def qKq_uniform(num_samples: int, qrbf: QuadratureRBFUniformMeasure):
if qrbf.integral_bounds is None:
bounds = qrbf.measure.bounds
samples = _sample_uniform(num_samples, bounds)
qKx = qrbf.qK(samples)
return np.mean(qKx)
else:
bounds = qrbf.integral_bounds._bounds
samples = _sample_uniform(num_samples, bounds)
qKx = qrbf.qK(samples) * qrbf.measure.compute_density(samples)[np.newaxis, :]
differences = np.array([x[1] - x[0] for x in bounds])
volume = np.prod(differences)
return np.mean(qKx) * volume
def qK_uniform(num_samples: int, qrbf: QuadratureRBFUniformMeasure, x2: np.ndarray):
if qrbf.integral_bounds is None:
bounds = qrbf.measure.bounds
samples = _sample_uniform(num_samples, bounds)
Kx = qrbf.K(samples, x2)
return np.mean(Kx, axis=0)
else:
bounds = qrbf.integral_bounds._bounds
samples = _sample_uniform(num_samples, bounds)
Kx = qrbf.K(samples, x2) * qrbf.measure.compute_density(samples)[:, np.newaxis]
differences = np.array([x[1] - x[0] for x in bounds])
volume = np.prod(differences)
return np.mean(Kx, axis=0) * volume
def qrbf_uniform_infinite():
x1 = np.array([[-1, 1], [0, 0], [-2, 0.1]])
x2 = np.array([[-1, 1], [0, 0], [-2, 0.1], [-3, 3]])
M1 = x1.shape[0]
M2 = x2.shape[0]
D = x1.shape[1]
# measure
measure_bounds = [(0, 2), (-4, 3)]
measure = UniformMeasure(bounds=measure_bounds)
gpy_kernel = GPy.kern.RBF(input_dim=D)
emukit_rbf = RBFGPy(gpy_kernel)
emukit_qrbf = QuadratureRBFUniformMeasure(rbf_kernel=emukit_rbf,
integral_bounds=None,
measure=measure)
return emukit_qrbf, x1, x2, M1, M2, D
gpy_kernel = GPy.kern.RBF(input_dim=D)
emukit_rbf = RBFGPy(gpy_kernel)
if MEASURE_INTBOUNDS == "Lebesgue-finite":
emukit_qrbf = QuadratureRBFLebesgueMeasure(emukit_rbf,
integral_bounds=[(-1, 2),
(-3, 3)])
elif MEASURE_INTBOUNDS == "GaussIso-infinite":
measure = IsotropicGaussianMeasure(mean=np.arange(D), variance=2.0)
emukit_qrbf = QuadratureRBFIsoGaussMeasure(rbf_kernel=emukit_rbf,
measure=measure)
elif MEASURE_INTBOUNDS == "Uniform-infinite":
measure = UniformMeasure(bounds=[(0, 2), (-4, 3)])
emukit_qrbf = QuadratureRBFUniformMeasure(emukit_rbf,
integral_bounds=None,
measure=measure)
elif MEASURE_INTBOUNDS == "Uniform-finite":
measure = UniformMeasure(bounds=[(1, 2), (-4, 2)])
emukit_qrbf = QuadratureRBFUniformMeasure(emukit_rbf,
integral_bounds=[(-1, 2),
(-3, 3)],
measure=measure)
else:
raise ValueError("Measure-integral-bounds combination not defined")
print()
print("measure: {}".format(MEASURE_INTBOUNDS))
print("no dimensions: {}".format(D))
print()