updated book
This commit is contained in:
Morten Hjorth-Jensen
@@ -218,6 +218,11 @@
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14. Building a Feed Forward Neural Network
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</a>
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</li>
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<li class="toctree-l1">
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<a class="reference internal" href="chapter11.html">
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15. Solving Differential Equations with Deep Learning
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</a>
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</li>
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</ul>
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</div>
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@@ -1106,10 +1111,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.055529303095955385
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3.9154537458386387
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[[1.0003451 2.94327895]
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[2.94327895 9.80021057]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.05805002932374468
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4.309519578637819
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[[ 1.23033954 3.6804336 ]
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[ 3.6804336 11.92527504]]
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</pre></div>
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</div>
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</div>
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@@ -1146,10 +1151,10 @@ a more brute force way. Here we scale the mean values for each column of the des
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.095786152583691
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1.5864689451163851
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[[1. 0.6713619]
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[0.6713619 1. ]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.09198004868226574
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1.9493620821393187
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[[1. 0.68904673]
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[0.68904673 1. ]]
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</pre></div>
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</div>
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</div>
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@@ -1179,30 +1184,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
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</div>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.10979444 1.25912505]
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[ 2.17273709 7.48017006]
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[ 0.31520842 0.66152576]
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[-0.07076926 -0.44655382]
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[ 0.24348403 0.38561052]
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[-0.57984245 -0.86011441]
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[ 0.42375621 -1.21244261]
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[-0.2407922 0.56831157]
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[-2.23691315 -6.6936767 ]
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[ 0.08292574 -1.14195542]]
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-1.13352411e+00 -4.86145508e+00]
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[ 5.06793578e-01 2.24339370e+00]
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[ 4.08359441e-03 -1.44109702e+00]
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[-2.02972824e-01 -1.17393096e+00]
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[ 9.99703985e-01 5.00745587e+00]
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[-1.05430325e-01 3.31446832e-02]
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[ 4.31082669e-01 6.38783434e-01]
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[ 3.40259257e-02 5.84099240e-01]
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[-8.44862840e-01 -2.71546272e+00]
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[ 3.11100342e-01 1.68506886e+00]]
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0 1
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0 -0.109794 1.259125
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1 2.172737 7.480170
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2 0.315208 0.661526
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3 -0.070769 -0.446554
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4 0.243484 0.385611
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5 -0.579842 -0.860114
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6 0.423756 -1.212443
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7 -0.240792 0.568312
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8 -2.236913 -6.693677
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9 0.082926 -1.141955
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0 -1.133524 -4.861455
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1 0.506794 2.243394
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2 0.004084 -1.441097
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3 -0.202973 -1.173931
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4 0.999704 5.007456
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5 -0.105430 0.033145
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6 0.431083 0.638783
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7 0.034026 0.584099
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8 -0.844863 -2.715463
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9 0.311100 1.685069
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0 1
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0 1.000000 0.931066
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1 0.931066 1.000000
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0 1.000000 0.958527
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1 0.958527 1.000000
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</pre></div>
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</div>
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</div>
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@@ -1259,37 +1264,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
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0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
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1 0.0 0.090107 0.080265 0.095180 0.087148 0.079801 0.089928 0.082666
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2 0.0 0.080265 0.073052 0.087032 0.080565 0.074557 0.083797 0.077645
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3 0.0 0.095180 0.087032 0.106946 0.099079 0.091756 0.104887 0.097150
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4 0.0 0.087148 0.080565 0.099079 0.092378 0.086076 0.098028 0.091253
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5 0.0 0.079801 0.074557 0.091756 0.086076 0.080678 0.091542 0.085627
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6 0.0 0.089928 0.083797 0.104887 0.098028 0.091542 0.105387 0.098187
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7 0.0 0.082666 0.077645 0.097150 0.091253 0.085627 0.098187 0.091855
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8 0.0 0.076121 0.072046 0.090099 0.085041 0.080173 0.091566 0.086006
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9 0.0 0.070212 0.066949 0.083672 0.079351 0.075151 0.085484 0.080612
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10 0.0 0.083337 0.078717 0.099609 0.093725 0.088085 0.101781 0.095275
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11 0.0 0.076774 0.072995 0.092276 0.087205 0.082303 0.094708 0.088983
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12 0.0 0.070866 0.067811 0.085627 0.081270 0.077021 0.088260 0.083228
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13 0.0 0.065545 0.063114 0.079598 0.075869 0.072197 0.082382 0.077968
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14 0.0 0.060748 0.058856 0.074130 0.070955 0.067793 0.077026 0.073162
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1 0.0 0.082212 0.080493 0.081616 0.077560 0.073611 0.073557 0.069528
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2 0.0 0.080493 0.080583 0.082413 0.079267 0.075998 0.075624 0.072071
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3 0.0 0.081616 0.082413 0.087107 0.084071 0.080840 0.082136 0.078414
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4 0.0 0.077560 0.079267 0.084071 0.081732 0.079085 0.080069 0.076853
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5 0.0 0.073611 0.075998 0.080840 0.079085 0.076946 0.077662 0.074900
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6 0.0 0.073557 0.075624 0.082136 0.080069 0.077662 0.079815 0.076731
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7 0.0 0.069528 0.072071 0.078414 0.076853 0.074900 0.076731 0.074079
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8 0.0 0.065794 0.068700 0.074858 0.073728 0.072170 0.073713 0.071447
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9 0.0 0.062352 0.065534 0.071499 0.070739 0.069526 0.070812 0.068888
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10 0.0 0.065582 0.068203 0.075503 0.074125 0.072352 0.074961 0.072447
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11 0.0 0.062022 0.064909 0.071917 0.070915 0.069494 0.071782 0.069625
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12 0.0 0.058765 0.061857 0.068581 0.067904 0.066793 0.068790 0.066951
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13 0.0 0.055788 0.059038 0.065492 0.065096 0.064256 0.065991 0.064434
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14 0.0 0.053069 0.056441 0.062636 0.062486 0.061885 0.063380 0.062076
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8 9 10 11 12 13 14
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0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
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1 0.076121 0.070212 0.083337 0.076774 0.070866 0.065545 0.060748
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2 0.072046 0.066949 0.078717 0.072995 0.067811 0.063114 0.058856
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3 0.090099 0.083672 0.099609 0.092276 0.085627 0.079598 0.074130
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4 0.085041 0.079351 0.093725 0.087205 0.081270 0.075869 0.070955
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5 0.080173 0.075151 0.088085 0.082303 0.077021 0.072197 0.067793
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6 0.091566 0.085484 0.101781 0.094708 0.088260 0.082382 0.077026
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7 0.086006 0.080612 0.095275 0.088983 0.083228 0.077968 0.073162
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8 0.080846 0.076068 0.089250 0.083659 0.078529 0.073827 0.069519
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9 0.076068 0.071841 0.083682 0.078720 0.074154 0.069956 0.066098
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10 0.089250 0.083682 0.099504 0.092936 0.086920 0.081414 0.076377
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11 0.083659 0.078720 0.092936 0.087096 0.081732 0.076810 0.072296
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12 0.078529 0.074154 0.086920 0.081732 0.076954 0.072557 0.068515
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13 0.073827 0.069956 0.081414 0.076810 0.072557 0.068633 0.065016
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14 0.069519 0.066098 0.076377 0.072296 0.068515 0.065016 0.061783
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1 0.065794 0.062352 0.065582 0.062022 0.058765 0.055788 0.053069
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2 0.068700 0.065534 0.068203 0.064909 0.061857 0.059038 0.056441
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3 0.074858 0.071499 0.075503 0.071917 0.068581 0.065492 0.062636
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4 0.073728 0.070739 0.074125 0.070915 0.067904 0.065096 0.062486
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5 0.072170 0.069526 0.072352 0.069494 0.066793 0.064256 0.061885
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6 0.073713 0.070812 0.074961 0.071782 0.068790 0.065991 0.063380
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7 0.071447 0.068888 0.072447 0.069625 0.066951 0.064434 0.062076
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8 0.069161 0.066912 0.069940 0.067442 0.065059 0.062803 0.060678
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9 0.066912 0.064945 0.067492 0.065289 0.063171 0.061154 0.059245
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10 0.069940 0.067492 0.071541 0.068800 0.066196 0.063738 0.061430
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11 0.067442 0.065289 0.068800 0.066372 0.064050 0.061846 0.059767
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12 0.065059 0.063171 0.066196 0.064050 0.061983 0.060011 0.058141
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13 0.062803 0.061154 0.063738 0.061846 0.060011 0.058249 0.056570
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14 0.060678 0.059245 0.061430 0.059767 0.058141 0.056570 0.055065
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</pre></div>
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</div>
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</div>
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@@ -2145,13 +2150,15 @@ set of <span class="math notranslate nohighlight">\(\lambda\)</span> values.</p>
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</div>
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<div class="cell_output docutils container">
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 2.03099776 -0.17917768 5.18029127]
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Training MSE for OLS
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</pre></div>
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</div>
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<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Training MSE for OLS
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0.009163470508352228
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Test MSE OLS
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0.008675369724976777
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</pre></div>
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</div>
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<img alt="_images/chapter2_249_1.png" src="_images/chapter2_249_1.png" />
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<img alt="_images/chapter2_249_2.png" src="_images/chapter2_249_2.png" />
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</div>
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</div>
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<p>Both these example send a clear message. The addition of a
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