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correcting typos

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Morten Hjorth-Jensen
2023-09-04 08:13:39 +02:00
parent 2a445d0f02
commit 25cf50425a
9 changed files with 73 additions and 85 deletions
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doc/Projects/2023/Project1/html/._Project1-bs000.html
+3 -5
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@@ -381,11 +381,9 @@ Give a
critical discussion of the three methods and a judgement of which
model fits the data best.
</p>
<p>v</p>
<h3 id="part-d-paper-and-pencil-part" class="anchor">Part d): Paper and pencil part </h3>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_self">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>).</p>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_self">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>). The exercise is also part of the weekly exercises for week 37.</p>
<p>The assumption we have made is
that there exists a continuous function \( f(\boldsymbol{x}) \) and a normal distributed error \( \boldsymbol{\varepsilon}\sim N(0, \sigma^2) \)
@@ -430,7 +428,7 @@ $$
\mbox{Var}(\boldsymbol{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}.
$$
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \). .
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \).
A given parameter \( \beta_j \) is given by the diagonal matrix element of the above matrix.
</p>
<h3 id="part-e-bias-variance-trade-off-and-resampling-techniques" class="anchor">Part e): Bias-variance trade-off and resampling techniques </h3>
@@ -504,7 +502,7 @@ $$
\mathrm{var}[\tilde{f}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
$$
<p>The answer to this exercise should be included in the theory part of the report.
<p>The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.
Explain what the terms mean and discuss their interpretations.
</p>
doc/Projects/2023/Project1/html/Project1-bs.html
+3 -5
View File
@@ -381,11 +381,9 @@ Give a
critical discussion of the three methods and a judgement of which
model fits the data best.
</p>
<p>v</p>
<h3 id="part-d-paper-and-pencil-part" class="anchor">Part d): Paper and pencil part </h3>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_self">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>).</p>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_self">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>). The exercise is also part of the weekly exercises for week 37.</p>
<p>The assumption we have made is
that there exists a continuous function \( f(\boldsymbol{x}) \) and a normal distributed error \( \boldsymbol{\varepsilon}\sim N(0, \sigma^2) \)
@@ -430,7 +428,7 @@ $$
\mbox{Var}(\boldsymbol{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}.
$$
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \). .
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \).
A given parameter \( \beta_j \) is given by the diagonal matrix element of the above matrix.
</p>
<h3 id="part-e-bias-variance-trade-off-and-resampling-techniques" class="anchor">Part e): Bias-variance trade-off and resampling techniques </h3>
@@ -504,7 +502,7 @@ $$
\mathrm{var}[\tilde{f}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
$$
<p>The answer to this exercise should be included in the theory part of the report.
<p>The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.
Explain what the terms mean and discuss their interpretations.
</p>
doc/Projects/2023/Project1/html/Project1.html
+3 -5
View File
@@ -417,11 +417,9 @@ Give a
critical discussion of the three methods and a judgement of which
model fits the data best.
</p>
<p>v</p>
<h3 id="part-d-paper-and-pencil-part">Part d): Paper and pencil part </h3>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_blank">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>).</p>
<p>This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a href="https://www.springer.com/gp/book/9780387848570" target="_blank">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>). The exercise is also part of the weekly exercises for week 37.</p>
<p>The assumption we have made is
that there exists a continuous function \( f(\boldsymbol{x}) \) and a normal distributed error \( \boldsymbol{\varepsilon}\sim N(0, \sigma^2) \)
@@ -466,7 +464,7 @@ $$
\mbox{Var}(\boldsymbol{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}.
$$
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \). .
<p>We can use the last expression when we define a so-called confidence interval for the parameters \( \beta \).
A given parameter \( \beta_j \) is given by the diagonal matrix element of the above matrix.
</p>
<h3 id="part-e-bias-variance-trade-off-and-resampling-techniques">Part e): Bias-variance trade-off and resampling techniques </h3>
@@ -540,7 +538,7 @@ $$
\mathrm{var}[\tilde{f}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2.
$$
<p>The answer to this exercise should be included in the theory part of the report.
<p>The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.
Explain what the terms mean and discuss their interpretations.
</p>
doc/Projects/2023/Project1/ipynb/Project1.ipynb
+54 -56
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@@ -2,7 +2,7 @@
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@@ -14,7 +14,7 @@
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@@ -27,7 +27,7 @@
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@@ -63,7 +63,7 @@
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@@ -85,7 +85,7 @@
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@@ -100,7 +100,7 @@
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@@ -133,7 +133,7 @@
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@@ -185,7 +185,7 @@
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@@ -207,7 +207,7 @@
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@@ -220,7 +220,7 @@
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@@ -232,7 +232,7 @@
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@@ -244,7 +244,7 @@
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@@ -254,7 +254,7 @@
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@@ -266,7 +266,7 @@
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{
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@@ -295,7 +295,7 @@
},
{
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"id": "c2078519",
"metadata": {
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@@ -313,7 +313,7 @@
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{
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"id": "b121745d",
"id": "f718aec9",
"metadata": {
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@@ -325,21 +325,19 @@
"you can also use the functionalities of **Scikit-Learn** (recommended). Keep in mind that the library **Scikit-Learn** excludes the intercept by default. \n",
"Give a\n",
"critical discussion of the three methods and a judgement of which\n",
"model fits the data best.\n",
"\n",
"v"
"model fits the data best."
]
},
{
"cell_type": "markdown",
"id": "56d96043",
"id": "d8b10104",
"metadata": {
"editable": true
},
"source": [
"### Part d): Paper and pencil part\n",
"\n",
"This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570)).\n",
"This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of [Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer](https://www.springer.com/gp/book/9780387848570)). The exercise is also part of the weekly exercises for week 37.\n",
"\n",
"The assumption we have made is \n",
"that there exists a continuous function $f(\\boldsymbol{x})$ and a normal distributed error $\\boldsymbol{\\varepsilon}\\sim N(0, \\sigma^2)$\n",
@@ -348,7 +346,7 @@
},
{
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"id": "c5267aae",
"metadata": {
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@@ -360,7 +358,7 @@
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@@ -371,7 +369,7 @@
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@@ -383,7 +381,7 @@
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@@ -395,7 +393,7 @@
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@@ -407,7 +405,7 @@
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@@ -418,7 +416,7 @@
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@@ -430,7 +428,7 @@
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"metadata": {
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@@ -443,7 +441,7 @@
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@@ -455,7 +453,7 @@
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{
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"metadata": {
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@@ -465,7 +463,7 @@
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{
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@@ -477,18 +475,18 @@
},
{
"cell_type": "markdown",
"id": "050e1f04",
"id": "78ec374f",
"metadata": {
"editable": true
},
"source": [
"We can use the last expression when we define a so-called confidence interval for the parameters $\\beta$. .\n",
"We can use the last expression when we define a so-called confidence interval for the parameters $\\beta$. \n",
"A given parameter $\\beta_j$ is given by the diagonal matrix element of the above matrix."
]
},
{
"cell_type": "markdown",
"id": "52486468",
"id": "74bec52c",
"metadata": {
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@@ -521,7 +519,7 @@
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@@ -533,7 +531,7 @@
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@@ -552,7 +550,7 @@
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@@ -578,7 +576,7 @@
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@@ -600,7 +598,7 @@
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@@ -612,7 +610,7 @@
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"source": [
"The answer to this exercise should be included in the theory part of the report.\n",
"The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.\n",
"Explain what the terms mean and discuss their interpretations.\n",
"\n",
"Perform then a bias-variance analysis of the Franke function by\n",
@@ -653,7 +651,7 @@
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@@ -678,7 +676,7 @@
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@@ -781,7 +779,7 @@
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doc/Projects/2023/Project1/ipynb/ipynb-Project1-src.tar.gz
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doc/Projects/2023/Project1/pdf/Project1.p.tex
+3 -5
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@@ -362,10 +362,8 @@ Give a
critical discussion of the three methods and a judgement of which
model fits the data best.
v
\paragraph{Part d): Paper and pencil part.}
This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}).
This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}). The exercise is also part of the weekly exercises for week 37.
The assumption we have made is
that there exists a continuous function $f(\bm{x})$ and a normal distributed error $\bm{\varepsilon}\sim N(0, \sigma^2)$
@@ -402,7 +400,7 @@ Show finally that the variance of $\bm{\beta}$ is
\mbox{Var}(\bm{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}.
\]
We can use the last expression when we define a so-called confidence interval for the parameters $\beta$. .
We can use the last expression when we define a so-called confidence interval for the parameters $\beta$.
A given parameter $\beta_j$ is given by the diagonal matrix element of the above matrix.
\paragraph{Part e): Bias-variance trade-off and resampling techniques.}
@@ -463,7 +461,7 @@ and
\[
\mathrm{var}[\tilde{f}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
\]
The answer to this exercise should be included in the theory part of the report.
The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.
Explain what the terms mean and discuss their interpretations.
Perform then a bias-variance analysis of the Franke function by
doc/Projects/2023/Project1/pdf/Project1.pdf
BIN
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doc/Projects/2023/Project1/pdf/Project1.tex
+3 -5
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@@ -332,10 +332,8 @@ Give a
critical discussion of the three methods and a judgement of which
model fits the data best.
v
\paragraph{Part d): Paper and pencil part.}
This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}).
This exercise deals with various mean values and variances in linear regression method (here it may be useful to look up chapter 3, equation (3.8) of \href{{https://www.springer.com/gp/book/9780387848570}}{Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer}). The exercise is also part of the weekly exercises for week 37.
The assumption we have made is
that there exists a continuous function $f(\bm{x})$ and a normal distributed error $\bm{\varepsilon}\sim N(0, \sigma^2)$
@@ -372,7 +370,7 @@ Show finally that the variance of $\bm{\beta}$ is
\mbox{Var}(\bm{\hat{\beta}}) = \sigma^2 \, (\mathbf{X}^{T} \mathbf{X})^{-1}.
\]
We can use the last expression when we define a so-called confidence interval for the parameters $\beta$. .
We can use the last expression when we define a so-called confidence interval for the parameters $\beta$.
A given parameter $\beta_j$ is given by the diagonal matrix element of the above matrix.
\paragraph{Part e): Bias-variance trade-off and resampling techniques.}
@@ -433,7 +431,7 @@ and
\[
\mathrm{var}[\tilde{f}]=\frac{1}{n}\sum_i(\tilde{y}_i-\mathbb{E}\left[\bm{\tilde{y}}\right])^2.
\]
The answer to this exercise should be included in the theory part of the report.
The answer to this exercise should be included in the theory part of the report. This exercise is also part of the weekly exercises of week 37.
Explain what the terms mean and discuss their interpretations.
Perform then a bias-variance analysis of the Franke function by