code: def model(X, Y, hypers, jitter=1.0e-4):
      S, P, N = hypers["expected_sparsity"], X.size(1), X.size(0)
  
      sigma = pyro.sample("sigma", dist.HalfNormal(hypers["alpha3"]))
      phi = sigma * (S / math.sqrt(N)) / (P - S)
      eta1 = pyro.sample("eta1", dist.HalfCauchy(phi))
  
      msq = pyro.sample(
          "msq", dist.InverseGamma(hypers["alpha1"], hypers["beta1"])
      )
      xisq = pyro.sample(
          "xisq", dist.InverseGamma(hypers["alpha2"], hypers["beta2"])
      )
  
      eta2 = eta1.pow(2.0) * xisq.sqrt() / msq
  
      lam = pyro.sample(
          "lambda",
          dist.HalfCauchy(torch.ones(P, device=X.device)).to_event(1),
      )
      kappa = msq.sqrt() * lam / (msq + (eta1 * lam).pow(2.0)).sqrt()
      kX = kappa * X
  
      # compute the kernel for the given hyperparameters
      k = kernel(kX, kX, eta1, eta2, hypers["c"]) + (
          sigma**2 + jitter
      ) * torch.eye(N, device=X.device)
  
      # observe the outputs Y
      pyro.sample(
          "Y",
          dist.MultivariateNormal(
              torch.zeros(N, device=X.device), covariance_matrix=k
          ),
          obs=Y,
      )
  
file_path: pyro/examples/sparse_regression.py
imports: import argparse
  import math
  import numpy
  import torch
  from torch.optim import Adam
  import pyro
  import pyro.distributions
  from pyro import poutine
  from pyro.infer import Trace_ELBO
  from pyro.infer.autoguide import AutoDelta, init_to_median
label_desc: Use image node_id 3 for calling a global function with example usage: model(X, Y, hypers, jitter) without return types