Typos in hw corrected
This commit is contained in:
mhjensen
@@ -128,7 +128,7 @@ MathJax.Hub.Config({
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<h2 id="___sec0" class="anchor">Exercise 1 </h2>
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<p>
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The first exercise here is of a mere technical art. We want you have installed
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The first exercise here is of a mere technical art. We want you to have
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<ul>
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<li> git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo <a href="https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html" target="_self">GitHub facilities</a>.</li>
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@@ -141,9 +141,7 @@ IPython/Jupyter notebooks invaluable in your work. You can run <b>R</b>
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codes in the Jupyter/IPython notebooks, with the immediate benefit of
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visualizing your data. You can also use compiled languages like C++,
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Rust, Fortran etc if you prefer. The focus in these lectures will be
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on Python, but we will provide many code examples for those of you who
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prefer R or compiled languages. You can integrate C++ codes and R in for example
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a Jupyter notebook.
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on Python.
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<p>
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If you have Python installed (we recommend Python3) and you feel
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@@ -209,7 +207,7 @@ We recommend using <b>Anaconda</b>.
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<h2 id="___sec1" class="anchor">Exercise 2 </h2>
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<p>
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We will generate our own dataset for function \( y(x) \) where \( x \in [0,2] \) and defined by random numbers computed with the uniform distribution. The function \( y \) is a quadratic polynomial in \( x \) with added stochastic noise according to the normal distribution \( \cal {N}(0,1) \).
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We will generate our own dataset for a function \( y(x) \) where \( x \in [0,1] \) and defined by random numbers computed with the uniform distribution. The function \( y \) is a quadratic polynomial in \( x \) with added stochastic noise according to the normal distribution \( \cal {N}(0,1) \).
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The following simple Python instructions define our \( x \) and \( y \) values (with 100 data points).
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<p>
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@@ -218,9 +216,9 @@ The following simple Python instructions define our \( x \) and \( y \) values (
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y <span style="color: #666666">=</span> <span style="color: #666666">5*</span>x<span style="color: #666666">*</span>x<span style="color: #666666">+0.1*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
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</pre></div>
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<ol>
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<li> Write your own code (following the examples under the <a href="https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html" target="_self">regression slides</a> for computing the parametrization of the data set fitting a second-order polynomial.</li>
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<li> Write your own code (following the examples under the <a href="https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html" target="_self">regression slides</a>) for computing the parametrization of the data set fitting a second-order polynomial.</li>
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<li> Use thereafter <b>scikit-learn</b> (see again the examples in the regression slides) and compare with your own code.</li>
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<li> Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as</li>
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<li> Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as</li>
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</ol>
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$$ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
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@@ -238,7 +236,7 @@ $$
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\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
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$$
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<p>
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You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
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Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
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<h2 id="___sec2" class="anchor">Exercise 3, variance of the parameters \( \beta \) in linear regression </h2>
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@@ -92,7 +92,7 @@ MathJax.Hub.Config({
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<h2 id="___sec0">Exercise 1 </h2>
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<p>
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The first exercise here is of a mere technical art. We want you have installed
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The first exercise here is of a mere technical art. We want you to have
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<ul>
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<li> git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo <a href="https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html" target="_blank">GitHub facilities</a>.</li>
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@@ -105,9 +105,7 @@ IPython/Jupyter notebooks invaluable in your work. You can run <b>R</b>
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codes in the Jupyter/IPython notebooks, with the immediate benefit of
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visualizing your data. You can also use compiled languages like C++,
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Rust, Fortran etc if you prefer. The focus in these lectures will be
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on Python, but we will provide many code examples for those of you who
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prefer R or compiled languages. You can integrate C++ codes and R in for example
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a Jupyter notebook.
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on Python.
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<p>
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If you have Python installed (we recommend Python3) and you feel
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@@ -173,7 +171,7 @@ We recommend using <b>Anaconda</b>.
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<h2 id="___sec1">Exercise 2 </h2>
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<p>
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We will generate our own dataset for function \( y(x) \) where \( x \in [0,2] \) and defined by random numbers computed with the uniform distribution. The function \( y \) is a quadratic polynomial in \( x \) with added stochastic noise according to the normal distribution \( \cal {N}(0,1) \).
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We will generate our own dataset for a function \( y(x) \) where \( x \in [0,1] \) and defined by random numbers computed with the uniform distribution. The function \( y \) is a quadratic polynomial in \( x \) with added stochastic noise according to the normal distribution \( \cal {N}(0,1) \).
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The following simple Python instructions define our \( x \) and \( y \) values (with 100 data points).
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<p>
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@@ -182,9 +180,9 @@ The following simple Python instructions define our \( x \) and \( y \) values (
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y <span style="color: #666666">=</span> <span style="color: #666666">5*</span>x<span style="color: #666666">*</span>x<span style="color: #666666">+0.1*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">100</span>,<span style="color: #666666">1</span>)
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</pre></div>
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<ol>
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<li> Write your own code (following the examples under the <a href="https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html" target="_blank">regression slides</a> for computing the parametrization of the data set fitting a second-order polynomial.</li>
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<li> Write your own code (following the examples under the <a href="https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html" target="_blank">regression slides</a>) for computing the parametrization of the data set fitting a second-order polynomial.</li>
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<li> Use thereafter <b>scikit-learn</b> (see again the examples in the regression slides) and compare with your own code.</li>
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<li> Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as</li>
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<li> Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as</li>
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</ol>
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$$ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
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@@ -202,7 +200,7 @@ $$
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\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
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$$
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<p>
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You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
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Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
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<h2 id="___sec2">Exercise 3, variance of the parameters \( \beta \) in linear regression </h2>
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Binary file not shown.
@@ -164,7 +164,7 @@ Aug 27, 2018
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\subsection{Exercise 1}
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The first exercise here is of a mere technical art. We want you have installed
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The first exercise here is of a mere technical art. We want you to have
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\begin{itemize}
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\item git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo \href{{https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html}}{GitHub facilities}.
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@@ -178,10 +178,7 @@ IPython/Jupyter notebooks invaluable in your work. You can run \textbf{R}
|
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codes in the Jupyter/IPython notebooks, with the immediate benefit of
|
||||
visualizing your data. You can also use compiled languages like C++,
|
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Rust, Fortran etc if you prefer. The focus in these lectures will be
|
||||
on Python, but we will provide many code examples for those of you who
|
||||
prefer R or compiled languages. You can integrate C++ codes and R in for example
|
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a Jupyter notebook.
|
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|
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on Python.
|
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If you have Python installed (we recommend Python3) and you feel
|
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pretty familiar with installing different packages, we recommend that
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@@ -246,7 +243,7 @@ We recommend using \textbf{Anaconda}.
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\subsection{Exercise 2}
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We will generate our own dataset for function $y(x)$ where $x \in [0,2]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\cal {N}(0,1)$.
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We will generate our own dataset for a function $y(x)$ where $x \in [0,1]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\cal {N}(0,1)$.
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The following simple Python instructions define our $x$ and $y$ values (with 100 data points).
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\bpycod
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x = np.random.rand(100,1)
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@@ -254,11 +251,11 @@ y = 5*x*x+0.1*np.random.randn(100,1)
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\epycod
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\begin{enumerate}
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\item Write your own code (following the examples under the \href{{https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html}}{regression slides} for computing the parametrization of the data set fitting a second-order polynomial.
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\item Write your own code (following the examples under the \href{{https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html}}{regression slides}) for computing the parametrization of the data set fitting a second-order polynomial.
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\item Use thereafter \textbf{scikit-learn} (see again the examples in the regression slides) and compare with your own code.
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\item Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as
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\item Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as
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\end{enumerate}
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\noindent
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@@ -274,7 +271,7 @@ where we have defined the mean value of $\hat{y}$ as
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\[
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\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
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\]
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|
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You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
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Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
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Binary file not shown.
@@ -134,7 +134,7 @@ Aug 27, 2018
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\subsection*{Exercise 1}
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The first exercise here is of a mere technical art. We want you have installed
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The first exercise here is of a mere technical art. We want you to have
|
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\begin{itemize}
|
||||
\item git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo \href{{https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html}}{GitHub facilities}.
|
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|
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@@ -148,10 +148,7 @@ IPython/Jupyter notebooks invaluable in your work. You can run \textbf{R}
|
||||
codes in the Jupyter/IPython notebooks, with the immediate benefit of
|
||||
visualizing your data. You can also use compiled languages like C++,
|
||||
Rust, Fortran etc if you prefer. The focus in these lectures will be
|
||||
on Python, but we will provide many code examples for those of you who
|
||||
prefer R or compiled languages. You can integrate C++ codes and R in for example
|
||||
a Jupyter notebook.
|
||||
|
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on Python.
|
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|
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If you have Python installed (we recommend Python3) and you feel
|
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pretty familiar with installing different packages, we recommend that
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@@ -216,7 +213,7 @@ We recommend using \textbf{Anaconda}.
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\subsection*{Exercise 2}
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We will generate our own dataset for function $y(x)$ where $x \in [0,2]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\cal {N}(0,1)$.
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We will generate our own dataset for a function $y(x)$ where $x \in [0,1]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\cal {N}(0,1)$.
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The following simple Python instructions define our $x$ and $y$ values (with 100 data points).
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\begin{print}
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x = np.random.rand(100,1)
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@@ -224,11 +221,11 @@ y = 5*x*x+0.1*np.random.randn(100,1)
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\end{print}
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\begin{enumerate}
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\item Write your own code (following the examples under the \href{{https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html}}{regression slides} for computing the parametrization of the data set fitting a second-order polynomial.
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\item Write your own code (following the examples under the \href{{https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html}}{regression slides}) for computing the parametrization of the data set fitting a second-order polynomial.
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|
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\item Use thereafter \textbf{scikit-learn} (see again the examples in the regression slides) and compare with your own code.
|
||||
|
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\item Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as
|
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\item Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as
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\end{enumerate}
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\noindent
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@@ -244,7 +241,7 @@ where we have defined the mean value of $\hat{y}$ as
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\[
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\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
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\]
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|
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You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
|
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Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
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@@ -5,7 +5,7 @@ DATE:Today
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===== Exercise 1 =====
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The first exercise here is of a mere technical art. We want you have installed
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The first exercise here is of a mere technical art. We want you to have
|
||||
* git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo "GitHub facilities":"https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html".
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* Install various Python packages
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|
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@@ -15,10 +15,7 @@ IPython/Jupyter notebooks invaluable in your work. You can run _R_
|
||||
codes in the Jupyter/IPython notebooks, with the immediate benefit of
|
||||
visualizing your data. You can also use compiled languages like C++,
|
||||
Rust, Fortran etc if you prefer. The focus in these lectures will be
|
||||
on Python, but we will provide many code examples for those of you who
|
||||
prefer R or compiled languages. You can integrate C++ codes and R in for example
|
||||
a Jupyter notebook.
|
||||
|
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on Python.
|
||||
|
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If you have Python installed (we recommend Python3) and you feel
|
||||
pretty familiar with installing different packages, we recommend that
|
||||
@@ -68,16 +65,16 @@ We recommend using _Anaconda_.
|
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|
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===== Exercise 2 =====
|
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|
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We will generate our own dataset for function $y(x)$ where $x \in [0,2]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\cal {N}(0,1)$.
|
||||
We will generate our own dataset for a function $y(x)$ where $x \in [0,1]$ and defined by random numbers computed with the uniform distribution. The function $y$ is a quadratic polynomial in $x$ with added stochastic noise according to the normal distribution $\cal {N}(0,1)$.
|
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The following simple Python instructions define our $x$ and $y$ values (with 100 data points).
|
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!bc pycod
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x = np.random.rand(100,1)
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y = 5*x*x+0.1*np.random.randn(100,1)
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!ec
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o Write your own code (following the examples under the "regression slides":"https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html" for computing the parametrization of the data set fitting a second-order polynomial.
|
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o Write your own code (following the examples under the "regression slides":"https://compphysics.github.io/MachineLearning/doc/pub/Regression/html/Regression-bs.html") for computing the parametrization of the data set fitting a second-order polynomial.
|
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o Use thereafter _scikit-learn_ (see again the examples in the regression slides) and compare with your own code.
|
||||
o Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as
|
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o Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as
|
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!bt
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\[ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
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\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2,
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@@ -96,7 +93,7 @@ where we have defined the mean value of $\hat{y}$ as
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\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
|
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\]
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!et
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|
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You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
|
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Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.
|
||||
|
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|
||||
|
||||
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Block a user