code: def model(self, x):
      x_size = x.size(0)
  
      # sample the global weights
      with pyro.plate("w_top_plate", self.top_width * self.mid_width):
          w_top = pyro.sample("w_top", Gamma(self.alpha_w, self.beta_w))
      with pyro.plate(
          "w_mid_plate", self.mid_width * self.bottom_width
      ):
          w_mid = pyro.sample("w_mid", Gamma(self.alpha_w, self.beta_w))
      with pyro.plate(
          "w_bottom_plate", self.bottom_width * self.image_size
      ):
          w_bottom = pyro.sample(
              "w_bottom", Gamma(self.alpha_w, self.beta_w)
          )
  
      # sample the local latent random variables
      # (the plate encodes the fact that the z's for different datapoints are conditionally independent)
      with pyro.plate("data", x_size):
          z_top = pyro.sample(
              "z_top",
              Gamma(self.alpha_z, self.beta_z)
              .expand([self.top_width])
              .to_event(1),
          )
          # note that we need to use matmul (batch matrix multiplication) as well as appropriate reshaping
          # to make sure our code is fully vectorized
          w_top = (
              w_top.reshape(self.top_width, self.mid_width)
              if w_top.dim() == 1
              else w_top.reshape(-1, self.top_width, self.mid_width)
          )
          mean_mid = torch.matmul(z_top, w_top)
          z_mid = pyro.sample(
              "z_mid",
              Gamma(self.alpha_z, self.beta_z / mean_mid).to_event(1),
          )
  
          w_mid = (
              w_mid.reshape(self.mid_width, self.bottom_width)
              if w_mid.dim() == 1
              else w_mid.reshape(-1, self.mid_width, self.bottom_width)
          )
          mean_bottom = torch.matmul(z_mid, w_mid)
          z_bottom = pyro.sample(
              "z_bottom",
              Gamma(self.alpha_z, self.beta_z / mean_bottom).to_event(
                  1
              ),
          )
  
          w_bottom = (
              w_bottom.reshape(self.bottom_width, self.image_size)
              if w_bottom.dim() == 1
              else w_bottom.reshape(
                  -1, self.bottom_width, self.image_size
              )
          )
          mean_obs = torch.matmul(z_bottom, w_bottom)
  
          # observe the data using a poisson likelihood
          pyro.sample("obs", Poisson(mean_obs).to_event(1), obs=x)
  
imports: import argparse
  import errno
  import os
  import numpy
  import torch
  import wget
  from torch.nn.functional import softplus
  import pyro
  import pyro.optim
  from pyro.contrib.easyguide import EasyGuide
  from pyro.contrib.examples.util import get_data_directory
  from pyro.distributions import Gamma, Normal, Poisson
  from pyro.infer import SVI, TraceMeanField_ELBO
  from pyro.infer.autoguide import AutoDiagonalNormal, init_to_feasible
label_desc: Use image node_id 2 for calling the SparseGammaDEF obj's underlying member method code with example usage: obj.model(x) without return types