Margianal likelihood of Gaussian process by using DensityDist

Questions
1

Dear all,

I want to know Margianal likelihood of Gaussian process by using DensityDist

I know there is already gaussian process module in pymc3 but this is practice for my use of pymc3

I made the code like this

def MarginalLikelihood(ls, eta, sigma, x, y):
    cov = eta**2 * ExpQuad(1,ls)(x)
    log_p1 = -1/2* y*cov*tt.transpose(y)
    log_p2 = tt.nlinalg.Det(cov)#-1/2*tt.log(tt.nlinalg.Det(cov))
    log_p3 = -y.size/2*np.log(2*np.pi)
    return log_p1+log_p2+log_p3


with pm.Model() as model:
    ls = pm.Normal('ls', mu=0, sd=10,  shape=1)
    eta = pm.Normal('eta', mu=0, sd=10, shape=1)
    sigma = 1e-8
#     pm.HalfNormal('sigma', sd=10)

    like = pm.DensityDist('ML', MarginalLikelihood, observed=dict(ls=ls,eta=eta,sigma=sigma,
                                                            x=X,
                                                            y=y))

    trace = pm.sample(2000)

and it gives the error

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-11-bdd19ba5bae4> in <module>()
     16     like = pm.DensityDist('ML', MarginalLikelihood, observed=dict(ls=ls,eta=eta,sigma=sigma,
     17                                                             x=X,
---> 18                                                             y=y))
     19 
     20     trace = pm.sample(2000)

~/anaconda3/lib/python3.6/site-packages/pymc3/distributions/distribution.py in __new__(cls, name, *args, **kwargs)
     35             total_size = kwargs.pop('total_size', None)
     36             dist = cls.dist(*args, **kwargs)
---> 37             return model.Var(name, dist, data, total_size)
     38         else:
     39             raise TypeError("Name needs to be a string but got: {}".format(name))

~/anaconda3/lib/python3.6/site-packages/pymc3/model.py in Var(self, name, dist, data, total_size)
    819             with self:
    820                 var = MultiObservedRV(name=name, data=data, distribution=dist,
--> 821                                       total_size=total_size, model=self)
    822             self.observed_RVs.append(var)
    823             if var.missing_values:

~/anaconda3/lib/python3.6/site-packages/pymc3/model.py in __init__(self, name, data, distribution, total_size, model)
   1341         self.missing_values = [datum.missing_values for datum in self.data.values()
   1342                                if datum.missing_values is not None]
-> 1343         self.logp_elemwiset = distribution.logp(**self.data)
   1344         # The logp might need scaling in minibatches.
   1345         # This is done in `Factor`.

<ipython-input-11-bdd19ba5bae4> in MarginalLikelihood(ls, eta, sigma, x, y)
      3     cov = eta**2 * ExpQuad(1,ls)(x)
      4     log_p1 = -1/2* y*cov*tt.transpose(y)
----> 5     log_p2 = tt.nlinalg.Det(cov)#-1/2*tt.log(tt.nlinalg.Det(cov))
      6     log_p3 = -y.size/2*np.log(2*np.pi)
      7     return log_p1+log_p2+log_p3

TypeError: object() takes no parameters

Is there anyone who can help to fix the error?

2

You are not calling the tt.nlinalg.Det correctly, it should be tt.nlinalg.Det()(cov) - you initialized the theano_op first by doing tt.nlinalg.Det().

3

Thank you for your reply.