def test_sparse_factorization(verbose=False):
n = 7
y_mat = toy_factorization_problem(n=n,
rk=4,
noise=1,
square=True,
prop_zeros=0.5)
tuples_dense = mat2tuples(y_mat, sparse=False)
tuples_sparse = mat2tuples(y_mat, sparse=True)
if verbose:
print(y_mat)
print(tuples_dense)
print(tuples_sparse)
u, v = svd_factorize_matrix(y_mat, rank=4,
return_embeddings=True) # exact svd solution
# emb0 = np.concatenate([u, v])
x_mat_est1 = u.dot(v.T)
u_dense = factorize_tuples(tuples_dense,
4,
emb0=None,
n_iter=500,
verbose=verbose,
eval_freq=100)[0]
# rr_sampler = all_tensor_indices(tuples_sparse, batch_size=n * n, prop_negatives=1)
# sampler = positive_and_negative_tuple_sampler(tuples_sparse, minibatch_size=10, prop_negatives=0.5, idx_ranges=[(0, n), (n, 2 * n)])
# u_sparse = factorize_tuples(sampler, 4, emb0=None, n_iter=500, verbose=verbose, eval_freq=100)[0]
x_mat_est_dense = np.dot(u_dense[:7], u_dense[7:].T)
# x_mat_est_sparse = np.dot(u_sparse[:7], u_sparse[7:].T)
if verbose:
print(np.linalg.norm(x_mat_est1 - x_mat_est_dense))
# print(np.linalg.norm(x_mat_est1 - x_mat_est_sparse))
# print(np.linalg.norm(x_mat_est_dense - x_mat_est_sparse))
else:
assert (np.linalg.norm(x_mat_est1 - x_mat_est_dense) < 1e-3)
def test_sparse_factorization(verbose=False):
n = 7
y_mat = toy_factorization_problem(n=n, rk=4, noise=1, square=True, prop_zeros=0.5)
tuples_dense = mat2tuples(y_mat, sparse=False)
tuples_sparse = mat2tuples(y_mat, sparse=True)
if verbose:
print(y_mat)
print(tuples_dense)
print(tuples_sparse)
u, v = svd_factorize_matrix(y_mat, rank=4, return_embeddings=True) # exact svd solution
# emb0 = np.concatenate([u, v])
x_mat_est1 = u.dot(v.T)
u_dense = factorize_tuples(tuples_dense, 4, emb0=None, n_iter=500, verbose=verbose, eval_freq=100)[0]
# rr_sampler = all_tensor_indices(tuples_sparse, batch_size=n * n, prop_negatives=1)
# sampler = positive_and_negative_tuple_sampler(tuples_sparse, minibatch_size=10, prop_negatives=0.5, idx_ranges=[(0, n), (n, 2 * n)])
# u_sparse = factorize_tuples(sampler, 4, emb0=None, n_iter=500, verbose=verbose, eval_freq=100)[0]
x_mat_est_dense = np.dot(u_dense[:7], u_dense[7:].T)
# x_mat_est_sparse = np.dot(u_sparse[:7], u_sparse[7:].T)
if verbose:
print(np.linalg.norm(x_mat_est1 - x_mat_est_dense))
# print(np.linalg.norm(x_mat_est1 - x_mat_est_sparse))
# print(np.linalg.norm(x_mat_est_dense - x_mat_est_sparse))
else:
assert(np.linalg.norm(x_mat_est1 - x_mat_est_dense) < 1e-3)
def test_learn_factorization(verbose=False):
y_mat = toy_factorization_problem(n=7, rk=4, noise=1, square=True)
u, v = svd_factorize_matrix(y_mat, rank=4, return_embeddings=True) # exact svd solution
emb0 = np.concatenate([u, v])
x_mat_est1 = u.dot(v.T)
u2 = factorize_tuples(mat2tuples(y_mat), 4, emb0=None, n_iter=500, verbose=verbose, eval_freq=100)[0]
x_mat_est2 = np.dot(u2[:7], u2[7:].T)
if verbose:
print(np.linalg.norm(x_mat_est1 - x_mat_est2))
else:
assert(np.linalg.norm(x_mat_est1 - x_mat_est2) < 1e-3)
def test_learn_factorization(verbose=False):
y_mat = toy_factorization_problem(n=7, rk=4, noise=1, square=True)
u, v = svd_factorize_matrix(y_mat, rank=4,
return_embeddings=True) # exact svd solution
emb0 = np.concatenate([u, v])
x_mat_est1 = u.dot(v.T)
u2 = factorize_tuples(mat2tuples(y_mat),
4,
emb0=None,
n_iter=500,
verbose=verbose,
eval_freq=100)[0]
x_mat_est2 = np.dot(u2[:7], u2[7:].T)
if verbose:
print(np.linalg.norm(x_mat_est1 - x_mat_est2))
else:
assert (np.linalg.norm(x_mat_est1 - x_mat_est2) < 1e-3)
def test_tuples_factorization_rectangular_matrix(verbose=False,
hermitian=False):
"""
In this test, we compare the solution of the factorization given by an exact SVD and the solution given by
the factorize_tuple function because with fully-observed matrix data and quadratic loss the solutions should match
exactly.
Args:
verbose: True for demo mode where explanations are printed in the standard output. Otherwise a test is run.
hermitian: Do we use the Hermitian product? (Hermitian product is asymmetric)
Returns:
Nothing
"""
y_mat = toy_factorization_problem(n=7, m=6, rk=4, noise=1)
n, m = y_mat.shape
rk = 4 # embedding size for the model
u, v = svd_factorize_matrix(y_mat, rank=4,
return_embeddings=True) # exact svd solution
emb0 = np.concatenate([u, v])
x_mat_est1 = u.dot(v.T)
emb0 = np.random.normal(size=(n + m, rk)) * 0.1
x_mat_init = np.dot(emb0[:n], emb0[n:].T) # the initial matrix
if verbose:
print(
'\n\n\nWe obtained a first exact solution by Singular Value Decomposition'
)
print(
'The difference between the observation matrix and the estimated solution is:'
)
print(np.linalg.norm(x_mat_est1 - y_mat))
print()
# conversion to tuples
indices = [[i, n + j] for i in range(n) for j in range(m)]
values = [y_mat[i, j] for i in range(n) for j in range(m)]
if not hermitian: # the dot product of real vectors
u2 = factorize_tuples((indices, values), rk, emb0=emb0, n_iter=500)[0]
x_mat_est2 = np.dot(u2[:n], u2[n:].T) # the initial matrix
coefs = None
else: # uses the complex numbers to score
scoring = lambda inputs: hermitian_tuple_scorer(
inputs,
rank=rk,
n_emb=n + m,
emb0=emb0,
symmetry_coef=(1.0, 1.0),
learn_symmetry_coef=True)
# optimization (we specify optional parameters, but the values by default could work as well)
u2, coefs = factorize_tuples((indices, values),
rk,
emb0=emb0,
n_iter=500,
scoring=scoring)
# recover the matrix based on the hermitian dot product of the embeddings
x_mat_est2_cplx = hermitian_dot(
u2[:n, :],
u2[n:, :].T) # fx.clpx2real(fx.hermitian_dot(u2[:n], u2[n:]))
x_mat_est2 = x_mat_est2_cplx[0] * coefs[0] + x_mat_est2_cplx[
1] * coefs[1]
if verbose:
print(x_mat_est2.shape, x_mat_init)
print(
'We computed an estimator by minimizing the square loss on the tuples extracted from the matrix'
)
print(
'The difference between the initial solution and the estimated solution is:'
)
print(np.linalg.norm(x_mat_est2 - x_mat_init))
print(
'The difference between the observations and the estimated solution is:'
)
print(np.linalg.norm(y_mat - x_mat_est2))
print(
'The difference between the exact solution and the estimated solution is:'
)
print(np.linalg.norm(x_mat_est1 - x_mat_est2))
if hermitian:
print('Symmetry coefficients: ', coefs)
else:
assert (np.linalg.norm(x_mat_est1 - x_mat_est2) < 1e-3)
def test_tuples_factorization_rectangular_matrix(verbose=False, hermitian=False):
"""
In this test, we compare the solution of the factorization given by an exact SVD and the solution given by
the factorize_tuple function because with fully-observed matrix data and quadratic loss the solutions should match
exactly.
Args:
verbose: True for demo mode where explanations are printed in the standard output. Otherwise a test is run.
hermitian: Do we use the Hermitian product? (Hermitian product is asymmetric)
Returns:
Nothing
"""
y_mat = toy_factorization_problem(n=7, m=6, rk=4, noise=1)
n, m = y_mat.shape
rk = 4 # embedding size for the model
u, v = svd_factorize_matrix(y_mat, rank=4, return_embeddings=True) # exact svd solution
emb0 = np.concatenate([u, v])
x_mat_est1 = u.dot(v.T)
emb0 = np.random.normal(size=(n + m, rk)) * 0.1
x_mat_init = np.dot(emb0[:n], emb0[n:].T) # the initial matrix
if verbose:
print('\n\n\nWe obtained a first exact solution by Singular Value Decomposition')
print('The difference between the observation matrix and the estimated solution is:')
print(np.linalg.norm(x_mat_est1-y_mat))
print()
# conversion to tuples
indices = [[i, n + j] for i in range(n) for j in range(m)]
values = [y_mat[i, j] for i in range(n) for j in range(m)]
if not hermitian: # the dot product of real vectors
u2 = factorize_tuples((indices, values), rk, emb0=emb0, n_iter=500)[0]
x_mat_est2 = np.dot(u2[:n], u2[n:].T) # the initial matrix
coefs = None
else: # uses the complex numbers to score
scoring = lambda inputs: hermitian_tuple_scorer(inputs, rank=rk, n_emb=n + m, emb0=emb0,
symmetry_coef=(1.0, 1.0),
learn_symmetry_coef=True)
# optimization (we specify optional parameters, but the values by default could work as well)
u2, coefs = factorize_tuples((indices, values), rk, emb0=emb0, n_iter=500, scoring=scoring)
# recover the matrix based on the hermitian dot product of the embeddings
x_mat_est2_cplx = hermitian_dot(u2[:n, :], u2[n:, :].T) # fx.clpx2real(fx.hermitian_dot(u2[:n], u2[n:]))
x_mat_est2 = x_mat_est2_cplx[0] * coefs[0] + x_mat_est2_cplx[1] * coefs[1]
if verbose:
print(x_mat_est2.shape, x_mat_init)
print('We computed an estimator by minimizing the square loss on the tuples extracted from the matrix')
print('The difference between the initial solution and the estimated solution is:')
print(np.linalg.norm(x_mat_est2-x_mat_init))
print('The difference between the observations and the estimated solution is:')
print(np.linalg.norm(y_mat-x_mat_est2))
print('The difference between the exact solution and the estimated solution is:')
print(np.linalg.norm(x_mat_est1-x_mat_est2))
if hermitian:
print('Symmetry coefficients: ', coefs)
else:
assert(np.linalg.norm(x_mat_est1-x_mat_est2) < 1e-3)
