Can't run "Multivariate forecasting" in Pyro tutorial - runtime-error

Question

I am trying just to run the sample program at https://pyro.ai/examples/forecast_simple.html.
It runs until it reaches "RuntimeError torch.linalg.cholesky: For batch 4284: U(2,2) is zero, singular U." Every time when I run the code, it stops at the same location with "batch 4284".
Can anyone teach me how to fix it?
I am using below versions.
Python 3.9.1
pyro-api 0.1.2
pyro-ppl 1.7.0
torch 1.19.0
Windows10Pro 64bit 20H2
VScode 1.60.0
INFO step 0 loss = 7.356
INFO step 50 loss = 1.87751
INFO step 100 loss = 1.55338
INFO step 150 loss = 1.40953
INFO step 200 loss = 1.31982
INFO step 250 loss = 1.2017
INFO step 300 loss = 1.1389
INFO step 350 loss = 1.10407
INFO step 400 loss = 1.07474
INFO step 450 loss = 1.06728
INFO step 500 loss = 1.0285
DEBUG crps = 0.59017
DEBUG mae = 0.866027
DEBUG num_samples = 100
DEBUG rmse = 1.02721
DEBUG seed = 1.23457e+09
DEBUG t0 = 0
DEBUG t1 = 2160
DEBUG t2 = 2496
DEBUG test_walltime = 0.411458
DEBUG train_walltime = 28.8177
DEBUG AutoNormal.locs.obs_corr = -1.62159
DEBUG AutoNormal.locs.trans_corr = 2.49729
DEBUG AutoNormal.locs.trans_loc = 0.904184
DEBUG AutoNormal.scales.obs_corr = 0.207397
DEBUG AutoNormal.scales.trans_corr = 0.0915508
DEBUG AutoNormal.scales.trans_loc = 0.0111603
INFO Training on window [168:2328], testing on window [2328:2664]
INFO step 0 loss = 7.37245
INFO step 50 loss = 1.87162
:
:
:
DEBUG crps = 0.62036
DEBUG mae = 0.907584
DEBUG num_samples = 100
DEBUG rmse = 1.08631
DEBUG seed = 1.23457e+09
DEBUG t0 = 1512
DEBUG t1 = 3672
DEBUG t2 = 4008
DEBUG test_walltime = 0.404958
DEBUG train_walltime = 26.7937
DEBUG AutoNormal.locs.obs_corr = -0.889496
DEBUG AutoNormal.locs.trans_corr = 1.85566
DEBUG AutoNormal.locs.trans_loc = 0.903074
DEBUG AutoNormal.scales.obs_corr = 0.247679
DEBUG AutoNormal.scales.trans_corr = 0.0577488
DEBUG AutoNormal.scales.trans_loc = 0.012068
INFO Training on window [1680:3840], testing on window [3840:4176]
INFO step 0 loss = 7.48406
INFO step 50 loss = 1.92277
INFO step 100 loss = 1.58563
INFO step 150 loss = 1.52081
INFO step 200 loss = 1.44076
INFO step 250 loss = 1.38033
INFO step 300 loss = 1.29202
INFO step 350 loss = 1.26101
INFO step 400 loss = 1.23141
INFO step 450 loss = 1.23901
INFO step 500 loss = 1.21247
RuntimeError: torch.linalg.cholesky: For batch 4284: U(2,2) is zero, singular U.
RuntimeError Traceback (most recent call last)
~\AppData\Local\Temp/ipykernel_16928/3907557438.py in <module>
15
16 args = parser.parse_args()
---> 17 main(args)
~\AppData\Local\Temp/ipykernel_16928/4270697941.py in main(args)
24 }
25
---> 26 metrics = backtest(
27 data,
28 covariates,
c:\Users\9033113\venv\lib\site-packages\pyro\contrib\forecast\evaluate.py in backtest(data, covariates, model_fn, forecaster_fn, metrics, transform, train_window, min_train_window, test_window, min_test_window, stride, seed, num_samples, batch_size, forecaster_options)
199 while True:
200 try:
--> 201 pred = forecaster(
202 train_data,
203 test_covariates,
c:\Users\9033113\venv\lib\site-packages\pyro\contrib\forecast\forecaster.py in __call__(self, data, covariates, num_samples, batch_size)
359 :rtype: ~torch.Tensor
360 """
--> 361 return super().__call__(data, covariates, num_samples, batch_size)
362
363 def forward(self, data, covariates, num_samples, batch_size=None):
c:\Users\9033113\venv\lib\site-packages\torch\nn\modules\module.py in _call_impl(self, *input, **kwargs)
1049 if not (self._backward_hooks or self._forward_hooks or self._forward_pre_hooks or
_global_backward_hooks
1050 or _global_forward_hooks or _global_forward_pre_hooks):
-> 1051 return forward_call(*input, **kwargs)
1052 # Do not call functions when jit is used
1053 full_backward_hooks, non_full_backward_hooks = [], []
c:\Users\9033113\venv\lib\site-packages\pyro\contrib\forecast\forecaster.py in forward(self, data, covariates, num_samples, batch_size)
388 stack.enter_context(poutine.replay(trace=tr.trace))
389 with pyro.plate("particles", num_samples, dim=dim):
--> 390 return self.model(data, covariates)
391
392
c:\Users\9033113\venv\lib\site-packages\pyro\nn\module.py in __call__(self, *args, **kwargs)
424 def __call__(self, *args, **kwargs):
425 with self._pyro_context:
--> 426 return super().__call__(*args, **kwargs)
427
428 def __getattr__(self, name):
c:\Users\9033113\venv\lib\site-packages\torch\nn\modules\module.py in _call_impl(self, *input, **kwargs)
1049 if not (self._backward_hooks or self._forward_hooks or self._forward_pre_hooks or
_global_backward_hooks
1050 or _global_forward_hooks or _global_forward_pre_hooks):
-> 1051 return forward_call(*input, **kwargs)
1052 # Do not call functions when jit is used
1053 full_backward_hooks, non_full_backward_hooks = [], []
c:\Users\9033113\venv\lib\site-packages\pyro\contrib\forecast\forecaster.py in forward(self, data, covariates)
183 self._forecast = None
184
--> 185 self.model(zero_data, covariates)
186
187 assert self._forecast is not None, ".predict() was not called by .model()"
~\AppData\Local\Temp/ipykernel_16928/1541431941.py in model(self, zero_data, covariates)
76
77 # The final statement registers our noise model and prediction.
---> 78 self.predict(noise_model, prediction)
c:\Users\9033113\venv\lib\site-packages\pyro\contrib\forecast\forecaster.py in predict(self, noise_dist, prediction)
155 # PrefixConditionMessenger is handled outside of the .model() call.
156 self._prefix_condition_data["residual"] = data - left_pred
--> 157 noise = pyro.sample("residual", noise_dist)
158 del self._prefix_condition_data["residual"]
159
c:\Users\9033113\venv\lib\site-packages\pyro\primitives.py in sample(name, fn, *args, **kwargs)
162 }
163 # apply the stack and return its return value
--> 164 apply_stack(msg)
165 return msg["value"]
166
c:\Users\9033113\venv\lib\site-packages\pyro\poutine\runtime.py in apply_stack(initial_msg)
215 break
216
--> 217 default_process_message(msg)
218
219 for frame in stack[-pointer:]:
c:\Users\9033113\venv\lib\site-packages\pyro\poutine\runtime.py in default_process_message(msg)
176 return msg
177
--> 178 msg["value"] = msg["fn"](*msg["args"], **msg["kwargs"])
179
180 # after fn has been called, update msg to prevent it from being called again.
c:\Users\9033113\venv\lib\site-packages\pyro\distributions\torch_distribution.py in __call__(self, sample_shape)
46 """
47 return (
---> 48 self.rsample(sample_shape)
49 if self.has_rsample
50 else self.sample(sample_shape)
c:\Users\9033113\venv\lib\site-packages\pyro\distributions\hmm.py in rsample(self, sample_shape)
582 )
583 trans = trans.expand(trans.batch_shape[:-1] + (self.duration,))
--> 584 z = _sequential_gaussian_filter_sample(self._init, trans, sample_shape)
585 x = self._obs.left_condition(z).rsample()
586 return x
c:\Users\9033113\venv\lib\site-packages\pyro\distributions\hmm.py in _sequential_gaussian_filter_sample(init, trans, sample_shape)
142 joint = (x + y).event_permute(perm)
143 tape.append(joint)
--> 144 contracted = joint.marginalize(left=state_dim)
145 if time > even_time:
146 contracted = Gaussian.cat((contracted, gaussian[..., -1:]), dim=-1)
c:\Users\9033113\venv\lib\site-packages\pyro\ops\gaussian.py in marginalize(self, left, right)
242 P_ba = self.precision[..., b, a]
243 P_bb = self.precision[..., b, b]
--> 244 P_b = cholesky(P_bb)
245 P_a = triangular_solve(P_ba, P_b, upper=False)
246 P_at = P_a.transpose(-1, -2)
c:\Users\9033113\venv\lib\site-packages\pyro\ops\tensor_utils.py in cholesky(x)
398 if x.size(-1) == 1:
399 return x.sqrt()
--> 400 return torch.linalg.cholesky(x)
401
402
RuntimeError: torch.linalg.cholesky: For batch 4284: U(2,2
) is zero, singular U
.