def best_degree(x, y, phi, dmax, folds):
for d in range(0, dmax+1):
if d == 0:
X = numpy.matrix(phi(0, x))
else:
X = numpy.vstack((X, phi(d, x)))
yield cross_validation(X, y, folds), d
def main(datadir, dmax, folds, plot_precision):
colors = pyplot.rcParams["axes.color_cycle"]
# Input
print("-> Reading data in folder \"{}\"".format(datadir))
x, y = read_data(datadir)
# Risk
print("-> Computing the average risk for polynomials of degrees between 0 and {},".format(dmax))
print(" using cross validation with {} folds :".format(folds))
risks = list(best_degree(x, y, phi, dmax, folds))
best_risk, best_d = min(risks)
risks, degrees = zip(*risks)
fig = pyplot.figure()
pyplot.yscale('log')
pyplot.plot(degrees, risks, zorder=2)
pyplot.plot([best_d], [best_risk], 'o', zorder=1)
pyplot.xlabel('degree')
pyplot.ylabel('average risk')
pyplot.show()
print(" -> The lowest risk ({:.2f}) is obtained with degree {}.".format(best_risk, best_d))
print("-> Computing the best function of degree {} predicting the value of y.".format(best_d))
X = numpy.matrix([phi(d,x) for d in range(0, best_d+1)])
theta = least_square(X, y)
print(" -> The best function is (approximately) : {}".format(f_str(theta)))
pyplot.plot(x, y, 'o', color=colors[1], zorder=2)
plot.plot_function(f(theta), plot_precision, color=colors[0], zorder=1)
pyplot.show()
