Multitask GPQR (Center-Gap)

import os

import torch
from torch.distributions import Normal
from gpytorch.variational import CholeskyVariationalDistribution
from gpytorch.variational import UnwhitenedVariationalStrategy
from gpytorch.means import ConstantMean, Mean
from gpytorch.kernels import RBFKernel, ScaleKernel
from gpytorch.mlls import VariationalELBO
import matplotlib.pyplot as plt

from gpytorch_qr.means import CenterGapMean
from gpytorch_qr.models import CenterGapQuantileGP
from gpytorch_qr.variational import CGLmcVariationalStrategy
from gpytorch_qr.likelihoods import MultitaskCenterGapQuantileGPLikelihood

try:
    import sys

    sys.path.insert(0, os.path.abspath(".."))

    import config_notebook
except ImportError:
    print("Output will not be deterministic SVG.")

torch.manual_seed(42)
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

n_epochs = int(os.getenv("GPYTORCHQR_N_EPOCHS", 10000))

Data preparation

def mean(x):
    return torch.cos(x * 2 * 3.14)


def std(x):
    return x + 0.1


x = torch.linspace(0, 1, 100).reshape(-1, 1).to(device)
y = (mean(x) + torch.randn(x.shape, device=device).mul(std(x))).squeeze()
q = torch.linspace(0.1, 0.9, 9).to(device)
true_quantiles = mean(x) + std(x) * Normal(0, 1).icdf(q)
x_pred = torch.linspace(0, 1.5, 100).reshape(-1, 1).to(device)

plt.scatter(x.cpu(), y.cpu(), c="k", marker=".")
plt.plot(x.cpu(), true_quantiles.cpu(), "--", c="gray")
plt.show()

Prior mean

class PriorMean(Mean):
    def __init__(self, batch_shape=torch.Size()):
        super().__init__()
        self.batch_shape = batch_shape

    def forward(self, x):
        return mean(x).squeeze(-1).expand(*self.batch_shape, x.shape[-2])


prior_mean = PriorMean().to(device)

plt.scatter(x.cpu(), y.cpu(), c="k", marker=".")
plt.plot(x_pred.cpu(), prior_mean(x_pred).detach().cpu())
plt.show()

Define models and likelihoods

class MyGP_PriorMean(CenterGapQuantileGP):
    def __init__(
        self,
        inducing_points,
        num_quantiles,
        num_lower_quantiles,
        num_latents,
    ):
        N, D = inducing_points.size()
        variational_distribution = CholeskyVariationalDistribution(
            N,
            batch_shape=torch.Size([num_latents]),
        )
        variational_strategy = CGLmcVariationalStrategy(
            UnwhitenedVariationalStrategy(
                self,
                inducing_points,
                variational_distribution,
                learn_inducing_locations=True,
            ),
            num_quantiles=num_quantiles,
            num_latents=num_latents,
        )

        mean = CenterGapMean(
            PriorMean(batch_shape=torch.Size([1])),
            ConstantMean(batch_shape=torch.Size([num_latents - 1])),
            latent_dim=-1,
        )
        covar = ScaleKernel(
            RBFKernel(ard_num_dims=D, batch_shape=torch.Size([num_latents])),
            batch_shape=torch.Size([num_latents]),
        )
        super().__init__(variational_strategy, mean, covar, -1, num_lower_quantiles)


inducing_points = x.detach().clone()
central_q_index = (q - 0.5).abs().argmin().item()
num_latents = len(q) - 2
gp_priormean = MyGP_PriorMean(inducing_points, len(q), central_q_index, num_latents).to(
    device
)
likelihood_priormean = MultitaskCenterGapQuantileGPLikelihood(q, central_q_index).to(
    device
)

Train

gp_priormean.train()
likelihood_priormean.train()
mll = VariationalELBO(likelihood_priormean, gp_priormean, num_data=y.numel())
optimizer = torch.optim.Adam(
    list(gp_priormean.parameters()) + list(likelihood_priormean.parameters()),
    lr=0.001,
)

for _ in range(n_epochs):
    output = gp_priormean(x)
    loss = -mll(output, y)
    loss.backward()
    optimizer.step()
    optimizer.zero_grad()

Evaluate

gp_priormean.eval()
with torch.no_grad():
    quantiles_priormean = gp_priormean.mean_quantiles_mc(x_pred)

Plot result

colors = plt.cm.tab10(range(len(q)))

plt.scatter(x.cpu(), y.cpu(), c="gray", marker=".", alpha=0.1)
plt.plot(x.cpu(), true_quantiles.cpu(), "--", c="gray", alpha=0.5)

for i in range(len(q)):
    plt.plot(x_pred.cpu(), quantiles_priormean[:, i].cpu(), color=colors[i])

plt.show()