# Dirichlet with random shape

**URL:** <https://discourse.pymc.io/t/dirichlet-with-random-shape/3015>\
**Category:** Questions\
**Created:** [March 27, 2019, 5:43pm UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015 "2019-03-27T17:43:54Z")\
**Posts on this page:** 8\
**Page:** 1

<div class="post-metadata">

**Author:** ![arraval](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/arraval/32/1691_2.png) [@arraval](https://discourse.pymc.io/u/arraval)\
**Post date:** [March 27, 2019, 5:43pm UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/1 "2019-03-27T17:43:54Z")

</div>

Hi,

I’m toying with a Normal MixtureModel. The weights are Dirichlet:

```
import pymc3 as pm
import numpy as np
import theano.tensor as tt
W = np.array([0.35, 0.4, 0.25])
with pm.Model() as model:
 w = pm.Dirichlet('w', np.ones_like(W)) 
 mu = pm.Normal('mu', 0., 10., shape=W.size)
 tau = pm.Gamma('tau', 1., 1., shape=W.size)
 x_obs = pm.NormalMixture('x_obs', w, mu, tau=tau, observed=x)

```

I am trying to change a bit the code so that instead of fixing the shape of the Dirichlet, the shape is a random uniform variable like this:

> k = pm.DiscreteUniform(‘k’,lower=2,upper=5)  
> c = tt.ones\_like(k)  
> w = pm.Dirichlet(‘w’, a=c)

but it is not working. The error is:

`TypeError: Expected int elements in shape`

I appreciate if you can help me how to go about this.  
Many thanks

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [March 28, 2019, 8:47am UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/2 "2019-03-28T08:47:03Z")

</div>

We do not allow dynamic shape in model, so currently this is impossible to do.  
One potential work around is having a fix shape `alpha` with a shape is equal to the max shape (5 in this case), and dynamically assign zeros to some element. But again, inferencing these kind of model is also very tricky.

---

<div class="post-metadata">

**Author:** ![arraval](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/arraval/32/1691_2.png) [@arraval](https://discourse.pymc.io/u/arraval)\
**Post date:** [March 28, 2019, 4:56pm UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/3 "2019-03-28T16:56:17Z")

</div>

Thanks for the response.  
Following your suggestion to dynamically assign zeros I have this attempt:

```
with pm.Model() as model:
 k = 5
 arr = []
 for j in range(k):
   arr.append(pm.Uniform('a'+str(j),lower=0,upper=0.99))
 w = pm.Dirichlet('w', a=tt.stack([arr[i] for i in range(k)]), shape=k)
 du = pm.DiscreteUniform('du',lower=0, upper=1,shape=k)
 mu = pm.Normal('mu', 0., 10., shape=k)
 tau = pm.Gamma('tau', 1., 1., shape=k)
 x_obs = pm.NormalMixture('x_obs', w, np.multiply(mu,du), tau=np.multiply(tau,du), observed=x)

```

Basically what I’m doing is to multiply by `0` or `1` the elements of `w`, `mu`, and `tau`. the `0`'s and `1`'s are those of the `DiscreteUniform`

It’s not working. The error is (only showing last fragment):

```
...........................................................................
/usr/local/lib/python2.7/dist-packages/pymc3/step_methods/hmc/base_hmc.py in astep(self=<pymc3.step_methods.hmc.nuts.NUTS object>, q0=array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
   0., 0.]))
144 self.iter_count,
145 None,
146 None,
147 )
148 self._warnings.append(warning)
--> 149 raise SamplingError("Bad initial energy")
150 
151 adapt_step = self.tune and self.adapt_step_size
152 step_size = self.step_adapt.current(adapt_step)
153 self.step_size = step_size

SamplingError: Bad initial energy

```

**I think the** `DiscreteUniform` **in particular** `lower=0` **is generating the error.**

If I change the bounds to something bigger than `0` it doesn’t throw the error but after sampling all `du`'s are `1`, defeating the purpose.

How can I implement the idea correctly?  
Thanks

---

<div class="post-metadata">

**Author:** ![arraval](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/arraval/32/1691_2.png) [@arraval](https://discourse.pymc.io/u/arraval)\
**Post date:** [March 28, 2019, 6:01pm UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/4 "2019-03-28T18:01:50Z")

</div>

I have something that seemingly answers my previous question:

```
with pm.Model() as model:
	k = 5
	w = pm.Dirichlet('w', a=tt.stack([0.1,0.1,0.1,0.1,0.1]), shape=k)
	du = pm.DiscreteUniform('du',lower=0, upper=1,shape=k)
	idx_arr = []
	for i in range(k):
		if du[i]:
			idx_arr.append(i)

	mu = pm.Normal('mu', 0., 10., shape=k)
	tau = pm.Gamma('tau', 1., 1., shape=k)
	x_obs = pm.NormalMixture('x_obs', tt.stack([w[h] for h in idx_arr ]), tt.stack([mu[h] for h in idx_arr ]), tau=tt.stack([tau[h] for h in idx_arr ]), observed=x)
	
with model:	
	trace = pm.sample(3000,n_init=10000, tune=500, random_seed=SEED)[1000:] 

```

**With respect to the first response, does this implements the suggestion of “dynamically assign zeros”?**

---

<div class="post-metadata">

**Author:** ![DoctorRad](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/doctorrad/32/1849_2.png) [@DoctorRad](https://discourse.pymc.io/u/DoctorRad)\
**Post date:** [December 22, 2020, 4:27pm UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/5 "2020-12-22T16:27:34Z")

</div>

Did this work for you @arraval - or did you find something else that worked? I’m facing the same issue…

---

<div class="post-metadata">

**Author:** ![aclam](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/aclam/32/6124_2.png) [@aclam](https://discourse.pymc.io/u/aclam)\
**Post date:** [February 14, 2023, 2:15am UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/6 "2023-02-14T02:15:40Z")

</div>

@junpenglao Is there currently any support for dynamic shapes (i.e. using a tensorvariable as input to the shape argument)? I am trying to estimate the parameters of a Compound Poisson process with a Binomial distribution as the underlying distribution. The number of Binomial RVs follow a Poisson distribution, so I need a way to either dynamically set the shape argument or generate those RVs in a loop.

---

<div class="post-metadata">

**Author:** ![junpenglao](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/junpenglao/32/8_2.png) [@junpenglao](https://discourse.pymc.io/u/junpenglao)\
**Post date:** [February 14, 2023, 7:01am UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/7 "2023-02-14T07:01:57Z")

</div>

We are definitely better at supporting dynamic shape, but I am not sure if your use case is supported yet. Could you open a new post with the example you have in mind?

---

<div class="post-metadata">

**Author:** ![aclam](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/aclam/32/6124_2.png) [@aclam](https://discourse.pymc.io/u/aclam)\
**Post date:** [February 14, 2023, 7:43am UTC](https://discourse.pymc.io/t/dirichlet-with-random-shape/3015/8 "2023-02-14T07:43:45Z")

</div>

@junpenglao Sounds good. I have opened a new post [here](https://discourse.pymc.io/t/problem-with-dynamically-generating-random-variables-in-a-compound-poisson-model/11397), thanks!