Run this code with ipython --pylab or use from pylab import *.
In [1]: A = randn(2,2)
In [2]: b = randn(2)
In [3]: X = randn(20,2)
In [4]: y = A.dot(X.T).T + b + randn(20,2)/5.
In [6]: solve(X.T.dot(X),X.T.dot(y)).T
Out[6]:
array([[-0.33567275, 1.44876796, 2.20848249],
[-1.6441768 , 0.46691108, 1.07798395]])
In [8]: A
Out[8]:
array([[-0.43447047, 1.46280608],
[-1.62196681, 0.46863636]])
In [9]: b
Out[9]: array([ 2.21737423, 1.16437595])In [1]: x = np.linspace(-10,10,25)
In [2]: y = 3*x**2 - 10*x + 30 + 50.*randn(25)
In [3]: plot(x,y,'ro')
Out[3]: [<matplotlib.lines.Line2D at 0x10d5e4c10>]
In [4]: from regression import PolyRegression
In [5]: m = PolyRegression(deg=4)
In [6]: m.condition_on(y,x,50*eye(25))
Out[6]: 46.8 x^0 + -5.36 x^1 + 2.79 x^2 + -0.058 x^3 + 0.00115 x^4
In [7]: t = linspace(-10,10,100)
In [8]: means, errs = m.predict(t,50*eye(100))
In [9]: plot(t,means)
Out[9]: [<matplotlib.lines.Line2D at 0x111865850>]See regression_experiments.py, e.g.
In [1]: import regression_experiments as r
In [2]: r.interactive(deg=4)The blue solid curve is the mean of the posterior predictive distribution, and blue dashed curves are +/- one standard deviation. Red curves are posterior samples.
