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updating week 39

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mhjensen
2020-09-25 06:37:00 +02:00
parent 7d18cc5cf6
commit 1d3281d7a2
8 changed files with 60 additions and 24 deletions
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doc/pub/week39/html/._week39-bs039.html
+7 -1
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@@ -281,11 +281,17 @@ x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(n,<span style="color: #666666">1</span>)
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((n,<span style="color: #666666">1</span>)), x]
<span style="color: #408080; font-style: italic"># Hessian matrix</span>
H <span style="color: #666666">=</span> (<span style="color: #666666">2.0/</span>n)<span style="color: #666666">*</span> X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X
<span style="color: #408080; font-style: italic"># Get the eigenvalues</span>
EigValues, EigVectors <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>eig(H)
<span style="color: #008000">print</span>(EigValues)
beta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X) <span style="color: #666666">@</span> X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y
<span style="color: #008000">print</span>(beta_linreg)
beta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
eta <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
eta <span style="color: #666666">=</span> <span style="color: #666666">1.0/</span>np<span style="color: #666666">.</span>max(EigValues)
Niterations <span style="color: #666666">=</span> <span style="color: #666666">1000</span>
<span style="color: #008000; font-weight: bold">for</span> <span style="color: #008000">iter</span> <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(Niterations):
doc/pub/week39/html/._week39-bs042.html
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@@ -273,10 +273,10 @@ MathJax.Hub.Config({
<span style="color: #408080; font-style: italic"># the number of datapoints</span>
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(m,<span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(m,<span style="color: #666666">1</span>)
x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(n,<span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(n,<span style="color: #666666">1</span>)
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((m,<span style="color: #666666">1</span>)), x]
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((n,<span style="color: #666666">1</span>)), x]
XT_X <span style="color: #666666">=</span> X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X
<span style="color: #408080; font-style: italic">#Ridge parameter lambda</span>
doc/pub/week39/html/week39-reveal.html
+10 -4
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@@ -1298,11 +1298,17 @@ x = <span style="color: #B452CD">2</span>*np.random.rand(n,<span style="color: #
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(n,<span style="color: #B452CD">1</span>)
X = np.c_[np.ones((n,<span style="color: #B452CD">1</span>)), x]
<span style="color: #228B22"># Hessian matrix</span>
H = (<span style="color: #B452CD">2.0</span>/n)* X.T @ X
<span style="color: #228B22"># Get the eigenvalues</span>
EigValues, EigVectors = np.linalg.eig(H)
<span style="color: #658b00">print</span>(EigValues)
beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y
<span style="color: #658b00">print</span>(beta_linreg)
beta = np.random.randn(<span style="color: #B452CD">2</span>,<span style="color: #B452CD">1</span>)
eta = <span style="color: #B452CD">0.1</span>
eta = <span style="color: #B452CD">1.0</span>/np.max(EigValues)
Niterations = <span style="color: #B452CD">1000</span>
<span style="color: #8B008B; font-weight: bold">for</span> <span style="color: #658b00">iter</span> <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(Niterations):
@@ -1398,10 +1404,10 @@ $$
<span style="color: #228B22"># the number of datapoints</span>
n = <span style="color: #B452CD">100</span>
x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(m,<span style="color: #B452CD">1</span>)
x = <span style="color: #B452CD">2</span>*np.random.rand(n,<span style="color: #B452CD">1</span>)
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(n,<span style="color: #B452CD">1</span>)
X = np.c_[np.ones((m,<span style="color: #B452CD">1</span>)), x]
X = np.c_[np.ones((n,<span style="color: #B452CD">1</span>)), x]
XT_X = X.T @ X
<span style="color: #228B22">#Ridge parameter lambda</span>
doc/pub/week39/html/week39-solarized.html
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@@ -1244,11 +1244,17 @@ x = <span style="color: #B452CD">2</span>*np.random.rand(n,<span style="color: #
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(n,<span style="color: #B452CD">1</span>)
X = np.c_[np.ones((n,<span style="color: #B452CD">1</span>)), x]
<span style="color: #228B22"># Hessian matrix</span>
H = (<span style="color: #B452CD">2.0</span>/n)* X.T @ X
<span style="color: #228B22"># Get the eigenvalues</span>
EigValues, EigVectors = np.linalg.eig(H)
<span style="color: #658b00">print</span>(EigValues)
beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y
<span style="color: #658b00">print</span>(beta_linreg)
beta = np.random.randn(<span style="color: #B452CD">2</span>,<span style="color: #B452CD">1</span>)
eta = <span style="color: #B452CD">0.1</span>
eta = <span style="color: #B452CD">1.0</span>/np.max(EigValues)
Niterations = <span style="color: #B452CD">1000</span>
<span style="color: #8B008B; font-weight: bold">for</span> <span style="color: #658b00">iter</span> <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(Niterations):
@@ -1336,10 +1342,10 @@ $$
<span style="color: #228B22"># the number of datapoints</span>
n = <span style="color: #B452CD">100</span>
x = <span style="color: #B452CD">2</span>*np.random.rand(m,<span style="color: #B452CD">1</span>)
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(m,<span style="color: #B452CD">1</span>)
x = <span style="color: #B452CD">2</span>*np.random.rand(n,<span style="color: #B452CD">1</span>)
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.randn(n,<span style="color: #B452CD">1</span>)
X = np.c_[np.ones((m,<span style="color: #B452CD">1</span>)), x]
X = np.c_[np.ones((n,<span style="color: #B452CD">1</span>)), x]
XT_X = X.T @ X
<span style="color: #228B22">#Ridge parameter lambda</span>
doc/pub/week39/html/week39.html
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@@ -1249,11 +1249,17 @@ x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(n,<span style="color: #666666">1</span>)
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((n,<span style="color: #666666">1</span>)), x]
<span style="color: #408080; font-style: italic"># Hessian matrix</span>
H <span style="color: #666666">=</span> (<span style="color: #666666">2.0/</span>n)<span style="color: #666666">*</span> X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X
<span style="color: #408080; font-style: italic"># Get the eigenvalues</span>
EigValues, EigVectors <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>eig(H)
<span style="color: #008000">print</span>(EigValues)
beta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X) <span style="color: #666666">@</span> X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y
<span style="color: #008000">print</span>(beta_linreg)
beta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
eta <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
eta <span style="color: #666666">=</span> <span style="color: #666666">1.0/</span>np<span style="color: #666666">.</span>max(EigValues)
Niterations <span style="color: #666666">=</span> <span style="color: #666666">1000</span>
<span style="color: #008000; font-weight: bold">for</span> <span style="color: #008000">iter</span> <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(Niterations):
@@ -1341,10 +1347,10 @@ $$
<span style="color: #408080; font-style: italic"># the number of datapoints</span>
n <span style="color: #666666">=</span> <span style="color: #666666">100</span>
x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(m,<span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(m,<span style="color: #666666">1</span>)
x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(n,<span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(n,<span style="color: #666666">1</span>)
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((m,<span style="color: #666666">1</span>)), x]
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((n,<span style="color: #666666">1</span>)), x]
XT_X <span style="color: #666666">=</span> X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X
<span style="color: #408080; font-style: italic">#Ridge parameter lambda</span>
doc/pub/week39/ipynb/ipynb-week39-src.tar.gz
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doc/pub/week39/ipynb/week39.ipynb
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@@ -1452,11 +1452,17 @@
"y = 4+3*x+np.random.randn(n,1)\n",
"\n",
"X = np.c_[np.ones((n,1)), x]\n",
"# Hessian matrix\n",
"H = (2.0/n)* X.T @ X\n",
"# Get the eigenvalues\n",
"EigValues, EigVectors = np.linalg.eig(H)\n",
"print(EigValues)\n",
"\n",
"beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y\n",
"print(beta_linreg)\n",
"beta = np.random.randn(2,1)\n",
"\n",
"eta = 0.1\n",
"eta = 1.0/np.max(EigValues)\n",
"Niterations = 1000\n",
"\n",
"for iter in range(Niterations):\n",
@@ -1589,10 +1595,10 @@
"\n",
"# the number of datapoints\n",
"n = 100\n",
"x = 2*np.random.rand(m,1)\n",
"y = 4+3*x+np.random.randn(m,1)\n",
"x = 2*np.random.rand(n,1)\n",
"y = 4+3*x+np.random.randn(n,1)\n",
"\n",
"X = np.c_[np.ones((m,1)), x]\n",
"X = np.c_[np.ones((n,1)), x]\n",
"XT_X = X.T @ X\n",
"\n",
"#Ridge parameter lambda\n",
doc/src/week39/week39.do.txt
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@@ -876,11 +876,17 @@ x = 2*np.random.rand(n,1)
y = 4+3*x+np.random.randn(n,1)
X = np.c_[np.ones((n,1)), x]
# Hessian matrix
H = (2.0/n)* X.T @ X
# Get the eigenvalues
EigValues, EigVectors = np.linalg.eig(H)
print(EigValues)
beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y
print(beta_linreg)
beta = np.random.randn(2,1)
eta = 0.1
eta = 1.0/np.max(EigValues)
Niterations = 1000
for iter in range(Niterations):
@@ -968,10 +974,10 @@ import sys
# the number of datapoints
n = 100
x = 2*np.random.rand(m,1)
y = 4+3*x+np.random.randn(m,1)
x = 2*np.random.rand(n,1)
y = 4+3*x+np.random.randn(n,1)
X = np.c_[np.ones((m,1)), x]
X = np.c_[np.ones((n,1)), x]
XT_X = X.T @ X
#Ridge parameter lambda