GPytorch - Manual prediction from a Guasisan process regressor is not the same as the built-in functionality

[Majeed7]

I am new to GPytorch and my question might seem rudimentary! but I am really stuck!

To explain my problem, I use a simple GP regressor to explain the problem. Let's say I have the following model in GPytorch to train a regressor:

import torch
import gpytorch
from gpytorch.kernels import RBFKernel
from gpytorch.means import ConstantMean, ZeroMean
from gpytorch.likelihoods import GaussianLikelihood
from gpytorch.models import ExactGP

# Generate synthetic data
torch.manual_seed(0)
train_x = torch.linspace(0, 1, 100)
train_y = torch.sin(train_x * (2 * torch.pi)) + torch.randn(train_x.size()) * 0.2

class GPRegressionModel(ExactGP):
    def __init__(self, train_x, train_y, likelihood):
        super(GPRegressionModel, self).__init__(train_x, train_y, likelihood)
        self.mean_module = ZeroMean()
        self.covar_module = RBFKernel()
    
    def forward(self, x):
        mean_x = self.mean_module(x)
        covar_x = self.covar_module(x)
        return gpytorch.distributions.MultivariateNormal(mean_x, covar_x)

likelihood = GaussianLikelihood()
model = GPRegressionModel(train_x, train_y, likelihood)

# Model training
model.train()
likelihood.train()
optimizer = torch.optim.Adam(model.parameters(), lr=0.1)
mll = gpytorch.mlls.ExactMarginalLogLikelihood(likelihood, model)
training_iterations = 50

for i in range(training_iterations):
    optimizer.zero_grad()
    output = model(train_x)
    loss = -mll(output, train_y)
    loss.backward()
    optimizer.step()

Now, I can do the prediction automatically by the GPytorch built-in functionality as:

# Example test instance
test_x = torch.tensor([0.5])

# Model prediction 
model.eval()
likelihood.eval()

with torch.no_grad(), gpytorch.settings.fast_pred_var():
    observed_pred = likelihood(model(test_x))
    model_mean = observed_pred.mean.item()
    model_variance = observed_pred.variance.item()

But since I would like to make some other inferences, I would use the optimized hyperparameters for some calculations; I realized that I could not even replicate the prediction made by the model as above! Here my code for making the prediction based on the model hyperparameters:

# Extract lengthscale and noise variance
lengthscale = model.covar_module.lengthscale.item()
noise_variance = model.likelihood.noise.item()

# Define the refined prediction function
def rbf_kernel(x1, x2, lengthscale):
    """Compute the RBF kernel between x1 and x2."""
    diff = x1.unsqueeze(1) - x2.unsqueeze(0)
    dists = torch.sum(diff ** 2, -1)
    return torch.exp(-0.5 * dists / lengthscale ** 2)

def predict_from_parameters(train_x, train_y, test_x, lengthscale, noise_variance):
    K = rbf_kernel(train_x, train_x, lengthscale) + noise_variance * torch.eye(train_x.size(0))
    K_s = rbf_kernel(train_x, test_x, lengthscale)
    K_ss = rbf_kernel(test_x, test_x, lengthscale) + noise_variance * torch.eye(test_x.size(0))

    L = torch.linalg.cholesky(K)
    alpha = torch.cholesky_solve(train_y.unsqueeze(-1), L)
    pred_mean = K_s.t().matmul(alpha).squeeze()
    v = torch.linalg.solve(L, K_s)
    pred_var = K_ss - v.t().matmul(v)
    return pred_mean, pred_var.diag()

# Manual prediction
pred_mean, pred_var = predict_from_parameters(train_x, train_y, test_x, lengthscale, noise_variance)

Problem:

The manual prediction (pred_mean and pred_var) is entirely different from those obtained from the GPytorch built-in functionality (model_mean, model_var). I have not been able to figure out where I go wrong.

Any help is highly appreciated!

[jacobrgardner]

Hi,

your train_x is the wrong shape for the RBF kernel as you've implemented it. Your train_x is torch.Size([100]). rbf_kernel(train_x, train_x, lengthscale) essentially returns a matrix of all zeros as implemented like that. Doing:

train_x = train_x.unsqueeze(-1)    # makes train_x [100, 1]

and then running your last block of code works.