https://github.com/GPflow/GPflow
Tip revision: 6bc57345a42f589fb1ce559ba47d1c667581e4ed authored by thevincentadam on 16 April 2018, 14:55:16 UTC
a first mixedmok test (#706)
a first mixedmok test (#706)
Tip revision: 6bc5734
test_multioutput.py
import gpflow
import numpy as np
import pytest
import gpflow.multioutput.features as mf
import gpflow.multioutput.kernels as mk
from gpflow.models import SVGP
from gpflow.kernels import RBF
from gpflow.features import InducingPoints
from gpflow.likelihoods import Gaussian
from gpflow.test_util import session_context
np.random.seed(1)
def predict(sess, model, Xnew, full_cov, full_cov_output):
m, v = model._build_predict(Xnew, full_cov=full_cov, full_cov_output=full_cov_output)
return sess.run([m, v])
def predict_all(sess, models, Xnew, full_cov, full_cov_output):
ms, vs = [], []
for model in models:
m, v = predict(sess, model, Xnew, full_cov, full_cov_output)
ms.append(m)
vs.append(v)
return ms, vs
def assert_all_array_elements_almost_equal(arr, decimal):
for i in range(len(arr) - 1):
np.testing.assert_almost_equal(arr[i], arr[i+1], decimal=decimal)
def check_equality_predictions(sess, models):
log_likelihoods = [m.compute_log_likelihood() for m in models]
# Check equality of log likelihood
assert_all_array_elements_almost_equal(log_likelihoods, decimal=5)
# Predict: full_cov = True and full_cov_output = True
means_tt, vars_tt = predict_all(sess, models, Data.Xs, full_cov=True, full_cov_output=True)
# Predict: full_cov = True and full_cov_output = False
means_tf, vars_tf = predict_all(sess, models, Data.Xs, full_cov=True, full_cov_output=False)
# Predict: full_cov = False and full_cov_output = True
means_ft, vars_ft = predict_all(sess, models, Data.Xs, full_cov=False, full_cov_output=True)
# Predict: full_cov = False and full_cov_output = False
means_ff, vars_ff = predict_all(sess, models, Data.Xs, full_cov=False, full_cov_output=False)
# check equality of all the means
all_means = means_tt + means_tf + means_ft + means_ff
assert_all_array_elements_almost_equal(all_means, decimal=5)
# check equality of all the variances within a category
# (e.g. full_cov=True and full_cov_output=False)
all_vars = [vars_tt, vars_tf, vars_ft, vars_ff]
_ = [assert_all_array_elements_almost_equal(var, decimal=4) for var in all_vars]
# Here we check that the variance in different categories are equal
# after transforming to the right shape.
var_tt = vars_tt[0] # N x P x N x P
var_tf = vars_tf[0] # P x N x N
var_ft = vars_ft[0] # N x P x P
var_ff = vars_ff[0] # N x P
np.testing.assert_almost_equal(np.diagonal(var_tt, axis1=1, axis2=3),
np.transpose(var_tf, [1, 2, 0]), decimal=4)
np.testing.assert_almost_equal(np.diagonal(var_tt, axis1=0, axis2=2),
np.transpose(var_ft, [1, 2, 0]), decimal=4)
np.testing.assert_almost_equal(np.diagonal(np.diagonal(var_tt, axis1=0, axis2=2)),
var_ff, decimal=4)
class Data:
X = np.random.rand(100)[:, None] * 10 - 5
G = np.hstack((0.5 * np.sin(3 * X) + X, 3.0 * np.cos(X) - X))
Ptrue = np.array([[0.5, -0.3, 1.5], [-0.4, 0.43, 0.0]])
Y = np.matmul(G, Ptrue)
Y += np.random.randn(*Y.shape) * [0.2, 0.2, 0.2]
Xs = np.linspace(-6, 6, 5)[:, None]
D = 1 # input dimension
M = 3 # inducing points
L = 2 # latent gps
P = 3 # output dimension
MAXITER = int(15e2)
def make_sqrt_data(rng, N, M):
return np.array([np.tril(rng.randn(M, M)) for _ in range(N)]) # N x M x M
def expand_cov(G, W):
''' G is L x M x M
W is L x L
Output is LM x LM
'''
L, M, _ = G.shape
O = np.zeros((L * M, L * M))
for l1 in range(L):
for l2 in range(L):
O[l1 * M:(l1 + 1) * M, l2 * M:(l2 + 1) * M] = W[l1, l2] * G[l1, :, :]
return O[None, :, :]
def q_sqrts_to_Q_sqrt(q_sqrt, W):
''' G is L x M x M
W is L x L
Output is LM x LM
'''
cov = np.matmul(q_sqrt, q_sqrt.transpose(0, 2, 1))
Cov = expand_cov(cov, W)
return np.linalg.cholesky(Cov)
def mus_to_Mu(mu, W):
M, L = mu.shape
Mu = np.zeros((M * L, 1))
for l1 in range(L):
for l2 in range(L):
Mu[l1 * M:(l1 + 1) * M, 0] += mu[:, l2] * W[l1, l2]
return Mu
class Datum:
N = 20
D = 1
M = 7
L = 3
P = 3
rng = np.random.RandomState(0)
mu_data = rng.randn(M, L) # M x N
sqrt_data = make_sqrt_data(rng, L, M) # L x M x M
W = np.eye(L)
mu_data_full = mus_to_Mu(mu_data, W)
sqrt_data_full = q_sqrts_to_Q_sqrt(sqrt_data, W)
X = np.random.rand(N, D) # N x D
G = np.hstack((0.5 * np.sin(3 * X) + X, X, 3.0 * np.cos(X) - X)) # N x D
Y = np.matmul(G, W)
Y += np.random.randn(*Y.shape) * np.ones((L,)) * 0.2
Xs = np.linspace(-6, 6, 5)[:, None]
MAXITER = int(15e2)
def test_shared_independent_mok():
"""
In this test we use the same kernel and the same inducing features
for each of the outputs. The outputs are considered to be uncorrelated.
This is how GPflow handled multiple outputs before the multioutput framework was added.
We compare three models here:
1) an inefffient one, where we use a SharedIndepedentMok with InducingPoints.
This combination will uses a Kff of size N x P x N x P, Kfu if size N x P x M x P
which is extremely inefficient as most of the elements are zero.
2) efficient: SharedIndependentMok and SharedIndependentMof
This combinations uses the most efficient form of matrices
3) the old way, efficient way: using Kernel and InducingPoints
Model 2) and 3) follow more or less the same code path.
"""
with session_context() as sess:
# Model 1
q_mu_1 = np.random.randn(Data.M * Data.P, 1) # MP x 1
q_sqrt_1 = np.tril(np.random.randn(Data.M * Data.P, Data.M * Data.P))[None, ...] # 1 x MP x MP
kernel_1 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P)
feature_1 = InducingPoints(Data.X[:Data.M,...].copy())
m1 = SVGP(Data.X, Data.Y, kernel_1, Gaussian(), feature_1, q_mu=q_mu_1, q_sqrt=q_sqrt_1)
m1.set_trainable(False)
m1.q_sqrt.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Data.MAXITER)
# Model 2
q_mu_2 = np.reshape(q_mu_1, [Data.M, Data.P]) # M x P
q_sqrt_2 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M
kernel_2 = RBF(Data.D, variance=0.5, lengthscales=1.2)
feature_2 = InducingPoints(Data.X[:Data.M, ...].copy())
m2 = SVGP(Data.X, Data.Y, kernel_2, Gaussian(), feature_2, q_mu=q_mu_2, q_sqrt=q_sqrt_2)
m2.set_trainable(False)
m2.q_sqrt.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Data.MAXITER)
# Model 3
q_mu_3 = np.reshape(q_mu_1, [Data.M, Data.P]) # M x P
q_sqrt_3 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M
kernel_3 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P)
feature_3 = mf.SharedIndependentMof(InducingPoints(Data.X[:Data.M, ...].copy()))
m3 = SVGP(Data.X, Data.Y, kernel_3, Gaussian(), feature_3, q_mu=q_mu_3, q_sqrt=q_sqrt_3)
m3.set_trainable(False)
m3.q_sqrt.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m3, maxiter=Data.MAXITER)
check_equality_predictions(sess, [m1, m2, m3])
def test_seperate_independent_mok():
"""
We use different independent kernels for each of the output dimensions.
We can achieve this in two ways:
1) efficient: SeparateIndependentMok with Shared/SeparateIndependentMof
2) inefficient: SeparateIndependentMok with InducingPoints
However, both methods should return the same conditional,
and after optimization return the same log likelihood.
"""
with session_context() as sess:
# Model 1 (INefficient)
q_mu_1 = np.random.randn(Data.M * Data.P, 1)
q_sqrt_1 = np.tril(np.random.randn(Data.M * Data.P, Data.M * Data.P))[None, ...] # 1 x MP x MP
kern_list_1 = [RBF(Data.D, variance=0.5, lengthscales=1.2) for _ in range(Data.P)]
kernel_1 = mk.SeparateIndependentMok(kern_list_1)
feature_1 = InducingPoints(Data.X[:Data.M,...].copy())
m1 = SVGP(Data.X, Data.Y, kernel_1, Gaussian(), feature_1, q_mu=q_mu_1, q_sqrt=q_sqrt_1)
m1.set_trainable(False)
m1.q_sqrt.set_trainable(True)
m1.q_mu.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Data.MAXITER)
# Model 2 (efficient)
q_mu_2 = np.random.randn(Data.M, Data.P)
q_sqrt_2 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M
kern_list_2 = [RBF(Data.D, variance=0.5, lengthscales=1.2) for _ in range(Data.P)]
kernel_2 = mk.SeparateIndependentMok(kern_list_2)
feature_2 = mf.SharedIndependentMof(InducingPoints(Data.X[:Data.M, ...].copy()))
m2 = SVGP(Data.X, Data.Y, kernel_2, Gaussian(), feature_2, q_mu=q_mu_2, q_sqrt=q_sqrt_2)
m2.set_trainable(False)
m2.q_sqrt.set_trainable(True)
m2.q_mu.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Data.MAXITER)
check_equality_predictions(sess, [m1, m2])
def test_seperate_independent_mof():
"""
Same test as above but we use different (i.e. separate) inducing features
for each of the output dimensions.
"""
with session_context() as sess:
# Model 1 (INefficient)
q_mu_1 = np.random.randn(Data.M * Data.P, 1)
q_sqrt_1 = np.tril(np.random.randn(Data.M * Data.P, Data.M * Data.P))[None, ...] # 1 x MP x MP
kernel_1 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P)
feature_1 = InducingPoints(Data.X[:Data.M,...].copy())
m1 = SVGP(Data.X, Data.Y, kernel_1, Gaussian(), feature_1, q_mu=q_mu_1, q_sqrt=q_sqrt_1)
m1.set_trainable(False)
m1.q_sqrt.set_trainable(True)
m1.q_mu.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Data.MAXITER)
# Model 2 (efficient)
q_mu_2 = np.random.randn(Data.M, Data.P)
q_sqrt_2 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M
kernel_2 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P)
feat_list_2 = [InducingPoints(Data.X[:Data.M, ...].copy()) for _ in range(Data.P)]
feature_2 = mf.SeparateIndependentMof(feat_list_2)
m2 = SVGP(Data.X, Data.Y, kernel_2, Gaussian(), feature_2, q_mu=q_mu_2, q_sqrt=q_sqrt_2)
m2.set_trainable(False)
m2.q_sqrt.set_trainable(True)
m2.q_mu.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Data.MAXITER)
check_equality_predictions(sess, [m1, m2])
# @pytest.mark.parametrize('shared_feat', [True, False])
# @pytest.mark.parametrize('shared_kern', [True, False])
def test_mixed_mok_with_Id_vs_independent_mok():
with session_context() as sess:
np.random.seed(0)
# Independent model
k1 = mk.SharedIndependentMok(RBF(Datum.D, variance=0.5, lengthscales=1.2), Datum.L)
f1 = InducingPoints(Datum.X[:Datum.M, ...].copy())
m1 = SVGP(Datum.X, Datum.Y, k1, Gaussian(), f1,
q_mu=Datum.mu_data_full, q_sqrt=Datum.sqrt_data_full)
m1.set_trainable(False)
m1.q_sqrt.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Datum.MAXITER)
# Mixed Model
kern_list = [RBF(Datum.D, variance=0.5, lengthscales=1.2) for _ in range(Datum.L)]
k2 = mk.SeparateMixedMok(kern_list, Datum.W)
f2 = InducingPoints(Datum.X[:Datum.M, ...].copy())
m2 = SVGP(Datum.X, Datum.Y, k2, Gaussian(), f2,
q_mu=Datum.mu_data_full, q_sqrt=Datum.sqrt_data_full)
m2.set_trainable(False)
m2.q_sqrt.set_trainable(True)
gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Datum.MAXITER)
# Check equality of log likelihood
np.testing.assert_allclose(m1.compute_log_likelihood(), m2.compute_log_likelihood())