def visualise_trajectory(Qs, acc_probs, log_pdf_q, D, log_pdf=None):
assert Qs.ndim == 2
plot_density = log_pdf is not None and D==2
plt.figure(figsize=(10, 12))
plt.subplot(411)
# plot density if given and dimension is 2
if plot_density:
Xs = np.linspace(-30, 30, 75)
Ys = np.linspace(-10, 20, len(Xs))
D, G = pdf_grid(Xs, Ys, log_pdf)
visualise_array(Xs, Ys, D)
plt.plot(Qs[:, 0], Qs[:, 1])
plt.plot(Qs[0, 0], Qs[0, 1], 'r*', markersize=15)
plt.title("Log-pdf surrogate")
plt.subplot(412)
if plot_density:
visualise_array(Xs, Ys, G)
plt.plot(Qs[:, 0], Qs[:, 1])
plt.plot(Qs[0, 0], Qs[0, 1], 'r*', markersize=15)
plt.title("Gradient norm surrogate")
plt.subplot(413)
plt.title("Acceptance probability")
plt.xlabel("Leap frog iteration")
plt.plot(acc_probs)
plt.plot([0, len(acc_probs)], [np.mean(acc_probs) for _ in range(2)], 'r--')
plt.xlim([0, len(acc_probs)])
plt.subplot(414)
plt.title("Target log-pdf")
plt.xlabel("Leap frog iteration")
plt.plot(log_pdf_q)
plt.xlim([0, len(log_pdf_q)])
def visualise_trace(samples, log_pdf_trajectory, accepted, step_sizes=None, log_pdf_density=None, idx0=0, idx1=1):
assert samples.ndim == 2
D = samples.shape[1]
plt.figure(figsize=(15, 12))
plt.subplot(421)
plt.plot(samples[:, idx0])
plt.title("Trace $x_%d$" % (idx0+1))
plt.xlabel("MCMC iteration")
plt.grid(True)
plt.subplot(422)
plt.plot(samples[:, idx1])
plt.title("Trace $x_%d$" % (idx1+1))
plt.xlabel("MCMC iteration")
plt.grid(True)
plt.subplot(423)
if not log_pdf_density is None and D == 2:
Xs = np.linspace(-28, 28, 50)
Ys = np.linspace(-6, 16, len(Xs))
D, _ = pdf_grid(Xs, Ys, log_pdf_density)
visualise_array(Xs, Ys, D)
plt.plot(samples[:, idx0], samples[:, idx1])
plt.title("Trace $(x_%d, x_%d)$" % (idx0+1, idx1+1))
plt.grid(True)
plt.xlabel("$x_%d$" % (idx0+1))
plt.ylabel("$x_%d$" % (idx1+1))
plt.subplot(424)
plt.plot(log_pdf_trajectory)
plt.title("log pdf along trajectory")
plt.xlabel("MCMC iteration")
plt.grid(True)
plt.subplot(425)
plt.plot(autocorr(samples[:, idx0]))
plt.title("Autocorrelation $x_%d$" % (idx0+1))
plt.xlabel("Lag")
plt.grid(True)
plt.subplot(426)
plt.plot(autocorr(samples[:, idx1]))
plt.title("Autocorrelation $x_%d$" % (idx1+1))
plt.xlabel("Lag")
plt.grid(True)
plt.subplot(427)
plt.plot(np.cumsum(accepted) / np.arange(1, len(accepted)+1))
plt.title("Average acceptance rate")
plt.xlabel("MCMC iterations")
plt.grid(True)
if step_sizes is not None:
plt.subplot(428)
if step_sizes.ndim>1:
for i in range(step_sizes.shape[1]):
plt.plot(step_sizes[:,i])
plt.title("Step sizes")
else:
plt.plot(step_sizes)
plt.title("Step size")
plt.xlabel("MCMC iterations")
plt.grid(True)
est = KernelExpFiniteGaussian(sigma, lmbda, m, D)
# only for plotting
all_data = []
# plotting grid
width = 6
Xs = np.linspace(-width, width, 50)
Ys = np.linspace(-width, width, 50)
# plot ground truth
plt.figure(figsize=(10, 10))
fig_count = 1
plt.subplot(3, 3, fig_count)
_, G_true = pdf_grid(Xs, Ys, ground_truth())
visualise_array(Xs, Ys, G_true)
plt.title("Gradient norm, ground truth")
# plot initial fit
fig_count += 1
plt.subplot(3, 3, fig_count)
D, G = pdf_grid(Xs, Ys, est)
visualise_array(Xs, Ys, G)
plt.title("Gradient norm, no data")
plt.tight_layout()
# online updates of the model
for i in range(7):
X = np.random.randn(3 * (i + 1), est.D)
# only for plotting
