Hi,
Pyro looks very interesting and promising, thank you.
is it possible to infer (to assess, to create) a multidimensional Gaussian Mixture Model just from the matrix of observation using Pyro?
(ideally the number of GMM modes should be also assessed from the data)
kind regards,
Valery
P.S. site sign-up and sign-in is like from 2005 – errors everywhere and activation email in gmail spam telling me that Google can’t ensure the email comes indeed from the sender stated in the email.
Hi, see the Gaussian mixture model tutorial for an introduction to mixture models in Pyro, and the Dirichlet process mixture model tutorial for an example of fitting a mixture model with an unknown number of components.
many thanks for the hint!
“we do not parameterize the covariance matrices of the Gaussians, though this should be done when analyzing a real-world dataset for more flexibility”
arghhh… the most interesting part is cut out from Dirichlet process mixture model tutorial 
any hint on this, please?
You can just sample multiple scales along with the means. For the simpler model in the Gaussian mixture model tutorial, that means moving the scale variable inside the components plate and indexing it with the assignment in the likelihood:
weights = pyro.sample('weights', dist.Dirichlet(0.5 * torch.ones(K)))
with pyro.plate('components', K):
scales = pyro.sample('scale', dist.LogNormal(0., 2.))
locs = pyro.sample('locs', dist.Normal(0., 10.))
with pyro.plate('data', len(data)):
assignment = pyro.sample('assignment', dist.Categorical(weights))
pyro.sample('obs', dist.Normal(locs[assignment], scales[assignment]), obs=data)
In the multivariate setting, you can do something similar using the LKJCorrCholesky distribution (docs, example) to define a prior distribution over covariance Cholesky factors for each mixture component.
regarding “Dirichlet process mixture model tutorial”:
This section of the tutorial doesn’t seem to be reproducible anymore:
0%| | 0/1500 [00:00<?, ?it/s]
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
~usr/local/lib/python3.6/dist-packages/pyro/poutine/trace_struct.py in compute_log_prob(self, site_filter)
215 try:
--> 216 log_p = site["fn"].log_prob(site["value"], *site["args"], **site["kwargs"])
217 except ValueError:
~usr/local/lib/python3.6/dist-packages/torch/distributions/poisson.py in log_prob(self, value)
60 if self._validate_args:
---> 61 self._validate_sample(value)
62 rate, value = broadcast_all(self.rate, value)
~usr/local/lib/python3.6/dist-packages/torch/distributions/distribution.py in _validate_sample(self, value)
252 if not self.support.check(value).all():
--> 253 raise ValueError('The value argument must be within the support')
254
ValueError: The value argument must be within the support
During handling of the above exception, another exception occurred:
ValueError Traceback (most recent call last)
<ipython-input-9-4e79a15ea6fc> in <module>
32 losses = []
33
---> 34 train(n_iter)
35
36 samples = torch.arange(0, 300).type(torch.float)
<ipython-input-6-c5d9a36e9211> in train(num_iterations)
7 pyro.clear_param_store()
8 for j in tqdm(range(num_iterations)):
----> 9 loss = svi.step(data)
10 losses.append(loss)
11
~usr/local/lib/python3.6/dist-packages/pyro/infer/svi.py in step(self, *args, **kwargs)
126 # get loss and compute gradients
127 with poutine.trace(param_only=True) as param_capture:
--> 128 loss = self.loss_and_grads(self.model, self.guide, *args, **kwargs)
129
130 params = set(site["value"].unconstrained()
~usr/local/lib/python3.6/dist-packages/pyro/infer/trace_elbo.py in loss_and_grads(self, model, guide, *args, **kwargs)
124 loss = 0.0
125 # grab a trace from the generator
--> 126 for model_trace, guide_trace in self._get_traces(model, guide, args, kwargs):
127 loss_particle, surrogate_loss_particle = self._differentiable_loss_particle(model_trace, guide_trace)
128 loss += loss_particle / self.num_particles
~usr/local/lib/python3.6/dist-packages/pyro/infer/elbo.py in _get_traces(self, model, guide, args, kwargs)
168 else:
169 for i in range(self.num_particles):
--> 170 yield self._get_trace(model, guide, args, kwargs)
~usr/local/lib/python3.6/dist-packages/pyro/infer/trace_elbo.py in _get_trace(self, model, guide, args, kwargs)
51 """
52 model_trace, guide_trace = get_importance_trace(
---> 53 "flat", self.max_plate_nesting, model, guide, args, kwargs)
54 if is_validation_enabled():
55 check_if_enumerated(guide_trace)
~usr/local/lib/python3.6/dist-packages/pyro/infer/enum.py in get_importance_trace(graph_type, max_plate_nesting, model, guide, args, kwargs, detach)
53 model_trace = prune_subsample_sites(model_trace)
54
---> 55 model_trace.compute_log_prob()
56 guide_trace.compute_score_parts()
57 if is_validation_enabled():
~usr/local/lib/python3.6/dist-packages/pyro/poutine/trace_struct.py in compute_log_prob(self, site_filter)
219 shapes = self.format_shapes(last_site=site["name"])
220 raise ValueError("Error while computing log_prob at site '{}':\n{}\n{}"
--> 221 .format(name, exc_value, shapes)).with_traceback(traceback)
222 site["unscaled_log_prob"] = log_p
223 log_p = scale_and_mask(log_p, site["scale"], site["mask"])
~usr/local/lib/python3.6/dist-packages/pyro/poutine/trace_struct.py in compute_log_prob(self, site_filter)
214 if "log_prob" not in site:
215 try:
--> 216 log_p = site["fn"].log_prob(site["value"], *site["args"], **site["kwargs"])
217 except ValueError:
218 _, exc_value, traceback = sys.exc_info()
~usr/local/lib/python3.6/dist-packages/torch/distributions/poisson.py in log_prob(self, value)
59 def log_prob(self, value):
60 if self._validate_args:
---> 61 self._validate_sample(value)
62 rate, value = broadcast_all(self.rate, value)
63 return (rate.log() * value) - rate - (value + 1).lgamma()
~usr/local/lib/python3.6/dist-packages/torch/distributions/distribution.py in _validate_sample(self, value)
251
252 if not self.support.check(value).all():
--> 253 raise ValueError('The value argument must be within the support')
254
255 def _get_checked_instance(self, cls, _instance=None):
ValueError: Error while computing log_prob at site 'obs':
The value argument must be within the support
Trace Shapes:
Param Sites:
Sample Sites:
beta dist 19 |
value 19 |
log_prob 19 |
lambda dist 20 |
value 20 |
log_prob 20 |
z dist 320 |
value 320 |
log_prob 320 |
obs dist 320 |
value 320 |
Hi All,
Forgive me, I am new to Pyro but I tried to implement the discussion above as I have a need for a multivariate mixture with a full covariance matrix. I thought the code would be too verbose so I included it in a gist here.
The model infers reasonably well however with two major problems:
If anyone has a chance to take a look that would be great.