def generate_train_vs_degree(x, y, z, reg, max_degree, hyperparam, filename):
'''
Function for plotting mse when the model is evaluated on the training set
ax = matplotlib.axis object
reg = regression function reg(X, data, hyperparam)
max_degree = maximum degree of polynomial
hyperparam = hyperparameter for calibrating model
'''
degrees = np.arange(0, max_degree+1)
outfile = open(filename, "a")
outfile.write("degree mse r2\n")
for degree in degrees:
"""Simple training with no cross validation"""
X = pf.generate_design_2Dpolynomial(x, y, degree)
beta = reg(X, z, hyperparam=hyperparam)
z_model = X @ beta
mse = pf.mse(z, z_model)
r2 = pf.mse(z, z_model)
outstring = f"{degree} {mse} {r2}\n"
outfile.write(outstring)
outfile.close()
def generate_train_vs_lambda(x, y, z, reg, degree, hyperparams, filename):
'''
Function for plotting mse ws hyperparam when the model is evaluated on
the training set
ax = matplotlib.axis object
reg = regression function reg(X, data, hyperparam)
degree = degree of polynomial
hyperparams = hyperparameter for calibrating model
'''
outfile = open(filename, "a")
outfile.write("lambda mse r2\n")
for hyperparam in hyperparams:
"""Simple training with no cross validation"""
X = pf.generate_design_2Dpolynomial(x, y, degree)
beta = reg(X, z, hyperparam=hyperparam)
z_model = X @ beta
mse = pf.mse(z, z_model)
r2 = pf.mse(z, z_model)
outstring = f"{hyperparam} {mse} {r2}\n"
outfile.write(outstring)
outfile.close()
def plot_bias_confidence(ax,
x,
y,
z,
reg,
degree,
hyperparam,
noise,
confidence=1.96,
**kwargs):
"""
Function plotting betas and their confidence intervalls
"""
X = pf.generate_design_2Dpolynomial(x, y, degree)
beta = reg(X, z, hyperparam=hyperparam)
weight = noise * np.sqrt(np.diag(np.linalg.inv(X.T @ X))) * confidence
print(2 * weight)
ax.errorbar(beta,
np.arange(1,
len(beta) + 1),
xerr=weight,
fmt='.',
**kwargs)
def plot_train_vs_degree(ax,
x,
y,
z,
reg,
max_degree,
hyperparam,
plot_r2=False,
**kwargs):
'''
Function for plotting mse when the model is evaluated on the training set
ax = matplotlib.axis object
reg = regression function reg(X, data, hyperparam)
max_degree = maximum degree of polynomial
hyperparam = hyperparameter for calibrating model
'''
degrees = np.arange(0, max_degree + 1)
error = []
for degree in degrees:
"""Simple training with no cross validation"""
X = pf.generate_design_2Dpolynomial(x, y, degree)
beta = reg(X, z, hyperparam=hyperparam)
z_model = X @ beta
if plot_r2:
#computing the MSE when no train test split is used
error.append(pf.r2(z, z_model))
label = 'R2 train'
else:
#computing the r2 score when no train test split is used
error.append(pf.mse(z, z_model))
label = 'MSE train'
ax.plot(degrees, error, **kwargs, label=label)
def plot_train_vs_lambda(ax,
x,
y,
z,
reg,
degree,
hyperparams,
r2=False,
**kwargs):
'''
Function for plotting mse ws hyperparam when the model is evaluated on
the training set
ax = matplotlib.axis object
reg = regression function reg(X, data, hyperparam)
degree = degree of polynomial
hyperparams = hyperparameter for calibrating model
'''
error = []
for hyperparam in hyperparams:
"""Simple training with no cross validation"""
X = pf.generate_design_2Dpolynomial(x, y, degree)
beta = reg(X, z, hyperparam=hyperparam)
z_model = X @ beta
if not r2:
#computing the MSE when no train test split is used
error.append(pf.mse(z, z_model))
label = 'MSE train'
if r2:
#computing the r2 score when no train test split is used
error.append(pf.r2(z, z_model))
label = 'R2 train'
ax.plot(hyperparams, error, **kwargs, label=label)
oslo_data = oslo_data[::reduction,::reduction]
x_grid = x_grid[::reduction,::reduction]
y_grid = y_grid[::reduction,::reduction]
#flatten the data
x = x_grid.ravel()
y = y_grid.ravel()
z = oslo_data.ravel()
#plotting
reg = pf.ridge_regression
hyperparam = 0
X = pf.generate_design_2Dpolynomial(x, y, degree=10)
beta = reg(X, z, hyperparam=hyperparam)
z_pred = X @ beta
z_pred_grid = z_pred.reshape(x_grid.shape)
plt.figure()
plt.imshow(z_pred_grid,cmap='gray')
plt.xlabel('X')
plt.ylabel('Y')
#plt.savefig(figdir+'terrainpicture_ridge.pdf')
plt.show()
'''
plt.figure()
#plt.title('Terrain over inner Oslo fjord')
plt.imshow(oslo_data, cmap='gray')