Scalable GP Classification in 1D (w/ SVGP)ΒΆ

This example shows how to use grid interpolation based variational classification with an AbstractVariationalGP using a VariationalStrategy module while learning the inducing point locations.

In [1]:
import math
import torch
import gpytorch
from matplotlib import pyplot as plt
from math import exp

%matplotlib inline
%load_ext autoreload
%autoreload 2
/home/gpleiss/anaconda3/envs/gpytorch/lib/python3.7/site-packages/matplotlib/__init__.py:999: UserWarning: Duplicate key in file "/home/gpleiss/.dotfiles/matplotlib/matplotlibrc", line #57
  (fname, cnt))
In [2]:
train_x = torch.linspace(0, 1, 260)
train_y = torch.cos(train_x * (2 * math.pi)) + 0.1 * torch.randn(260)
In [3]:
from gpytorch.models import AbstractVariationalGP
from gpytorch.variational import CholeskyVariationalDistribution
from gpytorch.variational import VariationalStrategy
class SVGPRegressionModel(AbstractVariationalGP):
    def __init__(self, inducing_points):
        variational_distribution = CholeskyVariationalDistribution(inducing_points.size(-1))
        variational_strategy = VariationalStrategy(self,
                                                   inducing_points,
                                                   variational_distribution,
                                                   learn_inducing_locations=True)
        super(SVGPRegressionModel, self).__init__(variational_strategy)
        self.mean_module = gpytorch.means.ConstantMean()
        self.covar_module = gpytorch.kernels.ScaleKernel(gpytorch.kernels.RBFKernel())

    def forward(self,x):
        mean_x = self.mean_module(x)
        covar_x = self.covar_module(x)
        latent_pred = gpytorch.distributions.MultivariateNormal(mean_x, covar_x)
        return latent_pred


# We'll initialize the inducing points to evenly span the space of train_x
inducing_points = torch.linspace(0, 1, 25)
model = SVGPRegressionModel(inducing_points)
likelihood = gpytorch.likelihoods.GaussianLikelihood()
In [4]:
from gpytorch.mlls.variational_elbo import VariationalELBO

# Find optimal model hyperparameters
model.train()
likelihood.train()

# Use the adam optimizer
optimizer = torch.optim.Adam([
    {'params': model.parameters()},
    {'params': likelihood.parameters()}
], lr=0.01)

# "Loss" for GPs - the marginal log likelihood
# n_data refers to the amount of training data
mll = VariationalELBO(likelihood, model, train_y.size(0), combine_terms=False)

def train():
    num_iter = 200
    for i in range(num_iter):
        optimizer.zero_grad()
        output = model(train_x)
        # Calc loss and backprop gradients
        log_lik, kl_div, log_prior = mll(output, train_y)
        loss = -(log_lik - kl_div + log_prior)
        loss.backward()
        if i % 50 == 0:
            print('Iter %d - Loss: %.3f [%.3f, %.3f, %.3f]' % (i + 1, loss.item(), log_lik.item(), kl_div.item(), log_prior.item()))
        optimizer.step()

# Get clock time
%time train()
Iter 1 - Loss: 1.495 [-1.487, 0.008, 0.000]
Iter 51 - Loss: 0.926 [-0.873, 0.054, 0.000]
Iter 101 - Loss: 0.573 [-0.447, 0.127, 0.000]
Iter 151 - Loss: 0.380 [-0.116, 0.264, 0.000]
CPU times: user 18.9 s, sys: 19.9 s, total: 38.9 s
Wall time: 5.57 s
In [5]:

test_x = torch.linspace(0, 1, 51)
observed_pred = likelihood(model(test_x))

with torch.no_grad():
    # Initialize plot
    f, ax = plt.subplots(1, 1, figsize=(4, 3))

    # Get upper and lower confidence bounds
    lower, upper = observed_pred.confidence_region()
    # Plot training data as black stars
    ax.plot(train_x.numpy(), train_y.numpy(), 'k*')
    # Plot predictive means as blue line
    ax.plot(test_x.numpy(), observed_pred.mean.detach().numpy(), 'b')
    # Shade between the lower and upper confidence bounds
    ax.fill_between(test_x.numpy(), lower.numpy(), upper.numpy(), alpha=0.5)
    ax.set_ylim([-3, 3])
    ax.legend(['Observed Data', 'Mean', 'Confidence'])
../../_images/examples_04_Scalable_GP_Regression_1D_SVGP_Regression_1D_5_0.png
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