如何使用pymc3找到dirichlet priors？
我尝试过以下方法：
import pymc3 as pm
import numpy as np
population = [139212, 70192, 50000, 21000, 16000, 5000, 2000, 500, 600, 100, 10, 5, 5, 5, 5]
with pm.Model() as model:
zipfy = pm.Dirichlet('zipfy', a=np.array([1.]), observed=population)
tr = pm.sample(100)
但它抛出ValueError：
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-14-623c21a4f35f> in <module>()
1 with pm.Model() as model:
2 zipfy = pm.Dirichlet('zipfy', a=np.array([1.]), observed=population)
----> 3 tr = pm.sample(100)
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/pymc3/sampling.py in sample(draws, step, init, n_init, start, trace, chain, njobs, tune, progressbar, model, random_seed)
147 # By default, use NUTS sampler
148 pm._log.info('Auto-assigning NUTS sampler...')
--> 149 start_, step = init_nuts(init=init, n_init=n_init, model=model)
150 if start is None:
151 start = start_
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/pymc3/sampling.py in init_nuts(init, n_init, model, **kwargs)
432
433 if init == 'advi':
--> 434 v_params = pm.variational.advi(n=n_init)
435 start = pm.variational.sample_vp(v_params, 1, progressbar=False, hide_transformed=False)[0]
436 cov = np.power(model.dict_to_array(v_params.stds), 2)
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/pymc3/variational/advi.py in advi(vars, start, model, n, accurate_elbo, optimizer, learning_rate, epsilon, random_seed)
122 # Create variational gradient tensor
123 elbo, shared = _calc_elbo(vars, model, n_mcsamples=n_mcsamples,
--> 124 random_seed=random_seed)
125
126 # Set starting values
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/pymc3/variational/advi.py in _calc_elbo(vars, model, n_mcsamples, random_seed)
179 logpt = tt.add(*map(tt.sum, factors))
180
--> 181 [logp], inarray = pm.join_nonshared_inputs([logpt], vars, shared)
182
183 uw = tt.vector('uw')
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/pymc3/theanof.py in join_nonshared_inputs(xs, vars, shared, make_shared)
180 inarray : vector of inputs
181 """
--> 182 joined = tt.concatenate([var.ravel() for var in vars])
183
184 if not make_shared:
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/theano/tensor/basic.py in concatenate(tensor_list, axis)
4608 "or a list, make sure you did not forget () or [] around "
4609 "arguments of concatenate.", tensor_list)
-> 4610 return join(axis, *tensor_list)
4611
4612
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/theano/tensor/basic.py in join(axis, *tensors_list)
4357 return tensors_list[0]
4358 else:
-> 4359 return join_(axis, *tensors_list)
4360
4361
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/theano/gof/op.py in __call__(self, *inputs, **kwargs)
613 """
614 return_list = kwargs.pop('return_list', False)
--> 615 node = self.make_node(*inputs, **kwargs)
616
617 if config.compute_test_value != 'off':
/Users/liling.tan/Library/Python/3.5/lib/python/site-packages/theano/tensor/basic.py in make_node(self, *axis_and_tensors)
4080 axis, tensors = axis_and_tensors[0], axis_and_tensors[1:]
4081 if not tensors:
-> 4082 raise ValueError('Cannot join an empty list of tensors')
4083 as_tensor_variable_args = [as_tensor_variable(x) for x in tensors]
4084
ValueError: Cannot join an empty list of tensors
zipfy应该是参数向量。
我试过这个：
import pymc3 as pm
import numpy as np
population = [139212, 70192, 50000, 21000, 16000, 5000, 2000, 500, 600, 100, 10, 5, 5, 5, 5]
with pm.Model() as model:
zipfy = pm.Dirichlet('zipfy', a=np.array(population))
tr = pm.sample(100)
print (tr['zipfy'])
print (len(tr['zipfy']), len(tr['zipfy'][0]) )
[OUT]：
array([[ 4.57466959e-01, 2.30024576e-01, 1.63655813e-01, ...,
2.79491587e-05, 1.15471055e-05, 1.21639409e-05],
[ 4.57466959e-01, 2.30024576e-01, 1.63655813e-01, ...,
2.79491587e-05, 1.15471055e-05, 1.21639409e-05],
[ 4.57550769e-01, 2.30182026e-01, 1.63985544e-01, ...,
1.61401840e-05, 2.90679821e-05, 2.47148304e-05],
...,
[ 4.56878341e-01, 2.31362382e-01, 1.63956669e-01, ...,
1.04361219e-05, 5.42454872e-06, 2.51727193e-05],
[ 4.57542706e-01, 2.30122065e-01, 1.63973662e-01, ...,
2.16784018e-05, 5.42709076e-06, 7.35651589e-06],
[ 4.56698065e-01, 2.30786537e-01, 1.64125287e-01, ...,
7.14659176e-06, 2.90901488e-05, 1.87413211e-05]])
(100, 15)
我期待一个dirichlet priors（即参数数组）的大小为1但它的大小为100.这是预期的行为吗？如何解释 trace['zipfy']的输出？啊，跟踪是pm.sample(100)的步骤？先验是在model对象里面吗？
所以给定一个离散值，让我们说5，我怎样才能找到我刚从采样器中学到的dirichlet先验？它在model对象或zipfy对象中吗？