如何在普通最小二乘回归图中使用OneHotEncoder输出

Question

I have been trying to perform Ordinary Least Squares regression using the scikit-learn library but have hit another rock.

I have used OneHotEncoder to binarize my (independent) dummy/categorical features and I have an array like so:

x = [[ 1.  0.  0. ...,  0.  0.  0.]
     [ 1.  0.  0. ...,  0.  0.  0.]
     [ 0.  1.  0. ...,  0.  0.  0.]
     ..., 
     [ 0.  0.  0. ...,  0.  0.  0.]
     [ 0.  0.  1. ...,  0.  0.  0.]
     [ 1.  0.  0. ...,  0.  0.  0.]]

The dependent variables (Y) are stored in a one dimensional array. Everything is wonderful, except now when I come to plot these values I get an error:

# Plot outputs
pl.scatter(x_test, y_test, color='black')

ValueError: x and y must be the same size

When I use numpy.size on X and Y respectively it is clear thats a reasonable error:

>>> print np.size(x)
5096
>>> print np.size(y)
98

Interestingly, the two sets of data are accepted by the fit method.

My question is how can I transform the output of OneHotEncoder to use in my regression?

Answer 1

If I understand you correctly, you have your X matrix as an input as an [mxn] matrix and some output Y of [nx 1], where m = number of features and n = number of data points.

Firstly, the linear regression fitting function will not care that X is of dimension [mxn] and Y of [nx 1] as it will simply use a parameter of dimension [1 xm], ie,

Y = theta * X

Unfortunately, as noted by eickenberg, you cannot plot all of the X features against the Y value using matplotlibs scatter call as you have, hence you get the error message of incompatible sizes, it wants to plot nxn not (nxm) x n.

To fix your problem, try looking at a single feature at a time:

pl.scatter(x_test[:,0], y_test, color='black')

Assuming you have standardised your data (subtracted the mean and divided by the average) a quick and dirty way to see the trends would be plot all of them on a single axes:

fig = plt.figure(0)
ax = fig.add_subplot(111)

n, m = x_test.size
for i in range(m):
   ax.scatter(x_test[:,m], y_test)

plt.show()

To visualise all at once on independent figures (depending on the number of features) then look at, eg, subplot2grid routines or another python module like pandas.