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silly typo

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Morten Hjorth-Jensen
2022-09-05 21:59:57 +02:00
parent 3a99e6d57e
commit 390623275f
9 changed files with 1182 additions and 1182 deletions
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doc/BookChapters/chapter2.do.txt
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@@ -2495,6 +2495,6 @@ $\beta_j$. The variance for the Laplace distribution is
$2\tau^2=1/\lambda$ while for the Gaussian distribution it is
$\sigma^2=1/(2\lambda)$. Thus, increasing the variance means
decreasing $\lambda$ and shrinking the variance means increasing
$\lamdbda$. When we increase $\lambda$, this corresponds to shrinking the role of less important features (small singular values).
$\lambda$. When we increase $\lambda$, this corresponds to shrinking the role of less important features (small singular values).
doc/LectureNotes/_build/.doctrees/chapter2.doctree
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doc/LectureNotes/_build/html/_sources/chapter2.ipynb
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doc/LectureNotes/_build/html/chapter2.html
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@@ -1210,10 +1210,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.01591355407242949
3.6808538439837775
[[ 0.96390357 2.99157584]
[ 2.99157584 10.31120247]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.02762405215108776
3.9005135872087155
[[0.81974332 2.54886137]
[2.54886137 8.96601782]]
</pre></div>
</div>
</div>
@@ -1250,10 +1250,10 @@ a more brute force way. Here we scale the mean values for each column of the des
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08612280083325631
1.6149274949460215
[[1. 0.66934291]
[0.66934291 1. ]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08356774001062162
1.415534701258823
[[1. 0.53815559]
[0.53815559 1. ]]
</pre></div>
</div>
</div>
@@ -1283,30 +1283,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
</div>
</div>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-1.04649105 -2.92658312]
[ 0.45985488 1.43876695]
[-0.41081513 -1.96426825]
[ 1.75703965 4.88736621]
[ 1.02698605 3.59304008]
[-0.71348713 -1.98249059]
[-0.22685646 0.37866422]
[-0.90559087 -1.31597731]
[-0.60349429 -3.47245463]
[ 0.66285434 1.36393643]]
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0.99594988 1.80661365]
[ 0.59616454 1.54671213]
[-0.93676229 -3.41351287]
[-0.2942772 -0.48952201]
[ 0.31574634 1.86425056]
[ 0.57888946 1.08188077]
[ 0.379203 0.55808001]
[ 0.55824107 2.14995486]
[ 0.20609082 0.88908038]
[-2.39924562 -5.99353748]]
0 1
0 -1.046491 -2.926583
1 0.459855 1.438767
2 -0.410815 -1.964268
3 1.757040 4.887366
4 1.026986 3.593040
5 -0.713487 -1.982491
6 -0.226856 0.378664
7 -0.905591 -1.315977
8 -0.603494 -3.472455
9 0.662854 1.363936
0 0.995950 1.806614
1 0.596165 1.546712
2 -0.936762 -3.413513
3 -0.294277 -0.489522
4 0.315746 1.864251
5 0.578889 1.081881
6 0.379203 0.558080
7 0.558241 2.149955
8 0.206091 0.889080
9 -2.399246 -5.993537
0 1
0 1.000000 0.948641
1 0.948641 1.000000
0 1.000000 0.970057
1 0.970057 1.000000
</pre></div>
</div>
</div>
@@ -1363,37 +1363,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
<div class="cell_output docutils container">
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.0 0.084846 0.071547 0.086679 0.078725 0.071480 0.079609 0.073320
2 0.0 0.071547 0.061716 0.073647 0.067908 0.062640 0.068417 0.063857
3 0.0 0.086679 0.073647 0.094619 0.086262 0.078697 0.090356 0.083579
4 0.0 0.078725 0.067908 0.086262 0.079483 0.073303 0.082874 0.077375
5 0.0 0.071480 0.062640 0.078697 0.073303 0.068345 0.076121 0.071741
6 0.0 0.079609 0.068417 0.090356 0.082874 0.076121 0.088460 0.082267
7 0.0 0.073320 0.063857 0.083579 0.077375 0.071741 0.082267 0.077131
8 0.0 0.067787 0.059824 0.077620 0.072521 0.067856 0.076821 0.072597
9 0.0 0.062888 0.056235 0.072352 0.068210 0.064388 0.072008 0.068573
10 0.0 0.071906 0.062551 0.083694 0.077291 0.071515 0.083361 0.077978
11 0.0 0.066654 0.058715 0.077948 0.072611 0.067767 0.078042 0.073548
12 0.0 0.062061 0.055344 0.072918 0.068500 0.064461 0.073380 0.069654
13 0.0 0.058033 0.052372 0.068505 0.064880 0.061538 0.069285 0.066223
14 0.0 0.054491 0.049747 0.064623 0.061685 0.058948 0.065680 0.063192
1 0.0 0.071441 0.075840 0.068261 0.072824 0.077706 0.057587 0.061646
2 0.0 0.075840 0.081837 0.071552 0.076958 0.082846 0.060016 0.064609
3 0.0 0.068261 0.071552 0.068799 0.073134 0.077711 0.060288 0.064431
4 0.0 0.072824 0.076958 0.073134 0.078101 0.083399 0.063979 0.068619
5 0.0 0.077706 0.082846 0.077711 0.083399 0.089524 0.067854 0.073045
6 0.0 0.057587 0.060016 0.060288 0.063979 0.067854 0.054411 0.058088
7 0.0 0.061646 0.064609 0.064431 0.068619 0.073045 0.058088 0.062195
8 0.0 0.066064 0.069651 0.068920 0.073668 0.078719 0.062064 0.066651
9 0.0 0.070874 0.075192 0.073777 0.079158 0.084920 0.066356 0.071476
10 0.0 0.047953 0.049858 0.051662 0.054774 0.058035 0.047737 0.050910
11 0.0 0.051391 0.053678 0.055302 0.058816 0.062517 0.051043 0.054582
12 0.0 0.055153 0.057877 0.059278 0.063241 0.067437 0.054650 0.058596
13 0.0 0.059272 0.062498 0.063619 0.068087 0.072839 0.058585 0.062983
14 0.0 0.063781 0.067585 0.068358 0.073391 0.078771 0.062874 0.067775
8 9 10 11 12 13 14
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.067787 0.062888 0.071906 0.066654 0.062061 0.058033 0.054491
2 0.059824 0.056235 0.062551 0.058715 0.055344 0.052372 0.049747
3 0.077620 0.072352 0.083694 0.077948 0.072918 0.068505 0.064623
4 0.072521 0.068210 0.077291 0.072611 0.068500 0.064880 0.061685
5 0.067856 0.064388 0.071515 0.067767 0.064461 0.061538 0.058948
6 0.076821 0.072008 0.083361 0.078042 0.073380 0.069285 0.065680
7 0.072597 0.068573 0.077978 0.073548 0.069654 0.066223 0.063192
8 0.068852 0.065514 0.073238 0.069578 0.066348 0.063493 0.060963
9 0.065514 0.062773 0.069044 0.066051 0.063401 0.061048 0.058955
10 0.073238 0.069044 0.079558 0.074881 0.070775 0.067162 0.063977
11 0.069578 0.066051 0.074881 0.070959 0.067506 0.064459 0.061765
12 0.066348 0.063401 0.070775 0.067506 0.064618 0.062062 0.059795
13 0.063493 0.061048 0.067162 0.064459 0.062062 0.059933 0.058038
14 0.060963 0.058955 0.063977 0.061765 0.059795 0.058038 0.056468
1 0.066064 0.070874 0.047953 0.051391 0.055153 0.059272 0.063781
2 0.069651 0.075192 0.049858 0.053678 0.057877 0.062498 0.067585
3 0.068920 0.073777 0.051662 0.055302 0.059278 0.063619 0.068358
4 0.073668 0.079158 0.054774 0.058816 0.063241 0.068087 0.073391
5 0.078719 0.084920 0.058035 0.062517 0.067437 0.072839 0.078771
6 0.062064 0.066356 0.047737 0.051043 0.054650 0.058585 0.062874
7 0.066651 0.071476 0.050910 0.054582 0.058596 0.062983 0.067775
8 0.071641 0.077062 0.054340 0.058416 0.062881 0.067769 0.073120
9 0.077062 0.083151 0.058040 0.062563 0.067525 0.072970 0.078942
10 0.054340 0.058040 0.042708 0.045603 0.048762 0.052206 0.055958
11 0.058416 0.062563 0.045603 0.048818 0.052330 0.056165 0.060349
12 0.062881 0.067525 0.048762 0.052330 0.056233 0.060502 0.065168
13 0.067769 0.072970 0.052206 0.056165 0.060502 0.065252 0.070453
14 0.073120 0.078942 0.055958 0.060349 0.065168 0.070453 0.076248
</pre></div>
</div>
</div>
@@ -3064,7 +3064,7 @@ C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{
<span class="math notranslate nohighlight">\(2\tau^2=1/\lambda\)</span> while for the Gaussian distribution it is
<span class="math notranslate nohighlight">\(\sigma^2=1/(2\lambda)\)</span>. Thus, increasing the variance means
decreasing <span class="math notranslate nohighlight">\(\lambda\)</span> and shrinking the variance means increasing
<span class="math notranslate nohighlight">\(\lamdbda\)</span>. When we increase <span class="math notranslate nohighlight">\(\lambda\)</span>, this corresponds to shrinking the role of less important features (small singular values).</p>
<span class="math notranslate nohighlight">\(\lambda\)</span>. When we increase <span class="math notranslate nohighlight">\(\lambda\)</span>, this corresponds to shrinking the role of less important features (small singular values).</p>
</div>
</div>
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doc/LectureNotes/_build/jupyter_execute/chapter2.py
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@@ -2274,4 +2274,4 @@ for i in range(nlambdas):
# $2\tau^2=1/\lambda$ while for the Gaussian distribution it is
# $\sigma^2=1/(2\lambda)$. Thus, increasing the variance means
# decreasing $\lambda$ and shrinking the variance means increasing
# $\lamdbda$. When we increase $\lambda$, this corresponds to shrinking the role of less important features (small singular values).
# $\lambda$. When we increase $\lambda$, this corresponds to shrinking the role of less important features (small singular values).
doc/LectureNotes/chapter2.ipynb
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