def __init__(self, Y, con, initial=1):
self.Y = Y
self.constraint = constraints((con.inequality,
con.inequality_offset),
None)
self.sigma = initial
self.constraint.covariance = self.sigma**2 * np.identity(con.dim)
def cone_with_slice(angles, which, fill_args={}, ax=None, label=None,
Y=None):
ax, poly, constraint, rays = cone_rays(angles, which, ax=ax, fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:,0], poly[:,1], label=r'$C(y)$', **fill_args)
ax.arrow(0,0,eta[0]/200.,eta[1]/200., label=r'$\eta$', linewidth=5, head_width=0.05, fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) /
np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp*eta /
np.linalg.norm(eta)**2),
(Yperp + Vm*eta /
np.linalg.norm(eta)**2)])
ax.plot(width_points[:,0], width_points[:,1], 'r--', linewidth=2)
ax.scatter(width_points[:,0], width_points[:,1], label=r'${\cal V}$', s=150, marker='x', linewidth=2, c='k')
return ax, poly, constraint, rays
def main():
# import the CGH data
mat = scipy.io.loadmat('y.mat')
v = mat['v']
v = v.ravel()
y = v - np.mean(v)
# initialize the design matrix
n = len(y)
D = (np.identity(n) - np.diag(np.ones(n - 1), 1))[:-1]
X = np.linalg.pinv(D)
# get the constraint matrix and vector to compute conf_intervals
A, b, X_e, beta, E, Proj = slope_constraints(X, y, 0.001)
C = constraints((A.dot(X_e.T), b), None, covariance=0.007 * np.eye(n))
# beta_interval = []
mean_interval = []
jump = []
'''
for i in range(len(E)):
beta_intv = C.interval(X_e[:,i], y)
beta_interval.append(beta_intv)
'''
for i in range(len(E)):
if i == 0 or E[i] - E[i - 1] > 5:
mean_intv = C.interval(Proj[:, E[i]], y)
mean_interval.append(mean_intv)
jump.append(E[i])
else:
eta = np.mean(Proj[:, E[i]:(E[i + 1] + 1)], axis=1)
mean_intv = C.interval(eta, y)
mean_interval[-1] = mean_intv
jump[-1] = E[i]
mean_interval.append(C.interval(Proj[:, -1], y))
print mean_interval
print jump
print E
fit_line = np.dot(X, beta) + np.mean(v)
low = [l for l, h in mean_interval]
high = [h for l, h in mean_interval]
low_fit = np.zeros((n, 1))
high_fit = np.zeros((n, 1))
left = 0
for idx, e in enumerate(jump):
right = e
low_fit[left:right] = low[idx]
high_fit[left:right] = high[idx]
left = right
low_fit[left:] = low[-1]
high_fit[left:] = high[-1]
low_fit += np.mean(v)
high_fit += np.mean(v)
print "before plotting"
plt.figure()
plt.scatter(range(n), v, s=40, facecolors='none', edgecolors='r')
plt.plot(range(n), fit_line, linewidth=2)
plt.plot(range(n), low_fit, linewidth=2, color='g')
plt.plot(range(n), high_fit, linewidth=2, color='y')
plt.xlim(0, n)
plt.show()
def main():
# import the CGH data
mat = scipy.io.loadmat('y.mat')
v = mat['v']
v = v.ravel()
y = v - np.mean(v)
# initialize the design matrix
n = len(y)
D = (np.identity(n) - np.diag(np.ones(n-1),1))[:-1]
X = np.linalg.pinv(D)
# get the constraint matrix and vector to compute conf_intervals
A, b, X_e, beta, E, Proj = slope_constraints(X, y, 0.001)
C = constraints((A.dot(X_e.T),b), None, covariance=0.007 * np.eye(n))
# beta_interval = []
mean_interval = []
jump = []
'''
for i in range(len(E)):
beta_intv = C.interval(X_e[:,i], y)
beta_interval.append(beta_intv)
'''
for i in range(len(E)):
if i == 0 or E[i] - E[i-1] > 5:
mean_intv = C.interval(Proj[:,E[i]], y)
mean_interval.append(mean_intv)
jump.append(E[i])
else:
eta = np.mean(Proj[:,E[i]:(E[i+1]+1)], axis=1)
mean_intv = C.interval(eta, y)
mean_interval[-1] = mean_intv
jump[-1] = E[i]
mean_interval.append(C.interval(Proj[:,-1], y))
print mean_interval
print jump
print E
fit_line = np.dot(X, beta) + np.mean(v)
low = [l for l,h in mean_interval]
high = [h for l,h in mean_interval]
low_fit = np.zeros((n,1))
high_fit = np.zeros((n,1))
left = 0
for idx, e in enumerate(jump):
right = e
low_fit[left:right] = low[idx]
high_fit[left:right] = high[idx]
left = right
low_fit[left:] = low[-1]
high_fit[left:] = high[-1]
low_fit += np.mean(v)
high_fit += np.mean(v)
print "before plotting"
plt.figure()
plt.scatter(range(n), v, s=40, facecolors='none', edgecolors='r')
plt.plot(range(n), fit_line, linewidth=2)
plt.plot(range(n), low_fit, linewidth=2, color='g')
plt.plot(range(n), high_fit, linewidth=2, color='y')
plt.xlim(0,n)
plt.show()
def cone_with_point(angles, which, fill_args={}, ax=None, label=None,
Y=None):
ax, poly, constraint, rays = cone_rays(angles, which, ax=ax, fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
return ax, poly, constraint, rays
def cone_with_point(angles, which, fill_args={}, ax=None, label=None, Y=None):
ax, poly, constraint, rays = cone_rays(angles,
which,
ax=ax,
fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
return ax, poly, constraint, rays
def cone_with_arrow(angles, which, fill_args={}, ax=None, label=None,
Y=None):
ax, poly, constraint, rays = cone_rays(angles, which, ax=ax, fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:,0], poly[:,1], label=r'$C(y)$', **fill_args)
ax.arrow(0,0,eta[0]/200.,eta[1]/200., label=r'$\eta$', linewidth=5, head_width=0.05, fc='k')
return ax, poly, constraint, rays
def hull_with_point(W, fill=True, fill_args={}, label=None, ax=None, Y=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A, b), None)
if Y is None:
Y = simulate_from_constraints(representation)
a = f.gca()
a.scatter(Y[0], Y[1], label=r'$y$', s=100)
return f, A, b, pairs, angles, perimeter
def hull_with_point(W, fill=True, fill_args={}, label=None, ax=None,
Y=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A,b), None)
if Y is None:
Y = simulate_from_constraints(representation)
a = f.gca()
a.scatter(Y[0], Y[1], label=r'$y$', s=100)
return f, A, b, pairs, angles, perimeter
def hull_with_slice(W,
fill=True,
fill_args={},
label=None,
ax=None,
Y=None,
eta=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A, b), None)
if Y is None:
Y = simulate_from_constraints(representation)
ax.scatter(Y[0], Y[1], label=r'$y$', s=100)
if eta is None:
eta = np.random.standard_normal(2)
ax.arrow(0, 0, eta[0], eta[1], linewidth=5, head_width=0.05, fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) / np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp * eta / np.linalg.norm(eta)**2),
(Yperp + Vm * eta / np.linalg.norm(eta)**2)])
ax.plot(width_points[:, 0], width_points[:, 1], 'r--', linewidth=2)
ax.scatter(width_points[:, 0],
width_points[:, 1],
label=r'${\cal V}$',
s=150,
marker='x',
linewidth=2,
c='k')
return f, A, b, pairs, angles, perimeter
def cone_with_slice(angles, which, fill_args={}, ax=None, label=None, Y=None):
ax, poly, constraint, rays = cone_rays(angles,
which,
ax=ax,
fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:, 0], poly[:, 1], label=r'$C(y)$', **fill_args)
ax.arrow(0,
0,
eta[0] / 200.,
eta[1] / 200.,
label=r'$\eta$',
linewidth=5,
head_width=0.05,
fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) / np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp * eta / np.linalg.norm(eta)**2),
(Yperp + Vm * eta / np.linalg.norm(eta)**2)])
ax.plot(width_points[:, 0], width_points[:, 1], 'r--', linewidth=2)
ax.scatter(width_points[:, 0],
width_points[:, 1],
label=r'${\cal V}$',
s=150,
marker='x',
linewidth=2,
c='k')
return ax, poly, constraint, rays
def cone_with_arrow(angles, which, fill_args={}, ax=None, label=None, Y=None):
ax, poly, constraint, rays = cone_rays(angles,
which,
ax=ax,
fill_args=fill_args)
eta = rays[0]
representation = constraints((constraint, np.zeros(2)), None)
if Y is None:
Y = simulate_from_constraints(representation)
pyplot.scatter(Y[0], Y[1], s=100, label=label)
ax.fill(poly[:, 0], poly[:, 1], label=r'$C(y)$', **fill_args)
ax.arrow(0,
0,
eta[0] / 200.,
eta[1] / 200.,
label=r'$\eta$',
linewidth=5,
head_width=0.05,
fc='k')
return ax, poly, constraint, rays
def hull_with_slice(W, fill=True, fill_args={}, label=None, ax=None,
Y=None,
eta=None):
f, A, b, pairs, angles, perimeter = just_hull(W,
fill=fill,
label=label,
ax=ax,
fill_args=fill_args)
representation = constraints((A,b), None)
if Y is None:
Y = simulate_from_constraints(representation)
ax.scatter(Y[0], Y[1], label=r'$y$', s=100)
if eta is None:
eta = np.random.standard_normal(2)
ax.arrow(0,0,eta[0],eta[1], linewidth=5, head_width=0.05, fc='k')
Vp, _, Vm = representation.pivots(eta, Y)[:3]
Yperp = Y - (np.dot(eta, Y) /
np.linalg.norm(eta)**2 * eta)
if Vm == np.inf:
Vm = 10000
width_points = np.array([(Yperp + Vp*eta /
np.linalg.norm(eta)**2),
(Yperp + Vm*eta /
np.linalg.norm(eta)**2)])
ax.plot(width_points[:,0], width_points[:,1], 'r--', linewidth=2)
ax.scatter(width_points[:,0], width_points[:,1], label=r'${\cal V}$', s=150, marker='x', linewidth=2, c='k')
return f, A, b, pairs, angles, perimeter
y = np.random.standard_normal(n) * sigma
L = lasso(y, X, frac=0.5)
L.fit(tol=1.e-14, min_its=200)
C = L.inactive_constraints
PR = np.identity(n) - L.PA
try:
U, D, V = np.linalg.svd(PR)
except np.linalg.LinAlgError:
D, U = np.linalg.eigh(PR)
keep = D >= 0.5
U = U[:,keep]
Z = np.dot(U.T, y)
Z_inequality = np.dot(C.inequality, U)
Z_constraint = constraints((Z_inequality, C.inequality_offset), None)
class variance_estimator(object):
def __init__(self, Y, con, initial=1):
self.Y = Y
self.constraint = constraints((con.inequality,
con.inequality_offset),
None)
self.sigma = initial
self.constraint.covariance = self.sigma**2 * np.identity(con.dim)
def draw_sample(self, ndraw=2000, burnin=1000):
"""
Draw a sample from the truncated normal
storing it as the attribute `sample`.
def __init__(self, Y, con, initial=1):
self.Y = Y
self.constraint = constraints((con.inequality, con.inequality_offset),
None)
self.sigma = initial
self.constraint.covariance = self.sigma**2 * np.identity(con.dim)
y = np.random.standard_normal(n) * sigma
L = lasso(y, X, frac=0.5)
L.fit(tol=1.e-14, min_its=200)
C = L.inactive_constraints
PR = np.identity(n) - L.PA
try:
U, D, V = np.linalg.svd(PR)
except np.linalg.LinAlgError:
D, U = np.linalg.eigh(PR)
keep = D >= 0.5
U = U[:, keep]
Z = np.dot(U.T, y)
Z_inequality = np.dot(C.inequality, U)
Z_constraint = constraints((Z_inequality, C.inequality_offset), None)
class variance_estimator(object):
def __init__(self, Y, con, initial=1):
self.Y = Y
self.constraint = constraints((con.inequality, con.inequality_offset),
None)
self.sigma = initial
self.constraint.covariance = self.sigma**2 * np.identity(con.dim)
def draw_sample(self, ndraw=2000, burnin=1000):
"""
Draw a sample from the truncated normal
storing it as the attribute `sample`.
"""
