def main():
"""Run the demo."""
# grab a test function
f = SubprocessQuery("bc <<< 'scale=8; x={}; -((x-3)^2)'")
bounds = [0, 8]
x = np.linspace(bounds[0], bounds[1], 500)
# solve the model
xbest, model, info = solve_bayesopt(f, bounds, niter=30, verbose=True)
mu, s2 = model.predict(x[:, None])
# plot the final model
ax = figure().gca()
ax.plot_banded(x, mu, 2 * np.sqrt(s2))
ax.axvline(xbest)
ax.scatter(info.x.ravel(), info.y)
ax.figure.canvas.draw()
show()
def main():
"""Run the demo."""
# grab some kernels
kernels = [SE(1, 1),
Matern(1, 1, d=5)]
# the points we'll test at
x = np.linspace(-5, 5, 500)
n = 1000
# seed the rng and create a figure
rng = np.random.RandomState(0)
fig = figure()
for i, kernel in enumerate(kernels):
# the true kernel
k1 = kernel.get_kernel([[0]], x[:, None]).ravel()
# the approximation
W, a = kernel.sample_spectrum(n, rng)
b = rng.rand(n) * 2 * np.pi
k2 = np.dot(np.cos(np.dot(x[:, None], W.T) + b), np.cos(b)) * 2 * a / n
# plot it
ax = fig.add_subplot(len(kernels), 1, 1+i)
ax.plot(x, k1, label='true kernel')
ax.plot(x, k2, label='feature approximation')
ax.set_title(kernel.__class__.__name__)
if i == 0:
ax.legend(loc=0)
# draw everything
fig.canvas.draw()
show()
def main():
"""Run the demo."""
# generate random data from a gp prior
rng = np.random.RandomState(0)
gp = make_gp(0.1, 1.0, 0.1, kernel='matern1')
X = rng.uniform(-2, 2, size=(20, 1))
Y = gp.sample(X, latent=False, rng=rng)
# create a new GP and optimize its hyperparameters
gp = make_gp(1, 1, 1, kernel='se')
gp.add_data(X, Y)
gp.optimize()
# get the posterior moments
x = np.linspace(X.min(), X.max(), 500)
mu, s2 = gp.predict(x[:, None])
# plot the posterior
ax = figure().gca()
ax.plot_banded(x, mu, 2 * np.sqrt(s2), label='posterior mean')
ax.scatter(X.ravel(), Y, label='observed data')
ax.legend(loc=0)
ax.set_title('Basic GP')
ax.set_xlabel('inputs, X')
ax.set_ylabel('outputs, Y')
# draw/show it
ax.figure.canvas.draw()
show()
def main():
"""Run the demo."""
# grab some kernels
kernels = [SE(1, 1), Matern(1, 1, d=5)]
# the points we'll test at
x = np.linspace(-5, 5, 500)
n = 1000
# seed the rng and create a figure
rng = np.random.RandomState(0)
fig = figure()
for i, kernel in enumerate(kernels):
# the true kernel
k1 = kernel.get_kernel([[0]], x[:, None]).ravel()
# the approximation
W, a = kernel.sample_spectrum(n, rng)
b = rng.rand(n) * 2 * np.pi
k2 = np.dot(np.cos(np.dot(x[:, None], W.T) + b), np.cos(b)) * 2 * a / n
# plot it
ax = fig.add_subplot(len(kernels), 1, 1 + i)
ax.plot(x, k1, label='true kernel')
ax.plot(x, k2, label='feature approximation')
ax.set_title(kernel.__class__.__name__)
if i == 0:
ax.legend(loc=0)
# draw everything
fig.canvas.draw()
show()
def main():
"""Run the demo."""
# generate random data from a gp prior
rng = np.random.RandomState(0)
gp = make_gp(0.1, 1.0, 0.1, kernel='matern1')
X = rng.uniform(-2, 2, size=(20, 1))
Y = gp.sample(X, latent=False, rng=rng)
# create a new GP and optimize its hyperparameters
gp = make_gp(1, 1, 1, kernel='se')
gp.add_data(X, Y)
gp.optimize()
# get the posterior moments
x = np.linspace(X.min(), X.max(), 500)
mu, s2 = gp.predict(x[:, None])
# plot the posterior
ax = figure().gca()
ax.plot_banded(x, mu, 2*np.sqrt(s2), label='posterior mean')
ax.scatter(X.ravel(), Y, label='observed data')
ax.legend(loc=0)
ax.set_title('Basic GP')
ax.set_xlabel('inputs, X')
ax.set_ylabel('outputs, Y')
# draw/show it
ax.figure.canvas.draw()
show()
def main():
"""Run the demo."""
# generate random data from a gp prior
rng = np.random.RandomState(0)
gp = make_gp(0.1, 1.0, 0.1, kernel='matern1')
X = rng.uniform(-2, 2, size=(20, 1))
Y = gp.sample(X, latent=False, rng=rng)
U = np.linspace(X.min(), X.max(), 10)[:, None]
# create a new (sparse) GP and optimize its hyperparameters
gp = make_gp(1, 1, 1, inf='fitc', U=U)
gp.add_data(X, Y)
gp.optimize()
# get the posterior moments
x = np.linspace(X.min(), X.max(), 500)
mu, s2 = gp.predict(x[:, None])
# plot the posterior
ax = figure().gca()
ax.plot_banded(x, mu, 2*np.sqrt(s2), label='posterior mean')
ax.scatter(X, Y, label='observed data')
ax.scatter(U, np.full_like(U, -1), marker='x', label='inducing points')
ax.legend(loc=0)
ax.set_xlabel('inputs, X')
ax.set_ylabel('outputs, Y')
ax.set_title('Sparse GP (FITC)')
# show the figure
ax.figure.canvas.draw()
show()
def main():
"""Run the demo."""
# define the model and sample an instance from it
n = 10
rng = np.random.RandomState(3)
model = BetaBernoulli(np.ones(n))
f = model.sample(rng=rng)
# grab the optimal latent value and make lists of observations
xopt = f.argmax()
fopt = f.max()
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# evaluate the posterior before updating the model for plotting
mu = model.get_quantile(0.5)
lo = model.get_quantile(0.05)
hi = model.get_quantile(0.95)
# get our index
target = mu.max()
index = model.get_improvement(target)
# query
x = index.argmax()
y = int(rng.uniform() < f[x])
# add the data
model.add_data(x, y)
# PLOT EVERYTHING
fig.clear()
ax1 = fig.add_subplotspec((2, 1), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 1), (1, 0), hidey=True, sharex=ax1)
ax1.errorbar(np.arange(n),
mu, (mu - lo, hi - mu),
ls='',
marker='s',
markersize=20,
capsize=30,
capthick=2)
ax1.axvline(xopt, zorder=-1)
ax1.axhline(fopt, zorder=-1)
ax1.set_ylim(0, 1)
ax1.set_xlim(-0.3, n - 1 + 0.3)
ax2.bar(np.arange(n) - 0.25, index, 0.5)
# draw
fig.canvas.draw()
show()
def main():
"""Run the demo."""
# define the model and sample an instance from it
n = 10
rng = np.random.RandomState(3)
model = BetaBernoulli(np.ones(n))
f = model.sample(rng=rng)
# grab the optimal latent value and make lists of observations
xopt = f.argmax()
fopt = f.max()
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# evaluate the posterior before updating the model for plotting
mu = model.get_quantile(0.5)
lo = model.get_quantile(0.05)
hi = model.get_quantile(0.95)
# get our index
target = mu.max()
index = model.get_improvement(target)
# query
x = index.argmax()
y = int(rng.uniform() < f[x])
# add the data
model.add_data(x, y)
# PLOT EVERYTHING
fig.clear()
ax1 = fig.add_subplotspec((2, 1), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 1), (1, 0), hidey=True, sharex=ax1)
ax1.errorbar(np.arange(n), mu, (mu-lo, hi-mu), ls='', marker='s',
markersize=20, capsize=30, capthick=2)
ax1.axvline(xopt, zorder=-1)
ax1.axhline(fopt, zorder=-1)
ax1.set_ylim(0, 1)
ax1.set_xlim(-0.3, n-1+0.3)
ax2.bar(np.arange(n)-0.25, index, 0.5)
# draw
fig.canvas.draw()
show()
def main():
"""Run the demo."""
# grab a test function
f = SubprocessQuery("bc <<< 'scale=8; x={}; -((x-3)^2)'")
bounds = [0, 8]
x = np.linspace(bounds[0], bounds[1], 500)
# solve the model
xbest, model, info = solve_bayesopt(f, bounds, niter=30, verbose=True)
mu, s2 = model.predict(x[:, None])
# plot the final model
ax = figure().gca()
ax.plot_banded(x, mu, 2*np.sqrt(s2))
ax.axvline(xbest)
ax.scatter(info.x.ravel(), info.y)
ax.figure.canvas.draw()
show()
def main():
"""Run the demo."""
# grab a test function
bounds = [0, 2*np.pi]
x = np.linspace(bounds[0], bounds[1], 500)
# solve the model
xbest, model, info = solve_bayesopt(f, bounds, niter=30, verbose=True)
# make some predictions
mu, s2 = model.predict(x[:, None])
# plot the final model
ax = figure().gca()
ax.plot_banded(x, mu, 2*np.sqrt(s2))
ax.axvline(xbest)
ax.scatter(info.x.ravel(), info.y)
ax.figure.canvas.draw()
show()
def main():
"""Run the demo."""
# initialize interactive function and 1d bounds
f = InteractiveQuery()
bounds = [0, 1]
x = np.linspace(bounds[0], bounds[1], 100)
# optimize the model and get final predictions
xbest, model, info = solve_bayesopt(f, bounds, niter=10)
mu, s2 = model.predict(x[:, None])
# plot the final model
fig = figure()
axs = fig.gca()
axs.plot_banded(x, mu, 2*np.sqrt(s2))
axs.axvline(xbest)
axs.scatter(info.x.ravel(), info.y)
fig.canvas.draw()
show()
def main():
"""Run the demo."""
# generate random data from a gp prior
rng = np.random.RandomState(1)
N = 5
X = rng.uniform(-2, 2, size=(N, 1))
Y = rng.uniform(-2, 2, size=N)
x = np.linspace(X.min(), X.max(), 500)
# create a GP and sample its prior
gp = make_gp(0.01, 1, 0.3, kernel='se')
pr_fs = gp.sample(x[:, None], 3, rng=rng)
pr_mu, pr_s2 = gp.predict(x[:, None])
# add data and sample the posterior
gp.add_data(X, Y)
po_fs = gp.sample(x[:, None], 3, rng=rng)
po_mu, po_s2 = gp.predict(x[:, None])
# plot the posterior
fig = figure(w_pad=3)
ax1 = fig.add_subplotspec((1, 2), (0, 0), hidexy=True)
ax2 = fig.add_subplotspec((1, 2), (0, 1), hidexy=True, sharey=ax1)
ax1.plot_banded(x, pr_mu, 3*np.sqrt(pr_s2))
ax1.plot(x, pr_fs.T, ls='--')
ax1.set_title('prior')
ax1.set_ylim(-3.5, 3.5)
ax2.plot_banded(x, po_mu, 3*np.sqrt(po_s2))
ax2.plot(x, po_fs.T, ls='--')
ax2.scatter(X.ravel(), Y, s=80, marker='+', zorder=3, lw=3)
ax2.set_title('posterior')
# draw/show it
fig.canvas.draw()
show()
def main():
"""Run the demo."""
# generate random data from a gp prior
rng = np.random.RandomState(1)
N = 5
X = rng.uniform(-2, 2, size=(N, 1))
Y = rng.uniform(-2, 2, size=N)
x = np.linspace(X.min(), X.max(), 500)
# create a GP and sample its prior
gp = make_gp(0.01, 1, 0.3, kernel='se')
pr_fs = gp.sample(x[:, None], 3, rng=rng)
pr_mu, pr_s2 = gp.predict(x[:, None])
# add data and sample the posterior
gp.add_data(X, Y)
po_fs = gp.sample(x[:, None], 3, rng=rng)
po_mu, po_s2 = gp.predict(x[:, None])
# plot the posterior
fig = figure(w_pad=3)
ax1 = fig.add_subplotspec((1, 2), (0, 0), hidexy=True)
ax2 = fig.add_subplotspec((1, 2), (0, 1), hidexy=True, sharey=ax1)
ax1.plot_banded(x, pr_mu, 3 * np.sqrt(pr_s2))
ax1.plot(x, pr_fs.T, ls='--')
ax1.set_title('prior')
ax1.set_ylim(-3.5, 3.5)
ax2.plot_banded(x, po_mu, 3 * np.sqrt(po_s2))
ax2.plot(x, po_fs.T, ls='--')
ax2.scatter(X.ravel(), Y, s=80, marker='+', zorder=3, lw=3)
ax2.set_title('posterior')
# draw/show it
fig.canvas.draw()
show()
def main():
"""Run the demo."""
# define the bounds over which we'll optimize, the optimal x for comparison,
# and a sequence of test points
bounds = np.array([[-5, 10.], [0, 15]])
xopt = np.array([np.pi, 2.275])
x1, x2 = np.meshgrid(np.linspace(*bounds[0], num=100),
np.linspace(*bounds[1], num=100))
xx = np.c_[x1.flatten(), x2.flatten()]
# get initial data and some test points.
X = list(inits.init_latin(bounds, 6))
Y = [f(x_) for x_ in X]
F = list()
# initialize the model
model = make_gp(0.01, 10, [1., 1.], 0)
model.add_data(X, Y)
# set a prior on the parameters
model.params['like.sn2'].set_prior('uniform', 0.005, 0.015)
model.params['kern.rho'].set_prior('lognormal', 0, 3)
model.params['kern.ell'].set_prior('lognormal', 0, 3)
model.params['mean.bias'].set_prior('normal', 0, 20)
# make a model which samples parameters
model = MCMC(model, n=10, rng=None)
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# get index to solve it and plot it
index = policies.EI(model, bounds, X, xi=0.1)
# get the recommendation and the next query
xbest = recommenders.best_incumbent(model, bounds, X)
xnext, _ = solvers.solve_lbfgs(index, bounds)
# observe and update model
ynext = f(xnext)
model.add_data(xnext, ynext)
# evaluate the posterior and the acquisition function
mu, s2 = model.predict(xx)
# record our data and update the model
X.append(xnext)
Y.append(ynext)
F.append(f(xbest))
fig.clear()
ax1 = fig.add_subplotspec((2, 2), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 2), (1, 0), hidey=True, sharex=ax1)
ax3 = fig.add_subplotspec((2, 2), (0, 1), rowspan=2)
# plot the posterior and data
ax1.contourf(x1, x2, mu.reshape(x1.shape), alpha=0.4)
X_ = np.array(X)
ax1.scatter(X_[:-1, 0], X_[:-1, 1], marker='.')
ax1.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax1.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax1.set_xlim(*bounds[0])
ax1.set_ylim(*bounds[1])
ax1.set_title('current model (xbest and xnext)')
# plot the acquisition function
ax2.contourf(x1, x2, index(xx).reshape(x1.shape), alpha=0.5)
ax2.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax2.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax2.set_xlim(*bounds[0])
ax2.set_ylim(*bounds[1])
ax2.set_title('current policy (xnext)')
# plot the latent function at recomended points
ax3.axhline(f(xopt))
ax3.plot(F)
ax3.set_ylim(-1., 0.)
ax3.set_title('value of recommendation')
# draw
fig.canvas.draw()
show(block=False)
def main():
"""Run the demo."""
# define the bounds over which we'll optimize, the optimal x for comparison,
# and a sequence of test points
bounds = np.array([[-5, 10.], [0, 15]])
xopt = np.array([np.pi, 2.275])
x1, x2 = np.meshgrid(np.linspace(*bounds[0], num=100),
np.linspace(*bounds[1], num=100))
xx = np.c_[x1.flatten(), x2.flatten()]
# get initial data and some test points.
X = list(inits.init_latin(bounds, 6))
Y = [f(x_) for x_ in X]
F = list()
# initialize the model
model = make_gp(0.01, 10, [1., 1.], 0)
model.add_data(X, Y)
# set a prior on the parameters
model.params['like.sn2'].set_prior('uniform', 0.005, 0.015)
model.params['kern.rho'].set_prior('lognormal', 0, 3)
model.params['kern.ell'].set_prior('lognormal', 0, 3)
model.params['mean.bias'].set_prior('normal', 0, 20)
# make a model which samples parameters
model = MCMC(model, n=10, rng=None)
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# get index to solve it and plot it
index = policies.EI(model, bounds, X, xi=0.1)
# get the recommendation and the next query
xbest = recommenders.best_incumbent(model, bounds, X)
xnext, _ = solvers.solve_lbfgs(index, bounds)
# observe and update model
ynext = f(xnext)
model.add_data(xnext, ynext)
# evaluate the posterior and the acquisition function
mu, s2 = model.predict(xx)
# record our data and update the model
X.append(xnext)
Y.append(ynext)
F.append(f(xbest))
fig.clear()
ax1 = fig.add_subplotspec((2, 2), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 2), (1, 0), hidey=True, sharex=ax1)
ax3 = fig.add_subplotspec((2, 2), (0, 1), rowspan=2)
# plot the posterior and data
ax1.contourf(x1, x2, mu.reshape(x1.shape), alpha=0.4)
X_ = np.array(X)
ax1.scatter(X_[:-1, 0], X_[:-1, 1], marker='.')
ax1.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax1.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax1.set_xlim(*bounds[0])
ax1.set_ylim(*bounds[1])
ax1.set_title('current model (xbest and xnext)')
# plot the acquisition function
ax2.contourf(x1, x2, index(xx).reshape(x1.shape), alpha=0.5)
ax2.scatter(xbest[0], xbest[1], linewidths=3, marker='o', color='r')
ax2.scatter(xnext[0], xnext[1], linewidths=3, marker='o', color='g')
ax2.set_xlim(*bounds[0])
ax2.set_ylim(*bounds[1])
ax2.set_title('current policy (xnext)')
# plot the latent function at recomended points
ax3.axhline(f(xopt))
ax3.plot(F)
ax3.set_ylim(-1., 0.)
ax3.set_title('value of recommendation')
# draw
fig.canvas.draw()
show(block=False)
def main():
"""Run the demo."""
# define the bounds over which we'll optimize, the optimal x for
# comparison, and a sequence of test points
bounds = np.array([[0.5, 2.5]])
xopt = 0.54856343
fopt = f(xopt)
x = np.linspace(bounds[0][0], bounds[0][1], 500)
# get initial data and some test points.
X = list(inits.init_latin(bounds, 3))
Y = [f(x_) for x_ in X]
F = []
# initialize the model
model = make_gp(0.01, 1.9, 0.1, 0)
model.add_data(X, Y)
# set a prior on the parameters
model.params['like.sn2'].set_prior('uniform', 0.005, 0.015)
model.params['kern.rho'].set_prior('lognormal', 0, 100)
model.params['kern.ell'].set_prior('lognormal', 0, 10)
model.params['mean.bias'].set_prior('normal', 0, 20)
# make a model which samples parameters
model = MCMC(model, n=20, rng=None)
# create a new figure
fig = figure(figsize=(10, 6))
while True:
# get acquisition function (or index)
index = policies.EI(model, bounds, X, xi=0.1)
# get the recommendation and the next query
xbest = recommenders.best_incumbent(model, bounds, X)
xnext, _ = solvers.solve_lbfgs(index, bounds)
ynext = f(xnext)
# evaluate the posterior before updating the model for plotting
mu, s2 = model.predict(x[:, None])
# record our data and update the model
X.append(xnext)
Y.append(ynext)
F.append(f(xbest))
model.add_data(xnext, ynext)
# PLOT EVERYTHING
fig.clear()
ax1 = fig.add_subplotspec((2, 2), (0, 0), hidex=True)
ax2 = fig.add_subplotspec((2, 2), (1, 0), hidey=True, sharex=ax1)
ax3 = fig.add_subplotspec((2, 2), (0, 1), rowspan=2)
# plot the posterior and data
ax1.plot_banded(x, mu, 2*np.sqrt(s2))
ax1.scatter(np.ravel(X), Y)
ax1.axvline(xbest)
ax1.axvline(xnext, color='g')
ax1.set_ylim(-6, 3)
ax1.set_title('current model (xbest and xnext)')
# plot the acquisition function
ax2.plot_banded(x, index(x[:, None]))
ax2.axvline(xnext, color='g')
ax2.set_xlim(*bounds)
ax2.set_title('current policy (xnext)')
# plot the latent function at recomended points
ax3.plot(F)
ax3.axhline(fopt)
ax3.set_ylim(0.4, 0.9)
ax3.set_title('value of recommendation')
# draw
fig.canvas.draw()
show(block=False)