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added more scikit-learn functionality

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mhjensen
2018-05-28 08:41:15 -04:00
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doc/src/How2ReadData/How2ReadData.do.txt
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@@ -85,7 +85,7 @@ into the hassle of exploring how to set up dependencies and paths, we
recommend two widely used distrubutions which set up all relevant
dependencies for Python, namely
o "Anaconda":"https://docs.anaconda.com/",
* "Anaconda":"https://docs.anaconda.com/",
which is an open source
distribution of the Python and R programming languages for large-scale
@@ -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 "Enthought canopy":"https://www.enthought.com/product/canopy/"
* "Enthought canopy":"https://www.enthought.com/product/canopy/"
is a Python
distribution for scientific and analytic computing distribution and
@@ -304,13 +304,15 @@ 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.
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
from sklearn.metrics import mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error
x = np.random.rand(100,1)
y = 2.0+ 5*x+0.5np.random.randn(100,1)
@@ -323,6 +325,10 @@ print('Coefficient beta : \n', linreg.coef_)
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))
# Mean squared log error
print('Mean squared log error: %.2f' % mean_squared_log_error(y, ypredict) )
# Mean absolute error
print('Mean absolute error: %.2f' % mean_absolute_error(y, ypredict))
plt.plot(x, ypredict, "r-")
plt.plot(x, y ,'ro')
plt.axis([0.0,1.0,1.5, 7.0])
@@ -351,19 +357,41 @@ 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
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
where we have defined the mean value of $\hat{y}$ as
!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 quantity will meet again in our discussions of regression analysis is
mean absolute error (MAE), a risk metric corresponding to the expected value of the absolute error loss or what we call the $l1$-norm loss. In our discussion above we presented the relative error.
The MAE is defined as follows
!bt
\[
\text{MAE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n-1} \left| y_i - \tilde{y}_i \right|.
\]
!et
Finally we present the
squared logarithmic (quadratic) error
!bt
\[
\text{MSLE}(\hat{y}, \hat{\tilde{y}}) = \frac{1}{n} \sum_{i=0}^{n - 1} (\log_e (1 + y_i) - \log_e (1 + \tilde{y}_i) )^2,
\]
!et
where $\log_e (x)$ stands for the natural logarithm of $x$. This error
estimate is best to use when targets having exponential growth, such
as population counts, average sales of a commodity over a span of
years etc.
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