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
D = Dataset(X=x, y=y)
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, D)
mll_eval_priors = mll(params, D, priors)
assert pytest.approx(mll_eval) == jnp.array(-103.28180663)
assert pytest.approx(mll_eval_priors) == jnp.array(-105.509218857)
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_sample_array(n, n_sample):
key = jr.PRNGKey(123)
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())
samples = sample(key, f, params, D, n_samples=n_sample)
assert samples.shape == (n_sample, sample_points.shape[0])
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)
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)(sample_points)
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_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_conjugate_variance():
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)
varf = variance(posterior, params, D)
sigma = varf(xtest)
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)
D = Dataset(X=x, y=y)
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, 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_non_conjugate_rv(n):
key = jr.PRNGKey(123)
f = posterior = Prior(kernel=RBF()) * Bernoulli()
x = jnp.sort(jr.uniform(key, shape=(n, 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)
sample_points = jnp.linspace(-1.0, 1.0, num=n).reshape(-1, 1)
hyperparams = {"lengthscale": jnp.array([1.0]), "variance": jnp.array([1.0])}
params = complete(hyperparams, posterior, x.shape[0])
rv = random_variable(f, params, D)
assert isinstance(rv, Callable)
fstar = rv(sample_points)
assert isinstance(fstar, tfd.ProbitBernoulli)
def test_spectral():
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)
D = Dataset(X=x, y=y)
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, D) == jnp.array(-1.0) * mll(params, D)
nmll = neg_mll(params, D)
assert nmll.shape == ()