This commit is contained in:
Morten Hjorth-Jensen
2021-09-08 06:34:56 +02:00
parent 9c3168fd83
commit 5fcdfec57b
6 changed files with 7 additions and 5 deletions
+1 -1
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@@ -649,7 +649,7 @@ which leads to
$$
\hat{\boldsymbol{\beta}}_i^{\mathrm{Lasso}} = \left\{\begin{array}{ccc}y_i-\frac{\lambda}{2} &\mathrm{if} & y_i> \frac{\lambda}{2}\\
y_i+\frac{\lambda}{2} &\mathrm{if} & y_i < -\frac{\lambda}{2}\\
0 &\mathrm{if} & \verty_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
$$
<p>&nbsp;<br>
+1 -1
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@@ -666,7 +666,7 @@ which leads to
$$
\hat{\boldsymbol{\beta}}_i^{\mathrm{Lasso}} = \left\{\begin{array}{ccc}y_i-\frac{\lambda}{2} &\mathrm{if} & y_i> \frac{\lambda}{2}\\
y_i+\frac{\lambda}{2} &\mathrm{if} & y_i < -\frac{\lambda}{2}\\
0 &\mathrm{if} & \verty_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
$$
<p>
+1 -1
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@@ -671,7 +671,7 @@ which leads to
$$
\hat{\boldsymbol{\beta}}_i^{\mathrm{Lasso}} = \left\{\begin{array}{ccc}y_i-\frac{\lambda}{2} &\mathrm{if} & y_i> \frac{\lambda}{2}\\
y_i+\frac{\lambda}{2} &\mathrm{if} & y_i < -\frac{\lambda}{2}\\
0 &\mathrm{if} & \verty_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
$$
<p>
Binary file not shown.
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@@ -764,7 +764,7 @@
"$$\n",
"\\hat{\\boldsymbol{\\beta}}_i^{\\mathrm{Lasso}} = \\left\\{\\begin{array}{ccc}y_i-\\frac{\\lambda}{2} &\\mathrm{if} & y_i> \\frac{\\lambda}{2}\\\\\n",
" y_i+\\frac{\\lambda}{2} &\\mathrm{if} & y_i< -\\frac{\\lambda}{2}\\\\\n",
"\t\t\t\t\t\t\t 0 &\\mathrm{if} & \\verty_i\\vert\\le \\frac{\\lambda}{2}\\end{array}\\right.\\\\.\n",
"\t\t\t\t\t\t\t 0 &\\mathrm{if} & \\vert y_i\\vert\\le \\frac{\\lambda}{2}\\end{array}\\right.\\\\.\n",
"$$"
]
},
@@ -778,6 +778,7 @@
"We will amongst other things show that the regularization parameter can reduce considerably the variance of the parameters $\\beta$.\n",
"\n",
"\n",
"\n",
"<!-- !split -->\n",
"## Linking the regression analysis with a statistical interpretation\n",
"\n",
+2 -1
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@@ -419,7 +419,7 @@ which leads to
\[
\hat{\bm{\beta}}_i^{\mathrm{Lasso}} = \left\{\begin{array}{ccc}y_i-\frac{\lambda}{2} &\mathrm{if} & y_i> \frac{\lambda}{2}\\
y_i+\frac{\lambda}{2} &\mathrm{if} & y_i< -\frac{\lambda}{2}\\
0 &\mathrm{if} & \verty_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
0 &\mathrm{if} & \vert y_i\vert\le \frac{\lambda}{2}\end{array}\right.\\.
\]
!et
@@ -429,6 +429,7 @@ We will now couple the discussions of ordinary least squares, Ridge and Lasso re
We will amongst other things show that the regularization parameter can reduce considerably the variance of the parameters $\beta$.
!split
===== Linking the regression analysis with a statistical interpretation =====