def create(m, n, d):
Xp = problem_util.normalized_data_matrix(m, d, 1)
Xn = problem_util.normalized_data_matrix(n, d, 1)
lam = 1
theta = cp.Variable(d)
f = ep.infinite_push(theta, Xp, Xn) + lam * cp.sum_squares(theta)
f_eval = lambda: f.value
return cp.Problem(cp.Minimize(f)), f_eval
def create(m, n, d):
Xp = problem_util.normalized_data_matrix(m, d, 1)
Xn = problem_util.normalized_data_matrix(n, d, 1)
lam = 1
theta = cp.Variable(d)
f = ep.infinite_push(theta, Xp, Xn) + lam*cp.sum_squares(theta)
f_eval = lambda: f.value
return cp.Problem(cp.Minimize(f)), f_eval
def create(**kwargs):
# m>k
k = kwargs['k'] #class
m = kwargs['m'] #instance
n = kwargs['n'] #dim
p = 5 #p-largest
q = 10
X = problem_util.normalized_data_matrix(m,n,1)
Y = np.random.randint(0, k-1, (q,m))
Theta = cp.Variable(n,k)
t = cp.Variable(q)
texp = cp.Variable(m)
f = cp.sum_largest(t, p)+cp.sum_entries(texp) + cp.sum_squares(Theta)
C = []
C.append(cp.log_sum_exp(X*Theta, axis=1) <= texp)
for i in range(q):
Yi = one_hot(Y[i], k)
C.append(-cp.sum_entries(cp.mul_elemwise(X.T.dot(Yi), Theta)) == t[i])
t_eval = lambda: np.array([
-cp.sum_entries(cp.mul_elemwise(X.T.dot(one_hot(Y[i], k)), Theta)).value for i in range(q)])
f_eval = lambda: cp.sum_largest(t_eval(), p).value \
+ cp.sum_entries(cp.log_sum_exp(X*Theta, axis=1)).value \
+ cp.sum_squares(Theta).value
return cp.Problem(cp.Minimize(f), C), f_val
def create(m, n):
mu = 1
rho = 1
sigma = 0.1
A = problem_util.normalized_data_matrix(m, n, mu)
x0 = sp.rand(n, 1, rho)
x0.data = np.random.randn(x0.nnz)
x0 = x0.toarray().ravel()
b = np.sign(A.dot(x0) + sigma * np.random.randn(m))
A[b > 0, :] += 0.7 * np.tile([x0], (np.sum(b > 0), 1))
A[b < 0, :] -= 0.7 * np.tile([x0], (np.sum(b < 0), 1))
P = la.block_diag(np.random.randn(n - 1, n - 1), 0)
lam = 1
x = cp.Variable(A.shape[1])
# Straightforward formulation w/ no constraints
# TODO(mwytock): Fix compiler so this works
z0 = 1 - sp.diags([b], [0]) * A * x + cp.norm1(P.T * x)
f_eval = lambda: (lam * cp.sum_squares(x) + cp.sum_entries(
cp.max_elemwise(z0, 0))).value
# Explicit epigraph constraint
t = cp.Variable(1)
z = 1 - sp.diags([b], [0]) * A * x + t
f = lam * cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z, 0))
C = [cp.norm1(P.T * x) <= t]
return cp.Problem(cp.Minimize(f), C), f_eval
def create(m, n):
mu = 1
rho = 1
sigma = 0.1
A = problem_util.normalized_data_matrix(m, n, mu)
x0 = sp.rand(n, 1, rho)
x0.data = np.random.randn(x0.nnz)
x0 = x0.toarray().ravel()
b = np.sign(A.dot(x0) + sigma*np.random.randn(m))
A[b>0,:] += 0.7*np.tile([x0], (np.sum(b>0),1))
A[b<0,:] -= 0.7*np.tile([x0], (np.sum(b<0),1))
P = la.block_diag(np.random.randn(n-1,n-1), 0)
lam = 1
x = cp.Variable(A.shape[1])
# Straightforward formulation w/ no constraints
# TODO(mwytock): Fix compiler so this works
z0 = 1 - sp.diags([b],[0])*A*x + cp.norm1(P.T*x)
f_eval = lambda: (lam*cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z0, 0))).value
# Explicit epigraph constraint
t = cp.Variable(1)
z = 1 - sp.diags([b],[0])*A*x + t
f = lam*cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z, 0))
C = [cp.norm1(P.T*x) <= t]
return cp.Problem(cp.Minimize(f), C), f_eval
def create(**kwargs):
# m>k
k = kwargs['k'] #class
m = kwargs['m'] #instance
n = kwargs['n'] #dim
p = 5 #p-largest
X = problem_util.normalized_data_matrix(m, n, 1)
Y = np.random.randint(0, k, m)
Theta = cp.Variable(n, k)
t = cp.Variable(1)
texp = cp.Variable(m)
f = t + cp.sum_largest(texp, p) + cp.sum_squares(Theta)
C = []
C.append(cp.log_sum_exp(X * Theta, axis=1) <= texp)
Yi = one_hot(Y, k)
C.append(-cp.sum_entries(cp.mul_elemwise(X.T.dot(Yi), Theta)) == t)
t_eval = lambda: \
-cp.sum_entries(cp.mul_elemwise(X.T.dot(one_hot(Y, k)), Theta)).value
f_eval = lambda: t_eval() \
+ cp.sum_largest(cp.log_sum_exp(X*Theta, axis=1), p).value \
+ cp.sum_squares(Theta).value
return cp.Problem(cp.Minimize(f), C), f_eval
def create(**kwargs):
m = kwargs["m"]
n = kwargs["n"]
k = 10
A = [problem_util.normalized_data_matrix(m,n,1) for i in range(k)]
B = problem_util.normalized_data_matrix(k,n,1)
c = np.random.rand(k)
x = cp.Variable(n)
t = cp.Variable(k)
f = cp.max_entries(t+cp.abs(B*x-c))
C = []
for i in range(k):
C.append(cp.pnorm(A[i]*x, 2) <= t[i])
t_eval = lambda: np.array([cp.pnorm(A[i]*x, 2).value for i in range(k)])
f_eval = lambda: cp.max_entries(t_eval() + cp.abs(B*x-c)).value
return cp.Problem(cp.Minimize(f), C), f_eval
def create(m, ni, K):
np.random.seed(0)
part = np.random.randint(1, ni, K)
n = np.sum(part)
p = 0.2
# Each part is pa[i]:pb[i]
pb = np.cumsum(part)
pa = np.hstack((0, pb[:-1]))
x0 = np.zeros(n)
for i in xrange(K):
if np.random.rand() < p:
x0[pa[i]:pb[i]] = np.random.randn(part[i])
A = problem_util.normalized_data_matrix(m, n, 1)
b = A.dot(x0) + np.sqrt(0.001) * np.random.randn(m)
lam = 0.1 * max(LA.norm(A[:, pa[i]:pb[i]].T.dot(b)) for i in xrange(K))
x = cp.Variable(n)
f = (0.5 * cp.sum_squares(A * x - b) +
lam * sum(cp.norm2(x[pa[i]:pb[i]]) for i in xrange(K)))
return cp.Problem(cp.Minimize(f))
def create(m, ni, K):
np.random.seed(0)
part = np.random.randint(1, ni, K)
n = np.sum(part)
p = 0.2
# Each part is pa[i]:pb[i]
pb = np.cumsum(part)
pa = np.hstack((0, pb[:-1]))
x0 = np.zeros(n)
for i in xrange(K):
if np.random.rand() < p:
x0[pa[i]:pb[i]] = np.random.randn(part[i])
A = problem_util.normalized_data_matrix(m, n, 1)
b = A.dot(x0) + np.sqrt(0.001)*np.random.randn(m)
lam = 0.1*max(LA.norm(A[:,pa[i]:pb[i]].T.dot(b)) for i in xrange(K))
x = cp.Variable(n)
f = (0.5*cp.sum_squares(A*x - b) +
lam*sum(cp.norm2(x[pa[i]:pb[i]]) for i in xrange(K)))
return cp.Problem(cp.Minimize(f))
