def regressionPlot(X, Y, M, w, basis_function):
pl.plot(X.T.tolist()[0],Y.T.tolist()[0], 'gs')
# You will need to write the designMatrix and regressionFit function
# constuct the design matrix (Bishop 3.16), the 0th column is just 1s.
#phi = _phi(X, M, basis_function)
# compute the weight vector
#w = max_likelihood_weight(X, Y, phi)
print 'w', w
# produce a plot of the values of the function
pts = np.array([[p] for p in pl.linspace(min(X), max(X), 100)])
Yp = pl.dot(w.T, _phi(pts, M, basis_function).T)
pl.plot(pts, Yp.tolist()[0])
pl.xlim(min(X), max(X))
pl.xlabel("X")
pl.ylabel("Y")
pl.title("Linear Regression (M={})".format(M))
pl.show()
def SSE(X, Y, M, Theta, basis_function):
phi = _phi(X, M, basis_function)
e = np.dot(phi, Theta) - Y
return np.dot(e.T, e)
def SSEfcn(X, Y, M, basis_function):
phi = _phi(X, M, basis_function)
return lambda Theta: np.linalg.norm(np.dot((np.dot(phi, Theta) - Y).T, np.dot(phi, Theta) - Y))
def SSEgrad(X, Y, M, Theta, basis_function):
phi = _phi(X, M, basis_function)
e = np.dot(phi, Theta) - Y
return 2*np.dot(phi.T, e)
