 # Simple Feature Allocation model

Hi all,

I am (very) new to Pyro; I am sorry if this (or similar) question has already been solved elsewhere. I spent some time looking around and could not find a solution to my problem. I am trying to write down a model for a feature allocation (admixture) model (concretely, the model in Figure 7/Equation 19 of https://www.cs.princeton.edu/courses/archive/fall11/cos597C/reading/griffiths11a.pdf).

This is a simple extension of a (Bayesian) mixture model in which each datapoint is allowed to belong to more than one “cluster”. In the simple “Gaussian-Linear” case, for a fixed integer K, we first draw K probabilities p_1, …, p_K i.i.d. from a Beta distribution with parameters a, b together with K locations mu_1, …, mu_K i.i.d. from a Gaussian (mu_0, sigma_0). A datapoint X_n is generated as follows: for every component k, z_{n,k} ~ Bernoulli(p_k) independently of everything else, and letting mu_n = z_{n,1} * mu_1 + … + z_{n,K} * mu_K, we have X_n ~ Normal(mu_n, sigma).

I thought that it should be a straightforward exercise to extend the Gaussian Mixture Model tutorial to this model but I’m having trouble with that.

e.g. if I try to replicate the steps in https://pyro.ai/examples/gmm.html but replace the model function with:

``````num_components = 3  # Fixed number of components.

@config_enumerate
def model(data):
# Global vbles
weights = pyro.sample('weights', dist.Beta(0.5 * torch.ones(num_components), 0.5 * torch.ones(num_components)))
scale = pyro.sample('scale', dist.LogNormal(0., 2.))
with pyro.plate('components', num_components):
locs = pyro.sample('locs', dist.Normal(0., 10.))
with pyro.plate('data', len(data)):
# Local variables.
assignment = pyro.sample('assignment', dist.Bernoulli(weights))
mu = torch.dot(assignment, locs)
pyro.sample('obs', dist.Normal(mu, scale), obs=data)
``````

then running the initialize(seed) function defined in https://pyro.ai/examples/gmm.html gives me the following error:

Shape mismatch inside plate(‘data’) at site assignment dim -1, 3000 vs 3

which seems to be related to my “assignment” statement in the model() function. I feel like I must be doing something very dumb, any help is greatly appreciated!

Hi @lnzmsr, welcome! I would suggest to draw a plate diagram first, then it will be easy for you to write the corresponding code. For example, if `weights`, `assignment` are under `components` plate, you should put them inside the `components` plate. For example

``````    scale = pyro.sample('scale', dist.LogNormal(0., 2.))
with pyro.plate('data', len(data), dim=-2):
with pyro.plate('components', num_components, dim=-1):
locs = pyro.sample('locs', dist.Normal(0., 10.))
weights = pyro.sample('weights', dist.Beta(0.5, 0.5))
assignment = pyro.sample('assignment', dist.Bernoulli(weights))
mu = torch.dot(assignment, locs)  # locs[assigments]...?
pyro.sample('obs', dist.Normal(mu, scale), obs=data.unsqueeze(-1))
``````

You will need to tune `mu` a bit to get correct result (i.e. the `data` dimension is the second one from the right).

You can also switch `data` and `components` dimensions. For example,

``````    with pyro.plate('data', len(data), dim=-1):
with pyro.plate('components', num_components, dim=-2):
locs = pyro.sample('locs', dist.Normal(0., 10.))
weights = pyro.sample('weights', dist.Beta(0.5, 0.5))
assignment = pyro.sample('assignment', dist.Bernoulli(weights))
mu = torch.dot(assignment, locs)  # locs[assigments]...?
pyro.sample('obs', dist.Normal(mu, scale), obs=data)
``````

to skip `unsqueeze` your data. Similarly, you will need to check again if `torch.dot` gives the expected result for `mu`. This time, make sure that the rightmost dimension of `mu` is `data` dimension.

In case it is helpful, this example has a bunch of mixture models and the corresponding plate diagrams. I believe it will be very helpful for you.

1 Like

@fehiepsi thanks for the quick and thorough reply! it looks very helpful!

Thanks for the useful replies; I am just writing to follow-up on this question since I’m still having troubles implementing this in an effective way in Pyro. In summary, I’m able to write an explicit model (looping over all variables) but struggling to write the equivalent model using the plate contexts.

To be concrete, the plate model I have in mind is the following:

I am facing the following issue: I write down the non-plate, sequential version of the model, I get something that seems to be compiling, however, the corresponding “plate notation” seems to be having issues. Any suggestion to make the code correct (I eventually would like to move to the case in which the data is in dimension d, i.e. i want to be using torch.matmul(assignments, mu) in place of torch.dot(assignment, mu)) would be greatly appreciated!

For completeness I attach the actual code I am running. For the “sequential”, non-plate version:

num_components = 2 # Fixed number of components.

def model(data):

``````N = len(data)
scale = torch.tensor(1.0)

# after all plates, weights and locs will be tensors of size (num_components,)
weights = torch.zeros(num_components)
locs = torch.zeros(num_components)
for k in range(num_components):
weights[k] = pyro.sample('weights_{}'.format(k), dist.Beta(0.5, 0.5))
locs[k] = pyro.sample('locs_{}'.format(k), dist.Normal(0., 10.))

for n in range(N):
Z = torch.zeros(num_components)
for k in range(num_components):
Z[k] = pyro.sample('assignments_{}_{}'.format(n,k), dist.Bernoulli(weights[k]))
pyro.sample('obs_{}'.format(n), dist.Normal(torch.dot(Z, locs), scale),obs=data[n])
``````

def guide(data):
N = len(data)
# register variational parameters, with the initial values
kappa = pyro.param(‘kappa’, lambda: dist.Uniform(0, 2).sample([num_components]), constraint=constraints.positive)
tau = pyro.param(‘tau’, lambda: dist.Normal(torch.zeros(1), 1).sample([num_components]))
phi = pyro.param(‘phi’, lambda: dist.Beta(1.,1.).sample([N, num_components]), constraint=constraints.unit_interval)

``````# register variational distributions
for k in range(num_components):
pyro.sample('weights_{}'.format(k),dist.Beta(1.0,kappa[k]))
pyro.sample('locs_{}'.format(k), dist.Normal(tau[k], 1.0))

for n in range(N):
for k in range(num_components):
pyro.sample('assignments_{}_{}'.format(n,k), dist.Bernoulli(phi[n,k]))
``````

optim = pyro.optim.Adam({‘lr’: 0.1, ‘betas’: [0.8, 0.99]})
elbo = Trace_ELBO()
svi = SVI(model, guide, optim, loss=elbo)
n_steps = 100
for step in range(n_steps):
svi.step(data)

The parallel, plate version:

def plate_model(data):
N = len(data)
scale = torch.tensor(1.0)
with pyro.plate(“components”, num_components):
weights = pyro.sample(‘weights’, dist.Beta(0.5, 0.5))
locs = pyro.sample(‘locs’, dist.Normal(0., 10.))

``````with pyro.plate('data', len(data), dim = -2):
# Local variables.
Z = pyro.sample('assignments', dist.Bernoulli(weights))
pyro.sample('obs', dist.Normal(torch.dot(Z, locs), scale), obs=data)
``````

def plate_guide(data):

``````# register variational parameters, with the initial values
kappa = pyro.param('kappa', lambda: dist.Uniform(0, 2).sample([num_components]), constraint=constraints.positive)
tau = pyro.param('tau', lambda: dist.Normal(torch.zeros(1), 1).sample([num_components]))
phi = pyro.param('phi', lambda: dist.Beta(1.,1.).sample([N, num_components]), constraint=constraints.unit_interval)

with pyro.plate("components", num_components):
weights = pyro.sample('weights', dist.Beta(0.5, kappa))
locs = pyro.sample('locs', dist.Normal(tau, 10.))

with pyro.plate('data', len(data), dim = -2):
Z = pyro.sample('assignments', dist.Bernoulli(phi))
``````

optim = pyro.optim.Adam({‘lr’: 0.1, ‘betas’: [0.8, 0.99]})
elbo = Trace_ELBO()

svi = SVI(plate_model, plate_guide, optim, loss=elbo)
for i in tqdm(range(200)):
loss = svi.step(data)

I get the following error:

RuntimeError: 1D tensors expected, got 2D, 2D tensors at /opt/conda/conda-bld/pytorch_1595629395347/work/aten/src/TH/generic/THTensorEvenMoreMath.cpp:83
Trace Shapes:
Param Sites:
Sample Sites:
components dist |
value 2 |
weights dist 2 |
value 2 |
locs dist 2 |
value 2 2 |
data dist |
value 100 |
assignments dist 100 2 |
value 100 2 |

If I remove the dim = -2 in the plate notation I get a different error (here I ran on data with data.shape = 100):

ValueError: Shape mismatch inside plate(‘data’) at site assignments dim -1, 100 vs 2
Trace Shapes:
Param Sites:
kappa 2
tau 2 1
phi 100 2
Sample Sites:
components dist |
value 2 |
weights dist 2 |
value 2 |
locs dist 2 2 |
value 2 2 |
data dist |
value 100 |

Another issue I’ve had is related to initialization in self-designed guides: I tried to look for examples of guides with initializations (in the spirit of init_loc_fn() in https://pyro.ai/examples/gmm.html) but I couldn’t find any.

Thanks!

@lnzmsr Could you format your post to make it displayed better? To debug the issue, you can

• run `model(data)` alone to see if it gives the expected results for you
• similarly, run `guide(data)` alone
• add some print statements after each `sample` statements to see if you get correct shapes of parameters (and they are consistent in both `model` and `guide`)
• check if operators such as `torch.dot` gives expected result for you

I would suggest doing those steps before running any inference code.