_PROBLEM CoEPrA-2006_Regression_003
 
_GROUP_NAME Curt Breneman

_GROUP_MEMBERS
Kristin Bennett
Charles Bergeron
Curt Breneman
Theresa Hepburn
Michael Krein
Min Li
Steven Mulick
Sukumar Nagamani
Matthew Sundling

_ADDRESS
Rensselaer Exploratory Centre for Cheminformatics Research,
 Rensselaer Polytechnic Institute,
 110 Eighth Street,
 Troy, New York 12180-3522,
 United States of America

_MODELING_PROCEDURE
For each nonapeptide, 5787 descriptors are provided.
 Additionally, 26 SIMIL descriptors were generated;
 these describe similarities in residues based on the following classes:
 tiny, small, positive, negative, polar, non-polar, aliphatic, and aromatic.


Each feature was centred to zero median and unit absolute deviation.

Lossless data compression was accomplished by seperately considering
 each amino acid's descriptors and the SIMIL descriptors.
 Principal components analysis on each descriptor subset was used to
 find components of nonzero variance. This resulted in 185 components.

Data reduction was accomplished by considering the covariance matrix C
 and an estimate S of how the covariance differs between the two sets.
 Minimum noise fractions, a generalized principal components analysis,
 was used. The generalized singular value decomposition of C with respect
 to S found "noise"-insensitive features. SNR is given by the singular
 values minus one; an SNR cutoff of 10 was chosen; hence, there remained
 148 features.

Kernel partial least squares was used for modeling. Model selection
 found that 4 latent variables and an exponential kernel function with
 sigma=258 was retained. The resulting q^2 was 0.3737 for leave-one-out
 cross-validation across the calibration set. Consider model f=KB+b where
 f is the prediction reported below, K is the kernel matrix, B are the
 regression coefficients and b is the bias constant.
 Then B and b are as follows:

B =

         -4.65780893230584
           -3.044205455589
          -2.7273910047405
         -2.99021775329602
         -2.28714389206887
         -2.18398009261683
          -1.3677498725995
         -2.55922898920449
         -1.83632011403016
        -0.881814537030342
         -1.93459145383112
        -0.984141821344775
         -1.68008003485747
         -2.52426483205893
         -1.29122623582194
          -1.8164070933939
         -1.24308353674936
         -1.39859170170583
         -1.53442753241892
         -1.96676288427374
        -0.790179375118618
          -1.3214842947126
         -1.86755941420426
        0.0225588851978941
         -1.71368324829605
         -1.10000910412161
        -0.709046373399389
         -1.03768548343576
         -2.10266104005197
       -0.0646447016128208
        -0.841066065073574
         0.219867990225757
         -0.66866393392111
         -1.22795080442789
         -1.78458298632885
         -1.29692026133468
        -0.376653135236765
        -0.967306035540786
         -1.03563813057063
         -1.31556075002486
         -1.49752939653057
        -0.152996771841856
         -1.12901052336988
           0.1245936376713
         -1.13811569893717
         -0.20230148685446
        -0.659276593772877
        -0.794408173466111
        -0.564588843322364
        -0.278656810543889
        -0.480031049649768
          -0.7072630229362
        -0.662303734497232
        -0.394291814630916
        -0.241047245711669
         0.772070719312108
        -0.310264269663842
         0.423682816840576
        -0.729356331635232
        -0.601307343395876
        -0.666697463921204
        -0.799767648586092
         -0.56989118673457
         -0.30200559798662
         0.955532870577628
         0.837748299042483
          1.00959319527227
         0.248409234459816
        -0.234635866678256
         0.433372480353231
         0.428066177293261
          0.13569155958648
         0.290283891513543
         0.899494932981337
        -0.651875493756399
          -0.7652982221412
         0.122172086015733
         -1.32933504752391
        -0.112344193381467
         0.746189838806726
        -0.278548302509599
         -0.81601149902944
           0.2018674065546
         -0.63668225135543
         0.361470897459492
         0.580016515345802
          1.03665742708775
         0.530935436132845
          1.43335715822245
          1.39352140034967
           1.3285667445702
          1.08912187944215
          2.19536654175393
         0.528290842963416
          1.25345034335052
          1.34554052470798
         0.655645810916116
        0.0772496369246297
          1.53828171182088
          1.16692252414339
          1.49576159288119
         0.540309211462448
         0.581960972776314
           1.4332594846753
          1.51248354582057
        -0.384929034591033
          1.12438037692173
         0.412254056593063
          2.57199841923713
          2.84895522609439
          1.75488890070644
         0.102543369115324
         0.501471040930447
          2.39546535568782
          1.58660478802458
          1.35713075883042
          1.76925061016415
          1.51602397448133
          2.68365095002253
         0.343826782208144
          1.29221586948335
           2.2398990765158
         0.842810229047111
          1.77748137186234
          2.70617859906574
          2.00833417774937
          2.83747187654392
          2.16871070450135
          1.87148681938346
          1.54295055600479
          2.27535446072186
          2.58385134442326
          2.33249484542578

b =

          7.08152631578948

_PREDICTION
Obj_00001 7.524
Obj_00002 6.448
Obj_00003 7.302
Obj_00004 6.902
Obj_00005 6.830
Obj_00006 6.795
Obj_00007 6.669
Obj_00008 7.526
Obj_00009 7.207
Obj_00010 6.895
Obj_00011 6.631
Obj_00012 7.446
Obj_00013 7.884
Obj_00014 7.286
Obj_00015 6.802
Obj_00016 6.954
Obj_00017 7.131
Obj_00018 6.786
Obj_00019 6.981
Obj_00020 7.963
Obj_00021 6.608
Obj_00022 7.192
Obj_00023 6.838
Obj_00024 7.283
Obj_00025 7.882
Obj_00026 7.275
Obj_00027 6.911
Obj_00028 6.160
Obj_00029 7.098
Obj_00030 6.387
Obj_00031 8.317
Obj_00032 7.596
Obj_00033 7.156
Obj_00034 6.307
Obj_00035 6.635
Obj_00036 6.802
Obj_00037 6.616
Obj_00038 8.098
Obj_00039 6.367
Obj_00040 6.547
Obj_00041 7.951
Obj_00042 7.541
Obj_00043 7.086
Obj_00044 6.680
Obj_00045 7.554
Obj_00046 6.979
Obj_00047 6.832
Obj_00048 6.773
Obj_00049 7.491
Obj_00050 6.813
Obj_00051 6.795
Obj_00052 7.120
Obj_00053 6.776
Obj_00054 6.784
Obj_00055 6.649
Obj_00056 6.379
Obj_00057 7.094
Obj_00058 7.092
Obj_00059 7.234
Obj_00060 7.350
Obj_00061 6.808
Obj_00062 8.511
Obj_00063 7.054
Obj_00064 6.743
Obj_00065 7.591
Obj_00066 7.319
Obj_00067 6.137
Obj_00068 7.261
Obj_00069 6.390
Obj_00070 7.571
Obj_00071 8.298
Obj_00072 7.153
Obj_00073 7.401
Obj_00074 7.662
Obj_00075 7.384
Obj_00076 6.854
Obj_00077 7.070
Obj_00078 7.408
Obj_00079 7.325
Obj_00080 7.225
Obj_00081 7.666
Obj_00082 7.120
Obj_00083 6.739
Obj_00084 7.071
Obj_00085 7.093
Obj_00086 6.639
Obj_00087 7.461
Obj_00088 6.070
Obj_00089 6.636
Obj_00090 6.692
Obj_00091 7.217
Obj_00092 6.882
Obj_00093 7.291
Obj_00094 7.091
Obj_00095 6.666
Obj_00096 7.139
Obj_00097 7.347
Obj_00098 6.677
Obj_00099 7.803
Obj_00100 7.445
Obj_00101 7.944
Obj_00102 7.437
Obj_00103 7.074
Obj_00104 8.492
Obj_00105 6.927
Obj_00106 6.813
Obj_00107 6.767
Obj_00108 7.652
Obj_00109 7.574
Obj_00110 6.619
Obj_00111 7.022
Obj_00112 6.938
Obj_00113 7.757
Obj_00114 6.867
Obj_00115 7.688
Obj_00116 7.220
Obj_00117 6.833
Obj_00118 7.209
Obj_00119 7.525
Obj_00120 6.221
Obj_00121 6.996
Obj_00122 7.084
Obj_00123 7.420
Obj_00124 7.403
Obj_00125 7.284
Obj_00126 6.920
Obj_00127 8.237
Obj_00128 7.544
Obj_00129 6.254
Obj_00130 6.798
Obj_00131 7.247
Obj_00132 7.234
Obj_00133 7.269