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)