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Added more scikit-learn functions

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mhjensen
2018-05-27 23:19:29 -04:00
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doc/src/How2ReadData/How2ReadData.do.txt
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@@ -93,7 +93,7 @@ data processing, predictive analytics, and scientific computing, that
aims to simplify package management and deployment. Package versions
are managed by the package management system _conda_.
o "Enthoughtmcanopy":"https://www.enthought.com/product/canopy/"
o "Enthought canopy":"https://www.enthought.com/product/canopy/"
is a Python
distribution for scientific and analytic computing distribution and
@@ -296,37 +296,74 @@ plt.title(r'Relative error')
plt.show()
!ec
Depending on the parameter in front of the normal distribution, we may have a small or larger relative error. Try to play around with different training data sets and study (graphically) the value of the relative error.
Depending on the parameter in front of the normal distribution, we may
have a small or larger relative error. Try to play around with
different training data sets and study (graphically) the value of the
relative error.
As mentioned above, _scikit-learn_ has an impressive functionality.
We can for example extract the values of $\alpha$ and $\beta$ and their error estimates,
or the variance and standard deviation and many other properties from the statistical data analysis. Here we show an example of the functionality of scikit-learn.
!bc pycod
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
As mentioned above, _scikit-learn_ has an impressive functionality.
We can for example extract the values of $\alpha$ and $\beta$ and
their error estimates, or the variance and standard deviation and many
other properties from the statistical data analysis. Here we show an
example of the functionality of scikit-learn.
!bc pycod
import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score
x = np.random.rand(100,1)
y = 2*x+np.random.randn(100,1)
y = 2.0+ 5*x+0.5np.random.randn(100,1)
linreg = LinearRegression()
linreg.fit(x,y)
ypredict = linreg.predict(x)
print('Coefficients: \n', linreg.coef_)
print('The intercept alpha: \n', linreg.intercept_)
print('Coefficient beta : \n', linreg.coef_)
# The mean squared error
print("Mean squared error: %.2f" % mean_squared_error(y, ypredict))
# Explained variance score: 1 is perfect prediction
print('Variance score: %.2f' % r2_score(y, ypredict))
plt.plot(x, ypredict, "r-")
plt.plot(x, y ,'ro')
plt.axis([0,1.0,0, 5.0])
plt.axis([0.0,1.0,1.5, 7.0])
plt.xlabel(r'$x$')
plt.ylabel(r'$y$')
plt.title(r'Linear Regression fit ')
plt.show()
!ec
We will come to the definition of these outputs later.
The function _coef_ gives us the parameter $\beta$ of our fit while _intercept_ yields
$\alpha$. Depending on the constant in front of the normal distribution, we get values near or far from $alpha =2$ and $\beta =5$. Try to play around with different parameters in front of the normal distribution. The function _meansquarederror_ gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as
!bt
\[ MSE(\hat{y},\hat{\tilde{y}}) = \frac{1}{n}
\sum_{i=0}^{n-1}(y_i-\tilde{y}_i)^2,
\]
!et
The smaller the value, the better the fit. Ideally we would like to
have an MSE equal zero. The attentive reader has probably recognized
this function as being similar to the $\chi^2$ function defined above.
The _r2score_ function computes $R^2$, the coefficient of
determination. It provides a measure of how well future samples are
likely to be predicted by the model. Best possible score is 1.0 and it
can be negative (because the model can be arbitrarily worse). A
constant model that always predicts the expected value of $\hat{y}$,
disregarding the input features, would get a $R^2$ score of $0.0$.
If $\tilde{\hat{y}}_i$ is the predicted value of the i-th sample and $y_i$ is the corresponding true value, then the score $R^2$ is defined as
!bt
\[
R^2(\hat{y}, \tilde{\hat{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i - \tilde{y}_i)^2}{\sum_{i=0}^{n - 1} (y_i - \bar{y})^2},
\]
!et
where the mean value
!bt
\[
\bar{y} = \frac{1}{n} \sum_{i=0}^{n - 1} y_i.
\]
!et
We will discuss in more detail these and more function in the various lectures.
Another useful Python package is
"pandas":"https://pandas.pydata.org/", which is an open source library