ITERATIONS

Primal Feasibility    =   7.3739016e-11
Dual Feasibility      =   2.2204460e-16
Complementarity Value =   2.2868557e-12
Duality Gap           =   2.2359068e-12
Termination Condition =   2.2832812e-12
18:ncall=19 gap=-2.77556e-17 obj=0.00156553 reg=0.00156553 risk=1.39944e-12 w=[-0.0429351,0.0358651]
[,1]
[1,]  TRUE
[2,]  TRUE
[3,]  TRUE
[4,]  TRUE
[5,]  TRUE
[6,]  TRUE
[7,]  TRUE
[8,]  TRUE
[9,]  TRUE
[10,]  TRUE
[11,]  TRUE
[12,]  TRUE
[13,]  TRUE
[14,]  TRUE
[15,]  TRUE
[16,]  TRUE
[17,]  TRUE
[18,]  TRUE
[19,]  TRUE
[20,]  TRUE
[21,]  TRUE
[22,]  TRUE
[23,]  TRUE
[24,]  TRUE
[25,]  TRUE
[26,]  TRUE
[27,]  TRUE
[28,]  TRUE
[29,]  TRUE
[30,]  TRUE
[31,]  TRUE
[32,]  TRUE
[33,]  TRUE
[34,]  TRUE
[35,]  TRUE
[36,]  TRUE
[37,]  TRUE
[38,]  TRUE
[39,]  TRUE
[40,]  TRUE
[41,]  TRUE
[42,]  TRUE
[43,]  TRUE
[44,]  TRUE
[45,]  TRUE
[46,]  TRUE
[47,]  TRUE
[48,]  TRUE
[49,]  TRUE
[50,]  TRUE
[51,] FALSE
[52,] FALSE
[53,] FALSE
[54,] FALSE
[55,] FALSE
[56,] FALSE
[57,] FALSE
[58,] FALSE
[59,] FALSE
[60,] FALSE
[61,] FALSE
[62,] FALSE
[63,] FALSE
[64,] FALSE
[65,] FALSE
[66,] FALSE
[67,] FALSE
[68,] FALSE
[69,] FALSE
[70,] FALSE
[71,] FALSE
[72,] FALSE
[73,] FALSE
[74,] FALSE
[75,] FALSE
[76,] FALSE
[77,] FALSE
[78,] FALSE
[79,] FALSE
[80,] FALSE
[81,] FALSE
[82,] FALSE
[83,] FALSE
[84,] FALSE
[85,] FALSE
[86,] FALSE
[87,] FALSE
[88,] FALSE
[89,] FALSE
[90,] FALSE
[91,] FALSE
[92,] FALSE
[93,] FALSE
[94,] FALSE
[95,] FALSE
[96,] FALSE
[97,] FALSE
[98,] FALSE
[99,] FALSE
[100,] FALSE
[101,] FALSE
[102,] FALSE
[103,] FALSE
[104,] FALSE
[105,] FALSE
[106,] FALSE
[107,] FALSE
[108,] FALSE
[109,] FALSE
[110,] FALSE
[111,] FALSE
[112,] FALSE
[113,] FALSE
[114,] FALSE
[115,] FALSE
[116,] FALSE
[117,] FALSE
[118,] FALSE
[119,] FALSE
[120,] FALSE
[121,] FALSE
[122,] FALSE
[123,] FALSE
[124,] FALSE
[125,] FALSE
[126,] FALSE
[127,] FALSE
[128,] FALSE
[129,] FALSE
[130,] FALSE
[131,] FALSE
[132,] FALSE
[133,] FALSE
[134,] FALSE
[135,] FALSE
[136,] FALSE
[137,] FALSE
[138,] FALSE
[139,] FALSE
[140,] FALSE
[141,] FALSE
[142,] FALSE
[143,] FALSE
[144,] FALSE
[145,] FALSE
[146,] FALSE
[147,] FALSE
[148,] FALSE
[149,] FALSE
[150,] FALSE
attr(,"decision.value")
[,1]
[1,]  0.022327597
[2,]  0.012982056
[3,]  0.028742087
[4,]  0.029449082
[5,]  0.030207613
[6,]  0.023793123
[7,]  0.040208613
[8,]  0.023034592
[9,]  0.030863072
[10,]  0.016568566
[11,]  0.016620102
[12,]  0.031621602
[13,]  0.017275561
[14,]  0.038743087
[15,]  0.010205612
[16,]  0.028845159
[17,]  0.023793123
[18,]  0.022327597
[19,]  0.007326097
[20,]  0.033087128
[21,]  0.005860571
[22,]  0.029500618
[23,]  0.047381633
[24,]  0.015154577
[25,]  0.031621602
[26,]  0.008688551
[27,]  0.023034592
[28,]  0.018034092
[29,]  0.014447582
[30,]  0.028742087
[31,]  0.020862072
[32,]  0.005860571
[33,]  0.039553154
[34,]  0.030259148
[35,]  0.016568566
[36,]  0.015861572
[37,]  0.005153577
[38,]  0.034501118
[39,]  0.034449582
[40,]  0.018741087
[41,]  0.026621102
[42,]  0.005050505
[43,]  0.041622602
[44,]  0.026621102
[45,]  0.033087128
[46,]  0.017275561
[47,]  0.033087128
[48,]  0.033035592
[49,]  0.020913607
[50,]  0.019448082
[51,] -0.070008531
[52,] -0.044247501
[53,] -0.069301537
[54,] -0.037884546
[55,] -0.062887047
[56,] -0.028539006
[57,] -0.036367485
[58,] -0.008537005
[59,] -0.063594042
[60,] -0.010657990
[61,] -0.027176551
[62,] -0.029952995
[63,] -0.062938582
[64,] -0.042126516
[65,] -0.020658990
[66,] -0.060714526
[67,] -0.017072480
[68,] -0.036419021
[69,] -0.071525593
[70,] -0.035005031
[71,] -0.022779975
[72,] -0.045713026
[73,] -0.065059567
[74,] -0.045713026
[75,] -0.055007031
[76,] -0.060007531
[77,] -0.075767562
[78,] -0.064301037
[79,] -0.037833011
[80,] -0.035712026
[81,] -0.034298036
[82,] -0.034298036
[83,] -0.036419021
[84,] -0.045006031
[85,] -0.008485470
[86,] -0.019900459
[87,] -0.060714526
[88,] -0.072232588
[89,] -0.017072480
[90,] -0.030711526
[91,] -0.027125016
[92,] -0.038540006
[93,] -0.040005531
[94,] -0.016417021
[95,] -0.027832011
[96,] -0.021365985
[97,] -0.024952495
[98,] -0.046420021
[99,] -0.013537505
[100,] -0.028539006
[101,] -0.036367485
[102,] -0.036419021
[103,] -0.081475057
[104,] -0.050713526
[105,] -0.055714026
[106,] -0.102942583
[107,] -0.004950495
[108,] -0.093648578
[109,] -0.082233588
[110,] -0.064249501
[111,] -0.048541006
[112,] -0.062180052
[113,] -0.068594542
[114,] -0.039298536
[115,] -0.032832511
[116,] -0.044247501
[117,] -0.055714026
[118,] -0.078544006
[119,] -0.121582129
[120,] -0.062938582
[121,] -0.065715026
[122,] -0.024245500
[123,] -0.114409109
[124,] -0.057886547
[125,] -0.053541506
[126,] -0.078595542
[127,] -0.050006531
[128,] -0.038540006
[129,] -0.058593542
[130,] -0.085768562
[131,] -0.101528593
[132,] -0.087131016
[133,] -0.058593542
[134,] -0.054300036
[135,] -0.052886047
[136,] -0.107236088
[137,] -0.032780975
[138,] -0.047834011
[139,] -0.034246500
[140,] -0.069301537
[141,] -0.060714526
[142,] -0.069301537
[143,] -0.036419021
[144,] -0.061421521
[145,] -0.053541506
[146,] -0.064301037
[147,] -0.065059567
[148,] -0.055714026
[149,] -0.028487470
[150,] -0.029952995
```

bmrm documentation built on May 2, 2019, 2:49 p.m.