code: def test_hmm_backward(hmm, X, priors):
      X = numpy.array([X])
      priors = priors.unsqueeze(0)
  
      y_hat = hmm.backward(X)
      assert_array_almost_equal(
          y_hat,
          [
              [
                  [-39.9505, -38.8647],
                  [-36.6752, -35.5766],
                  [-31.9407, -30.8421],
                  [-24.6495, -25.1184],
                  [-22.4807, -21.3821],
                  [-12.6419, -13.0719],
                  [-10.9597, -9.8611],
                  [-5.0633, -5.4492],
                  [-3.8699, -2.7714],
                  [1.8499, 1.1644],
                  [-0.6931, -0.6931],
              ]
          ],
          4,
      )
  
      y_hat = hmm.backward(X, priors=priors)
      assert_array_almost_equal(
          y_hat,
          [
              [
                  [-55.7255, -54.6397],
                  [-51.7571, -50.6585],
                  [-46.3294, -45.2308],
                  [-39.0382, -39.5071],
                  [-36.1763, -35.0777],
                  [-25.9039, -26.4107],
                  [-23.6907, -22.5921],
                  [-18.5856, -17.4870],
                  [-12.9685, -13.6616],
                  [1.1567, 0.4712],
                  [-0.6931, -0.6931],
              ]
          ],
          4,
      )
  
imports: import os
  import numpy
  import torch
  import pytest
  from pomegranate.gmm import GeneralMixtureModel
  from pomegranate.hmm import DenseHMM
  from pomegranate.distributions import Exponential
  from nose.tools import assert_raises
  from numpy.testing import assert_array_equal
  from numpy.testing import assert_array_almost_equal
label_desc: Use image node_id 27 for calling a global function with example usage: test_hmm_backward(hmm, X, priors) without return types