def test_prior_sample(n, n_sample):
key = jr.PRNGKey(123)
f = Prior(kernel=RBF())
sample_points = jnp.linspace(-1.0, 1.0, num=n).reshape(-1, 1)
params = initialise(RBF())
samples = sample(key, f, params, sample_points, n_samples=n_sample)
assert samples.shape == (n_sample, sample_points.shape[0])
def _get_conjugate_posterior_params() -> dict:
kernel = RBF()
prior = Prior(kernel=kernel)
lik = Gaussian()
posterior = prior * lik
params = initialise(posterior)
return params, posterior
def test_prior_random_variable(n):
f = Prior(kernel=RBF())
sample_points = jnp.linspace(-1.0, 1.0, num=n).reshape(-1, 1)
D = Dataset(X=sample_points)
params = initialise(RBF())
rv = random_variable(f, params, D)
assert isinstance(rv, tfd.MultivariateNormalFullCovariance)
def test_prior_mll():
"""
Test that the MLL evaluation works with priors attached to the parameter values.
"""
key = jr.PRNGKey(123)
x = jnp.sort(jr.uniform(key, minval=-5.0, maxval=5.0, shape=(100, 1)),
axis=0)
f = lambda x: jnp.sin(jnp.pi * x) / (jnp.pi * x)
y = f(x) + jr.normal(key, shape=x.shape) * 0.1
posterior = Prior(kernel=RBF()) * Gaussian()
params = initialise(posterior)
config = get_defaults()
constrainer, unconstrainer = build_all_transforms(params.keys(), config)
params = unconstrainer(params)
print(params)
mll = marginal_ll(posterior, transform=constrainer)
priors = {
"lengthscale": tfd.Gamma(1.0, 1.0),
"variance": tfd.Gamma(2.0, 2.0),
"obs_noise": tfd.Gamma(2.0, 2.0),
}
mll_eval = mll(params, x, y)
mll_eval_priors = mll(params, x, y, priors)
assert pytest.approx(mll_eval) == jnp.array(-103.28180663)
assert pytest.approx(mll_eval_priors) == jnp.array(-105.509218857)
def test_posterior_random_variable(n):
f = Prior(kernel=RBF()) * Gaussian()
x = jnp.linspace(-1.0, 1.0, 10).reshape(-1, 1)
y = jnp.sin(x)
sample_points = jnp.linspace(-1.0, 1.0, num=n).reshape(-1, 1)
params = initialise(f)
rv = random_variable(f, params, sample_points, x, y)
assert isinstance(rv, tfd.MultivariateNormalFullCovariance)
def test_constrain(likelihood):
posterior = Prior(kernel=RBF()) * likelihood()
params = initialise(posterior, 10)
config = get_defaults()
transform_map = build_constrain(params.keys(), config)
transformed_params = transform_map(params)
assert transformed_params.keys() == params.keys()
for u, v in zip(transformed_params.values(), params.values()):
assert u.dtype == v.dtype
def test_posterior_sample(n, n_sample):
key = jr.PRNGKey(123)
f = Prior(kernel=RBF()) * Gaussian()
x = jnp.linspace(-1.0, 1.0, 10).reshape(-1, 1)
y = jnp.sin(x)
sample_points = jnp.linspace(-1.0, 1.0, num=n).reshape(-1, 1)
params = initialise(f)
rv = random_variable(f, params, sample_points, x, y)
samples = sample(key, rv, n_samples=n_sample)
assert samples.shape == (n_sample, sample_points.shape[0])
def test_posterior_random_variable(n):
f = Prior(kernel=RBF()) * Gaussian()
x = jnp.linspace(-1.0, 1.0, 10).reshape(-1, 1)
y = jnp.sin(x)
D = Dataset(X=x, y=y)
sample_points = jnp.linspace(-1.0, 1.0, num=n).reshape(-1, 1)
params = initialise(f)
rv = random_variable(f, params, D)
assert isinstance(rv, Callable)
fstar = rv(sample_points)
assert isinstance(fstar, tfd.MultivariateNormalFullCovariance)
def test_conjugate_variance():
key = jr.PRNGKey(123)
x = jr.uniform(key, shape=(20, 1), minval=-3.0, maxval=3.0)
y = jnp.sin(x)
posterior = Prior(kernel=RBF()) * Gaussian()
params = initialise(posterior)
xtest = jnp.linspace(-3.0, 3.0, 30).reshape(-1, 1)
sigma = variance(posterior, params, xtest, x, y)
assert sigma.shape == (xtest.shape[0], xtest.shape[0])
def test_non_conjugate():
posterior = Prior(kernel=RBF()) * Bernoulli()
n = 20
x = jnp.linspace(-1.0, 1.0, n).reshape(-1, 1)
y = jnp.sin(x)
params = initialise(posterior, 20)
config = get_defaults()
unconstrainer, constrainer = build_all_transforms(params.keys(), config)
params = unconstrainer(params)
mll = marginal_ll(posterior, transform=constrainer)
assert isinstance(mll, Callable)
neg_mll = marginal_ll(posterior, transform=constrainer, negative=True)
assert neg_mll(params, x, y) == jnp.array(-1.0) * mll(params, x, y)
def test_conjugate_mean():
key = jr.PRNGKey(123)
x = jr.uniform(key, shape=(20, 1), minval=-3.0, maxval=3.0)
y = jnp.sin(x)
D = Dataset(X=x, y=y)
posterior = Prior(kernel=RBF()) * Gaussian()
params = initialise(posterior)
xtest = jnp.linspace(-3.0, 3.0, 30).reshape(-1, 1)
meanf = mean(posterior, params, D)
mu = meanf(xtest)
assert mu.shape == (xtest.shape[0], y.shape[1])
def test_non_conjugate_variance():
key = jr.PRNGKey(123)
x = jnp.sort(jr.uniform(key, shape=(10, 1), minval=-1.0, maxval=1.0), axis=0)
y = 0.5 * jnp.sign(jnp.cos(3 * x + jr.normal(key, shape=x.shape) * 0.05)) + 0.5
D = Dataset(X=x, y=y)
xtest = jnp.linspace(-1.05, 1.05, 50).reshape(-1, 1)
posterior = Prior(kernel=RBF()) * Bernoulli()
params = initialise(posterior, x.shape[0])
varf = variance(posterior, params, D)
sigma = varf(xtest)
assert sigma.shape == (xtest.shape[0],)
def test_non_conjugate_mean():
key = jr.PRNGKey(123)
x = jnp.sort(jr.uniform(key, shape=(10, 1), minval=-1.0, maxval=1.0),
axis=0)
y = 0.5 * jnp.sign(
jnp.cos(3 * x + jr.normal(key, shape=x.shape) * 0.05)) + 0.5
xtest = jnp.linspace(-1.05, 1.05, 50).reshape(-1, 1)
posterior = Prior(kernel=RBF()) * Bernoulli()
params = initialise(posterior, x.shape[0])
mu = mean(posterior, params, xtest, x, y)
assert mu.shape == (xtest.shape[0], )
def test_conjugate():
posterior = Prior(kernel=RBF()) * Gaussian()
x = jnp.linspace(-1.0, 1.0, 20).reshape(-1, 1)
y = jnp.sin(x)
D = Dataset(X=x, y=y)
params = initialise(posterior)
config = get_defaults()
unconstrainer, constrainer = build_all_transforms(params.keys(), config)
params = unconstrainer(params)
mll = marginal_ll(posterior, transform=constrainer)
assert isinstance(mll, Callable)
neg_mll = marginal_ll(posterior, transform=constrainer, negative=True)
assert neg_mll(params, D) == jnp.array(-1.0) * mll(params, D)
def test_spectral_sample():
key = jr.PRNGKey(123)
M = 10
x = jnp.linspace(-1.0, 1.0, 20).reshape(-1, 1)
y = jnp.sin(x)
D = Dataset(X=x, y=y)
sample_points = jnp.linspace(-1.0, 1.0, num=50).reshape(-1, 1)
kernel = to_spectral(RBF(), M)
post = Prior(kernel=kernel) * Gaussian()
params = initialise(key, post)
sparams = {"basis_fns": params["basis_fns"]}
del params["basis_fns"]
posterior_rv = random_variable(post, params, D, static_params=sparams)(sample_points)
assert isinstance(posterior_rv, tfd.Distribution)
assert isinstance(posterior_rv, tfd.MultivariateNormalFullCovariance)
def test_conjugate():
key = jr.PRNGKey(123)
kern = to_spectral(RBF(), 10)
posterior = Prior(kernel=kern) * Gaussian()
x = jnp.linspace(-1.0, 1.0, 20).reshape(-1, 1)
y = jnp.sin(x)
params = initialise(key, posterior)
config = get_defaults()
unconstrainer, constrainer = build_all_transforms(params.keys(), config)
params = unconstrainer(params)
mll = marginal_ll(posterior, transform=constrainer)
assert isinstance(mll, Callable)
neg_mll = marginal_ll(posterior, transform=constrainer, negative=True)
assert neg_mll(params, x, y) == jnp.array(-1.0) * mll(params, x, y)
nmll = neg_mll(params, x, y)
assert nmll.shape == ()
def test_build_all_transforms(likelihood):
posterior = Prior(kernel=RBF()) * likelihood()
params = initialise(posterior, 10)
config = get_defaults()
t1, t2 = build_all_transforms(params.keys(), config)
constrainer = build_constrain(params.keys(), config)
constrained = t1(params)
constrained2 = constrainer(params)
assert constrained2.keys() == constrained2.keys()
for u, v in zip(constrained.values(), constrained2.values()):
assert_array_equal(u, v)
assert u.dtype == v.dtype
unconstrained = t2(params)
unconstrainer = build_unconstrain(params.keys(), config)
unconstrained2 = unconstrainer(params)
for u, v in zip(unconstrained.values(), unconstrained2.values()):
assert_array_equal(u, v)
assert u.dtype == v.dtype
def plot(kernel: Kernel, X: Array, params: dict = None, ax = None):
"""
Plot the kernel's Gram matrix.
:param kernel: The kernel function that generates the Gram matrix
:param X: The data points for which the Gram matrix is computed on.
:param params: A dictionary containing the kernel parameters
:param ax: An optional matplotlib axes
:return:
"""
if params is None:
params = initialise(kernel)
cols = get_cmap()
if ax is None:
fig, ax = plt.subplots()
K = gpjax.kernels.gram(kernel, X, params)
ax.matshow(K, cmap = cols)
def fit(posterior, nits, data, configs):
params = initialise(posterior)
constrainer, unconstrainer = build_all_transforms(params.keys(), configs)
mll = jit(marginal_ll(posterior, transform=constrainer, negative=True))
opt_init, opt_update, get_params = optimizers.adam(step_size=0.05)
opt_state = opt_init(params)
def step(i, opt_state):
p = get_params(opt_state)
v, g = value_and_grad(mll)(p, data)
return opt_update(i, g, opt_state), v
for i in range(nits):
opt_state, mll_estimate = step(i, opt_state)
print(f"{posterior.prior.kernel.name} GP's marginal log-likelihood: {mll_estimate: .2f}")
final_params = constrainer(get_params(opt_state))
return final_params
def plot(kernel: Kernel, X: Array, Y: Array, params: dict = None, ax=None):
"""
Plot the kernel's cross-covariance matrix.
:param kernel: The kernel function that generates the covariance matrix
:param X: The first set of data points for which the covariance matrix is computed on.
:param Y: The second set of data points for which the covariance matrix is computed on.
:param params: A dictionary containing the kernel parameters
:param ax: An optional matplotlib axes
:return:
"""
if params is None:
params = initialise(kernel)
cols = get_cmap()
if ax is None:
fig, ax = plt.subplots()
fig.set_tight_layout(False)
K = gpjax.kernels.cross_covariance(kernel, X, Y, params)
c = ax.matshow(K, cmap = cols)
def plot(kernel: Kernel, params: dict = None, ax=None, xrange: Tuple[float, float] = (-10, 10.)):
"""
Plot the kernel's shape.
:param kernel: The kernel function
:param params: A dictionary containing the kernel parameters
:param ax: An optional matplotlib axes
:param xrange The tuple pair lower and upper values over which the kernel should be evaluated.
:return:
"""
if params is None:
params = initialise(kernel)
cols = get_colours()
if ax is None:
fig, ax = plt.subplots()
X = jnp.linspace(xrange[0], xrange[1], num=200).reshape(-1, 1)
x1 = jnp.array([[0.0]])
K = gpjax.kernels.cross_covariance(kernel, X, x1, params)
ax.plot(X, K.T, color=cols['base'])
mplcyberpunk.add_underglow(ax=ax)
def test_output(transformation, likelihood):
posterior = Prior(kernel=RBF()) * likelihood()
params = initialise(posterior, 10)
config = get_defaults()
transform_map = transformation(params.keys(), config)
assert isinstance(transform_map, Callable)
